andy
5a94c5ff1a
Affected files: STEM/AI/Kalman Filter.md STEM/Signal Proc/Convolution.md STEM/Signal Proc/Image/Tracking.md STEM/Signal Proc/Pole-Zero.md STEM/Signal Proc/Transfer Function.md STEM/Speech/Linguistics/Consonants.md STEM/Speech/Linguistics/Linguistics.md STEM/Speech/Linguistics/README.md STEM/Speech/Linguistics/Terms.md STEM/Speech/Linguistics/Vowels.md STEM/Speech/NLP/Jargon.md STEM/Speech/NLP/NLP.md STEM/Speech/NLP/README.md STEM/Speech/NLP/Recognition.md STEM/Speech/Perception/Perception.md STEM/Speech/Perception/README.md STEM/Speech/Speech Processing/Applications.md STEM/Speech/Speech Processing/README.md STEM/Speech/Speech Processing/Source-Filter.md STEM/Speech/Speech Processing/Vocal Tract.md STEM/img/english-phoneme-table.png STEM/img/formant.png STEM/img/pole-zero-attenuation.png STEM/img/pole-zero-feedback.png STEM/img/pole-zero-stable.png STEM/img/roc-right-left.png STEM/img/roc-two-sided.png STEM/img/spectrum-vocal-tract.png STEM/img/transfer-stable-unstable.png STEM/img/vowel-chart.png STEM/img/vowel-spaces.png
16 lines
575 B
Markdown
16 lines
575 B
Markdown
- Input and output signals are real
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- Filter coefficients are real for rational $H(z)$
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- Poles/zeros either real or complex conjugate pairs
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- BIBO stability important
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# Frequency Response
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- Sample along unit circle
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- $|z|=\left|e^{i\omega}\right|=1$
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# Magnitude Response
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$$\left|H(e^{i\omega})\right|=\frac{b_0|e^{i\omega}-\beta_1|\cdot\cdot\cdot|e^{i\omega}-\beta_q|}{|e^{i\omega}-\alpha_1|\cdot\cdot\cdot|e^{i\omega}-\alpha_p|}$$
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- LPC & Cepstral Analysis to separate
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- Residual allows more accurate estimation of pitch period |