2023-12-27 22:38:56 +00:00
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---
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tags:
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- speech
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---
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2023-06-06 17:01:49 +01:00
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- 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
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