3200 lines
62 KiB
Plaintext
3200 lines
62 KiB
Plaintext
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\pdf_title "Linear Predictive Speech Synthesizer"
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\pdf_author "Andy Pack"
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\pdf_subject "EEEM030 Speech & Audio Processing & Recognition"
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\begin_body
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\begin_layout Title
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\size giant
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Linear Predictive Speech Synthesizer
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\end_layout
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\begin_layout Author
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Andy Pack
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EEEM030
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November 2020
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\size large
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Department of Electrical and Electronic Engineering
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Faculty of Engineering and Physical Sciences
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University of Surrey
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\end_layout
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\begin_layout Abstract
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A system implementing the source-filter model of speech is presented and
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evaluated using vowel segments as subjects.
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Linear predictive coding is used to estimate the formant frequencies of
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the samples while the cepstrum is used to identify the fundamental frequency.
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Comparisons of the LPC filter spectrum with the original audio spectrum
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are provided.
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A periodic impulse train of the same pitch period is used to synthesise
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vowel samples, a subjective analysis of the segment quality is given.
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Evaluations of various parameter variations are also presented.
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\end_layout
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Andy Pack / 6420013
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\end_layout
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\begin_layout Left Footer
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November 2020
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\end_layout
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\begin_layout Left Header
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EEEM030 Coursework
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\end_layout
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\begin_layout Section
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Introduction
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\end_layout
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\begin_layout Standard
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Speech analysis and processing is an ever-expanding space with applications
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from data compression to speech recognition.
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The latter is a particularly relevant and popular area, presenting an important
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domain for AI and machine learning applications.
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\end_layout
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\begin_layout Standard
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Prior to these, however, the ability to analyse, transform and identify
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key parameters for a speech signal are important tools that will be explored
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herein.
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\end_layout
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\begin_layout Subsection
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Brief
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\end_layout
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\begin_layout Standard
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The aim of this report is to demonstrate how digital signal processing technique
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s can be used to analyse, model and synthesise speech.
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The task will be considered as two areas of concern, that of modelling
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and synthesis.
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\end_layout
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\begin_layout Standard
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The modelling stage will utilise Linear Predictive Coding
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\begin_inset CommandInset citation
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LatexCommand cite
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key "all-pole-resonance"
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literal "false"
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\end_inset
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and the source-filter model of speech
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\begin_inset CommandInset citation
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LatexCommand cite
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key "source-filter-macquaire"
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literal "false"
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\end_inset
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to construct an all-pole filter that acts similarly to the vocal tract's
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effect on sound produced by the vocal chords.
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Comparisons of the frequency response for both the estimated filter and
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the original sound will be presented, the effect of different filter orders
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will also be demonstrated.
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Relevant parameters of the original vowel speech segment will be presented
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including the fundamental frequency
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\begin_inset CommandInset citation
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LatexCommand cite
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key "aalto-fundamental-freq"
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literal "false"
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\end_inset
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and formant frequencies.
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\end_layout
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\begin_layout Standard
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The synthesis stage will complete the source-filter model of speech by creating
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a suitable periodic sound source to be modulated by the previous filter.
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With a complete source-filter model, artificial vowel sounds will be synthesise
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d and analysed.
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Subjective assessments will be made as to the differences between the original
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sound and the final product of the model when system parameters are varied.
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\end_layout
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\begin_layout Section
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Implementation
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\end_layout
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\begin_layout Standard
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The implementation of this system was completed using
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\noun on
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Matlab
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\noun default
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with aid from functions in the digital signal processing toolbox among
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others.
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Following loading a vowel sample, a segment of given length (100ms was
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typical) was clipped for processing.
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The investigations were conducted on two samples,
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\begin_inset listings
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hood_m.wav
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and
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head_f.wav
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\end_inset
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, any results from other samples are identified as such.
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\end_layout
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\begin_layout Subsection
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Modelling
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\begin_inset CommandInset label
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LatexCommand label
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name "subsec:Modelling"
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\end_inset
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\end_layout
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\begin_layout Standard
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In order to estimate the filter state of the vocal tract, the linear predictive
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coding coefficients of varying orders were calculated using the
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\begin_inset listings
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lstparams "language=Matlab,basicstyle={\ttfamily},tabsize=4"
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inline true
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lpc(signal, order)
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\end_layout
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\end_inset
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function.
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In order to compare the frequency response of the LPC filter with the original
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signal, the Fourier transform of the signal was calculated.
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The frequency domain representation of the LPC filter was found using the
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\begin_inset listings
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inline true
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freqz(b, a, n, f)
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\end_inset
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function and co-plotted with the original signal.
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This frequency plot of the LPC filter constitutes the spectral envelope
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of the signal and the vowel formant frequencies can be found at the maxima
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of the spectrum.
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The smooth profile of the LPC spectrum allowed the formant frequencies
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to be estimated by identifying the local maxima
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\begin_inset CommandInset citation
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LatexCommand cite
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key "max-min,islocalmax"
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literal "false"
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\end_inset
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of the function.
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\end_layout
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\begin_layout Standard
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In order to find the fundamental frequency of the signal, the cepstrum
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\begin_inset CommandInset citation
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LatexCommand cite
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key "quefrency"
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literal "false"
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\end_inset
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was used.
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Regular periodic frequencies in the time domain present as peaks in the
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quefrency domain, these can also be identified with an auto-corelation
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function.
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The use of a low-pass filter was investigated in order to smooth the cepstrum
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before programmatically finding pitch period candidates by applying
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\begin_inset Formula $x$
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\end_inset
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and
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\begin_inset Formula $y$
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\end_inset
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thresholds.
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Firstly, local maxima of the cepstrum function were found using the
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\begin_inset listings
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lstparams "language=Matlab,basicstyle={\ttfamily}"
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islocalmax(x)
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\end_layout
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\end_inset
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function
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\begin_inset CommandInset citation
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LatexCommand cite
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key "islocalmax"
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literal "false"
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\end_inset
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.
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A minimum quefrency threshold of 20 was applied to ignore the transient-like
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oscillations at small
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\begin_inset Formula $x$
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\end_inset
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values.
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Lowering the quefrency corresponds to an increase in frequency, thus it
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is reasonable to discard these values when 20 samples represents 1200Hz
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when sampled at 24kHz, a frequency higher than that of the fundamental
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frequency being investigated.
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Additionally a minimum cepstrum threshold of 0.075 was used, from here the
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quefrency candidate with the highest value was used as the pitch period.
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\end_layout
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\begin_layout Subsection
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Synthesis
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\end_layout
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\begin_layout Standard
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In order to synthesise speech, a periodic impulse train at the identified
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fundamental frequency of the original vowel was generated.
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As the fundamental frequency of speech is far lower than a typical audio
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signal would be sampled at, a carrier signal of the same sampling frequency
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as the original sound was modulated by the lower frequency impulse train,
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see listing
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "get_impulse_train_function"
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plural "false"
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caps "false"
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noprefix "false"
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\end_inset
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.
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In order to produce the final synthesised speech, the generated impulse
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train must be convolved (in the time domain) with the transfer function
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of the LPC filter representing the vocal tract
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\begin_inset CommandInset citation
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LatexCommand cite
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key "source-filter-macquaire"
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literal "false"
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\end_inset
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.
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In
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\noun on
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Matlab
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\noun default
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this can be completed with the
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\begin_inset listings
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lstparams "language=Matlab,basicstyle={\ttfamily}"
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status open
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\begin_layout Plain Layout
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filter(b, a, x)
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\end_layout
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\end_inset
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which takes the provided coefficients (
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\begin_inset Formula $a,b$
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\end_inset
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) and applies the transfer function these describe.
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This final signal was written to disk and played for comparison to the
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original.
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\end_layout
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\begin_layout Section
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Results
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\end_layout
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\begin_layout Subsection
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LPC Filter
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\end_layout
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\begin_layout Standard
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LPC filter coefficients of varying orders were calculated, the values for
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each vowel sample at order 20 can be seen in table
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "tab:Order-20-LPC-Coeffs"
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plural "false"
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caps "false"
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noprefix "false"
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\end_inset
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.
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The frequency response for similar filters of order 25 can be seen in figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "fig:stacked-spectra"
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plural "false"
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caps "false"
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noprefix "false"
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\end_inset
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, as described in section
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "subsec:Modelling"
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plural "false"
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caps "false"
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noprefix "false"
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\end_inset
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the local maxima of the filter response were also plotted as red crosses.
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\end_layout
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\begin_layout Standard
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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1
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hood_m
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1
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0.5570
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1.0068
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0.1029
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|
|
|
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|
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|
|
|
|
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|
|
|
|
|
|
\end_layout
|
|
|
|
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|
|
|
|
\size small
|
|
\begin_inset VSpace medskip
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
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|
|
\noindent
|
|
\align center
|
|
|
|
\size small
|
|
\begin_inset Tabular
|
|
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|
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<features tabularvalignment="middle">
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<column alignment="center" valignment="top">
|
|
<column alignment="center" valignment="top">
|
|
<column alignment="center" valignment="top">
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|
<column alignment="center" valignment="top">
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|
<column alignment="center" valignment="top">
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<column alignment="center" valignment="top">
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|
<column alignment="center" valignment="top">
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|
<column alignment="center" valignment="top">
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|
<column alignment="center" valignment="top">
|
|
<column alignment="center" valignment="top">
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|
<column alignment="center" valignment="top">
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<row>
|
|
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|
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|
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\end_layout
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|
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|
|
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|
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|
|
|
|
\size small
|
|
12
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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|
\begin_inset Text
|
|
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|
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|
|
|
|
\size small
|
|
13
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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|
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|
|
|
|
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|
|
|
|
\size small
|
|
14
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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|
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|
|
|
|
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|
|
|
|
\size small
|
|
15
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
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|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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|
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|
|
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|
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|
|
|
|
\size small
|
|
16
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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|
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|
|
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|
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|
|
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|
\size small
|
|
17
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
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|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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|
\begin_inset Text
|
|
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|
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|
|
|
|
\size small
|
|
18
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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|
\begin_inset Text
|
|
|
|
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|
|
|
|
\size small
|
|
19
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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|
\begin_inset Text
|
|
|
|
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|
|
|
|
\size small
|
|
20
|
|
\end_layout
|
|
|
|
\end_inset
|
|
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|
|
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|
\begin_inset Text
|
|
|
|
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|
|
|
|
\size small
|
|
21
|
|
\end_layout
|
|
|
|
\end_inset
|
|
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|
|
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|
|
<row>
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|
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|
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|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\size small
|
|
head_f
|
|
\end_layout
|
|
|
|
\end_inset
|
|
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|
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|
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|
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|
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-0.3812
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|
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|
|
|
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|
|
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|
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|
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|
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|
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|
|
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|
|
-0.5842
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|
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|
|
|
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|
|
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|
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|
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|
|
|
|
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|
|
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|
|
0.2820
|
|
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|
|
|
|
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|
|
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|
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|
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|
|
|
|
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|
|
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|
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|
|
0.7351
|
|
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|
|
|
|
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|
|
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|
|
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|
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|
|
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|
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|
|
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|
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|
|
-0.8951
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|
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|
|
|
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|
|
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|
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|
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|
|
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|
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|
|
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|
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|
|
0.1172
|
|
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|
|
|
|
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|
|
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|
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|
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|
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|
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|
|
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|
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\begin_inset Caption Standard
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\begin_layout Plain Layout
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Order 20 LPC coefficients for both investigated samples, source segments
|
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taken from the first 100ms of each vowel sample
|
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\begin_inset CommandInset label
|
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LatexCommand label
|
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name "tab:Order-20-LPC-Coeffs"
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Float figure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\noindent
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\align center
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\begin_inset Float figure
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wide false
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sideways false
|
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status open
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\begin_layout Plain Layout
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\noindent
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\align center
|
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\begin_inset Graphics
|
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filename ../resources/head_f_spect_25.png
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lyxscale 10
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width 90col%
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\begin_layout Plain Layout
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lstparams "basicstyle={\ttfamily}"
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inline true
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status open
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|
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head_f
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\end_layout
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\end_inset
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, order 25
|
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\noindent
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filename ../resources/hood_m_spect_25.png
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lyxscale 10
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width 90col%
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\end_inset
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\end_layout
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\begin_inset listings
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lstparams "basicstyle={\ttfamily}"
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inline true
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status open
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hood_m
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\end_layout
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\end_inset
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, order 25
|
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
|
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\begin_layout Plain Layout
|
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\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
LPC filter and vowel segment spectra for both investigated samples
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:stacked-spectra"
|
|
|
|
\end_inset
|
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|
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\end_layout
|
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\end_inset
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\end_layout
|
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\end_inset
|
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\end_layout
|
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|
|
\begin_layout Standard
|
|
As the spectra are plotted with the same frequency axes bounds, the peaks
|
|
of the filter response corresponding to estimations of the formant frequencies
|
|
can be compared between the male and females voice.
|
|
In general the male's formant frequencies are lower than for the female's
|
|
sample, this can be seen specifically with the first few peaks.
|
|
It's worth noting that the first local maxima identified in the
|
|
\begin_inset listings
|
|
lstparams "basicstyle={\ttfamily}"
|
|
inline true
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
head_f
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
sample does not appear to have identified a peak that would be considered
|
|
a formant.
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Order Variation
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The effect of increasing the order of the LPC filter can be seen in figure
|
|
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:Spectrum-Tile"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
, the order of the
|
|
\begin_inset listings
|
|
lstparams "basicstyle={\ttfamily}"
|
|
inline true
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
hood_m
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
filter is repeatably incremented by 5.
|
|
In general, as the order of the filter is increased, the spectral response
|
|
of the LPC filter closer fits the spectrum of the original vowel segment.
|
|
At lower orders, the filter's response can smooth over multiple peaks and
|
|
valleys in the original signal as can be seen at order 6, whereas by order
|
|
36 the LPC spectrum follows all of the major motions of the speech signal.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
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|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../resources/hood_m_lpc_tile.png
|
|
lyxscale 20
|
|
width 100col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Effect of increasing LPC filter order on the
|
|
\begin_inset listings
|
|
lstparams "basicstyle={\ttfamily}"
|
|
inline true
|
|
status open
|
|
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|
\begin_layout Plain Layout
|
|
|
|
hood_m
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
sample
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:Spectrum-Tile"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
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|
\end_inset
|
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\end_layout
|
|
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\begin_layout Plain Layout
|
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\end_layout
|
|
|
|
\end_inset
|
|
|
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|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Source Segment Length Variation
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:seg_length"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
presents the speech sample and LPC filter spectral response for different
|
|
source sample lengths.
|
|
As the source sample length increases the spectral profile becomes less
|
|
smooth with higher peaks and deeper troughs throughout.
|
|
Additionally the mid to higher frequencies are affected more, the first
|
|
few formants are less affected.
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename /mnt/files/dev/matlab/lpss/resources/hood_m_25spect.png
|
|
lyxscale 10
|
|
width 25col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Graphics
|
|
filename /mnt/files/dev/matlab/lpss/resources/hood_m_50spect.png
|
|
lyxscale 10
|
|
width 25col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Graphics
|
|
filename /mnt/files/dev/matlab/lpss/resources/hood_m_100spect.png
|
|
lyxscale 10
|
|
width 25col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Graphics
|
|
filename /mnt/files/dev/matlab/lpss/resources/hood_m_200spect.png
|
|
lyxscale 10
|
|
width 25col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Increasing source segment lengths for the
|
|
\begin_inset listings
|
|
lstparams "basicstyle={\ttfamily}"
|
|
inline true
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
hood_m
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
sample
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:seg_length"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Spectral Analysis
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Formant Frequencies
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
As described previously, the smooth profile of the LPC filter spectra allows
|
|
the local maxima to be used as reasonable estimations of the peaks.
|
|
The first three formants for the order 25 filters seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:stacked-spectra"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
can be seen in table
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "tab:formant-frequencies"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
, as described above the first local maxima for the female
|
|
\begin_inset listings
|
|
lstparams "basicstyle={\ttfamily}"
|
|
inline true
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
head_f
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
sample was not included as
|
|
\begin_inset Formula $f_{1}$
|
|
\end_inset
|
|
|
|
as it did not refer to a maximum that would indicate a formant.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float table
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="5" columns="3">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="center" valignment="top">
|
|
<column alignment="center" valignment="top">
|
|
<column alignment="center" valignment="top">
|
|
<row>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset listings
|
|
lstparams "basicstyle={\ttfamily}"
|
|
inline true
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
head_f
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset listings
|
|
lstparams "basicstyle={\ttfamily}"
|
|
inline true
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
hood_m
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $f_{1}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
719.4
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
369.7
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $f_{2}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
2,218.2
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1,578.7
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $f_{3}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
3,197.3
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
2,278.1
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $f_{2}-f_{1}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1,498.8
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1,209.0
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
First formant frequencies at order 25, Hz
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "tab:formant-frequencies"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Table
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "tab:IPA-vowels"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
presents average formant frequencies for the investigated vowel sounds
|
|
as displayed in
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
key "formant-frequencies"
|
|
literal "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
The percentage difference between these averages and the calculated estimations
|
|
are also presented.
|
|
The female sample was closer to the averages than the male sample.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float table
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="4" columns="8">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="center" valignment="top">
|
|
<column alignment="center" valignment="top">
|
|
<column alignment="center" valignment="top">
|
|
<column alignment="center" valignment="top">
|
|
<column alignment="center" valignment="top">
|
|
<column alignment="center" valignment="top">
|
|
<column alignment="center" valignment="top">
|
|
<column alignment="center" valignment="top">
|
|
<row>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Average Frequency
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
key "formant-frequencies"
|
|
literal "false"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell multicolumn="2" alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell multicolumn="2" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Measured % Difference
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell multicolumn="2" alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell multicolumn="2" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Sample
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Vowel
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $f_{1}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $f_{2}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $f_{2}-f_{1}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $f_{1}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $f_{2}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $f_{2}-f_{1}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset listings
|
|
lstparams "basicstyle={\ttfamily}"
|
|
inline true
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
head_f
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
/ɛ/
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
731
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
2,058
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1,327
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1.6
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
7.8
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
12.9
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset listings
|
|
lstparams "basicstyle={\ttfamily}"
|
|
inline true
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
hood_m
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
/ʊ/
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
469
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1,122
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
653
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
21.2
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
40.7
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
85.1
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Relevant IPA vowels and their average formant frequencies
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
key "formant-frequencies"
|
|
literal "false"
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "tab:IPA-vowels"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Cepstrum Smoothing
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The effect of smoothing the cepstrum with a low-pass filter is presented
|
|
in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:smoothed-cepstrum"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
, [1 -0.7] were used as coefficients.
|
|
When employing smoothing, the peak corresponding to the pitch period has
|
|
been amplified compared to the unsmoothed curve where the pitch period
|
|
does not reach far beyond the noise of the rest of the function.
|
|
As a result of this, smoothing was employed in the following when identifying
|
|
the fundamental frequency.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../resources/head_f_rcep_~smooth.png
|
|
lyxscale 10
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Graphics
|
|
filename ../resources/head_f_rcep_smooth.png
|
|
lyxscale 10
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Real cepstrum for
|
|
\begin_inset listings
|
|
lstparams "basicstyle={\ttfamily}"
|
|
inline true
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
head_f
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
with and without low-pass filtering, thresholded local maxima crossed,
|
|
smoothing coefficients: [1 -0.7]
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:smoothed-cepstrum"
|
|
|
|
\end_inset
|
|
|
|
|
|
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Subsubsection
|
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Fundamental Frequency
|
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\end_layout
|
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\begin_layout Standard
|
|
The fundamental frequency was calculated by identifying the pitch period
|
|
in the real cepstrum.
|
|
The cepstrums for either sample were thresholded and the candidates can
|
|
be seen in figure
|
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\begin_inset CommandInset ref
|
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LatexCommand ref
|
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reference "fig:cepstrums-w-pitch-period"
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plural "false"
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caps "false"
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noprefix "false"
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\end_inset
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.
|
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The identified quefrency pitch period,
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\begin_inset Formula $q_{p}$
|
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\end_inset
|
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, and the corresponding fundamental frequency,
|
|
\begin_inset Formula $f_{f}$
|
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\end_inset
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, can be seen in table
|
|
\begin_inset CommandInset ref
|
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LatexCommand ref
|
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reference "tab:fund-freq"
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plural "false"
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caps "false"
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noprefix "false"
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\end_inset
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.
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\begin_inset Formula $f_{f}$
|
|
\end_inset
|
|
|
|
was calculated using the following where
|
|
\begin_inset Formula $f_{s}$
|
|
\end_inset
|
|
|
|
is the sample frequency,
|
|
\end_layout
|
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|
\begin_layout Standard
|
|
\begin_inset Formula
|
|
\[
|
|
f_{f}=\frac{1}{\nicefrac{q_{p}}{f_{s}}}
|
|
\]
|
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Float figure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\noindent
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\align center
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\begin_inset Graphics
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filename ../resources/head_f_rcep_smooth_X.png
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\end_inset
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\begin_inset Graphics
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filename ../resources/hood_m_rcep_smooth_X.png
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\end_inset
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\begin_inset Caption Standard
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\begin_layout Plain Layout
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Real cepstrums with candidate pitch periods highlighted
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\begin_inset CommandInset label
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LatexCommand label
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name "fig:cepstrums-w-pitch-period"
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\begin_layout Standard
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\begin_inset Float table
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\noindent
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\align center
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\begin_inset Tabular
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<lyxtabular version="3" rows="3" columns="3">
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<features tabularvalignment="middle">
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\begin_inset Text
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
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\begin_inset listings
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lstparams "basicstyle={\ttfamily}"
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
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\begin_inset listings
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lstparams "basicstyle={\ttfamily}"
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inline true
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status open
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\begin_layout Plain Layout
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hood_m
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\end_inset
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</cell>
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</row>
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<row>
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
|
|
Pitch Period, samples
|
|
\end_layout
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\end_inset
|
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</cell>
|
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
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105
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\end_layout
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\end_inset
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</cell>
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
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255
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\end_layout
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</cell>
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</row>
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<row>
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
|
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Fundamental Frequency, Hz
|
|
\end_layout
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\end_inset
|
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</cell>
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
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228.57
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\end_layout
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\end_inset
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</cell>
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
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94.12
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\end_layout
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\end_inset
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</cell>
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</row>
|
|
</lyxtabular>
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\end_inset
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\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Pitch period and fundamental frequency as calculated from the real cepstrum
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "tab:fund-freq"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
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|
\end_inset
|
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|
\end_layout
|
|
|
|
\end_inset
|
|
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|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Synthesis
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Following the convolution of the impulse train and the LPC filter, the spectrogr
|
|
ams for the original and synthesised sound can be seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:Spectrograms-synth"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
The circled areas highlight similar portions, the formant frequencies can
|
|
be seen as bright horizontal lines in both.
|
|
Despite being quasi-stationary, some variation in time can be seen throughout
|
|
the original signal.
|
|
The stationary synthesised signal, however, has a flat profile in time.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../resources/hood_m_gram.png
|
|
lyxscale 10
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Graphics
|
|
filename ../resources/hood_m_gram_synth.png
|
|
lyxscale 10
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Spectrograms for the original and synthesised vowel segment, areas of comparison
|
|
highlighted
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:Spectrograms-synth"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
At lower filter orders (< 10), the synthesised speech has a
|
|
\emph on
|
|
buzzy
|
|
\emph default
|
|
quality resembling a sawtooth wave of the same pitch as the original voice
|
|
sample.
|
|
At these orders, the synthesised sound can not accurately be discerned
|
|
as speech.
|
|
As the filter order increases, the tone of the sound becomes less harsh
|
|
and by around order 20 the sample could be identified as being of a voice.
|
|
By order 40, much of the harsh tone has been smoothed and the sample subjective
|
|
ly sounds as close to human speech as could be achieved.
|
|
Beyond this order, although the sound does change and smooth, it does not
|
|
appear to further approach the quality of the original sound.
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Discussion
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
As presented, the order of the LPC filter is a critical parameter for audio
|
|
quality.
|
|
An order that is too low will not allow the filter to accurately map to
|
|
the desired vowel spectrum leaving a sound that, although at the right
|
|
pitch, does not appreciably sound like the source segment.
|
|
At the other end, increasing the order beyond a certain complexity can
|
|
result in diminishing returns.
|
|
Although the sound sounded smoother, beyond around order 40 it did not
|
|
noticeably further approach the original sound.
|
|
Subjectively, an order of 30 provided a good approximation of the input
|
|
sound with acceptable quality for low bandwidth transmission.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The use of low-pass filtering on the cepstrum when identifying the fundamental
|
|
frequency was effective in accentuating the peak corresponding to the pitch
|
|
period.
|
|
With this, a higher
|
|
\begin_inset Formula $y$
|
|
\end_inset
|
|
|
|
threshold could be used that would be further from the noise of the function
|
|
while still consistently identifying the correct peak.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The relative frequencies for male and female speech was as expected with
|
|
the male speech segment having both lower fundamental frequencies and formant
|
|
frequencies.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Note Comment
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
A 100ms vowel segment sampled at 24kHz totals to 2,400 samples.
|
|
Assuming that each is represented by a float of 4 bytes, this uncompressed
|
|
vowel segment would fill 9600 bytes of storage.
|
|
Encoding the same 100ms of information via LPC using an order 30 filter
|
|
could reduce this to 120 bytes, just 1% of the previous space.
|
|
This is particularly important for audio transmission such as in mobile
|
|
telecoms, the GSM standard uses codecs based on LPC
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
key "etsi-gsm"
|
|
literal "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Conclusion
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Within this work, a complete source-filter model of speech has been presented,
|
|
analysing vowel samples and re-synthesising them while compressing the
|
|
data representation.
|
|
The effect of changing the complexity of this representation was investigated
|
|
by varying the order of the LPC filter and describing the effect on the
|
|
final audio sample.
|
|
Various statistics about the original samples were calculated including
|
|
the formant frequencies and the fundamental frequency.
|
|
With a sufficient filter order, sound samples comparable to human speech
|
|
were generated.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Newpage newpage
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "sec:bibliography"
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset CommandInset bibtex
|
|
LatexCommand bibtex
|
|
btprint "btPrintCited"
|
|
bibfiles "references"
|
|
options "bibtotoc"
|
|
|
|
\end_inset
|
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|
|
\begin_inset Newpage pagebreak
|
|
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|
\end_layout
|
|
|
|
\begin_layout Section
|
|
\start_of_appendix
|
|
Source Code
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "sec:Code"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
While much of the code was developed in individual scripts in order to experimen
|
|
t with separate aspects of the system, for collecting results a script which
|
|
constitutes the entire system was written,
|
|
\begin_inset listings
|
|
lstparams "basicstyle={\ttfamily}"
|
|
inline true
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
lpss.m
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Additional helper functions were written to plot and manipulate data.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset CommandInset include
|
|
LatexCommand lstinputlisting
|
|
filename "../lpss.m"
|
|
lstparams "breaklines=true,frame=tb,language=Matlab,basicstyle={\\ttfamily},commentstyle={\\color{commentgreen}\\itshape},keywordstyle={\\color{blue}},emphstyle={\\color{red}},stringstyle={\\color{red}},identifierstyle={\\color{cyan}},morekeywords={audioread, aryule, xcorr, freqz, spectrogram, mfcc, spectro, fft_, autocorr, clip_segment, islocalmax, ms_to_samples, rceps, cceps, ones, audioplayer, play, get_impulse_train, lpc, strcat, num2str, xlim},caption={Main script including source-filter model and spectral analysis},label={main_script}"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset CommandInset include
|
|
LatexCommand lstinputlisting
|
|
filename "../func/spectro.m"
|
|
lstparams "breaklines=true,frame=tb,language=Matlab,basicstyle={\\ttfamily},commentstyle={\\color{commentgreen}\\itshape},keywordstyle={\\color{blue}},emphstyle={\\color{red}},stringstyle={\\color{red}},identifierstyle={\\color{cyan}},morekeywords={audioread, aryule, xcorr, freqz, spectrogram, ms_to_samples, xlim},caption={Spectrogram plotting wrapper function},label={spectrogram_function}"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset CommandInset include
|
|
LatexCommand lstinputlisting
|
|
filename "../func/fft_.m"
|
|
lstparams "breaklines=true,frame=tb,language=Matlab,basicstyle={\\ttfamily},commentstyle={\\color{commentgreen}\\itshape},keywordstyle={\\color{blue}},emphstyle={\\color{red}},stringstyle={\\color{red}},identifierstyle={\\color{cyan}},morekeywords={audioread, aryule, xcorr, freqz, spectrogram, xlim},caption={Fast Fourier transform wrapper function},label={fft_function}"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset CommandInset include
|
|
LatexCommand lstinputlisting
|
|
filename "../func/autocorr.m"
|
|
lstparams "breaklines=true,frame=tb,language=Matlab,basicstyle={\\ttfamily},commentstyle={\\color{commentgreen}\\itshape},keywordstyle={\\color{blue}},emphstyle={\\color{red}},stringstyle={\\color{red}},identifierstyle={\\color{cyan}},morekeywords={audioread, aryule, xcorr, freqz, spectrogram, xlim},caption={Autocorrelation plotting wrapper function},label={autocorr_function}"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset CommandInset include
|
|
LatexCommand lstinputlisting
|
|
filename "../func/clip_segment.m"
|
|
lstparams "breaklines=true,frame=tb,language=Matlab,basicstyle={\\ttfamily},commentstyle={\\color{commentgreen}\\itshape},keywordstyle={\\color{blue}},emphstyle={\\color{red}},stringstyle={\\color{red}},identifierstyle={\\color{cyan}},morekeywords={audioread, aryule, xcorr, freqz, spectrogram, ms_to_samples, xlim},caption={Retrieve a segment of the original speech signal},label={clip_segment_function}"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset CommandInset include
|
|
LatexCommand lstinputlisting
|
|
filename "../func/ms_to_samples.m"
|
|
lstparams "breaklines=true,frame=tb,language=Matlab,basicstyle={\\ttfamily},commentstyle={\\color{commentgreen}\\itshape},keywordstyle={\\color{blue}},emphstyle={\\color{red}},stringstyle={\\color{red}},identifierstyle={\\color{cyan}},morekeywords={audioread, aryule, xcorr, freqz, spectrogram, xlim},caption={Transform time in milliseconds into the respective number of samples},label={ms_to_samples_function}"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset CommandInset include
|
|
LatexCommand lstinputlisting
|
|
filename "../func/get_impulse_train.m"
|
|
lstparams "breaklines=true,frame=tb,language=Matlab,basicstyle={\\ttfamily},commentstyle={\\color{commentgreen}\\itshape},keywordstyle={\\color{blue}},emphstyle={\\color{red}},stringstyle={\\color{red}},identifierstyle={\\color{cyan}},morekeywords={audioread, aryule, xcorr, freqz, spectrogram, ms_to_samples, repmat, xlim},caption={Generate an impulse rate of given fundamental frequency at a provided sampling frequency for a given length of time},label={get_impulse_train_function}"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_body
|
|
\end_document
|