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Speech
Speech Processing
Vocal Tract
  • Input and output signals are real
    • Filter coefficients are real for rational H(z)H(z)
    • Poles/zeros either real or complex conjugate pairs
  • BIBO stability important

Frequency Response

  • Sample along unit circle
    • ∣z∣=∣eiω∣=1|z|=\left|e^{i\omega}\right|=1

Magnitude Response

∣H(eiω)∣=b0∣eiω−β1∣⋅⋅⋅∣eiω−βq∣∣eiω−α1∣⋅⋅⋅∣eiω−αp∣\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|}

  • LPC & Cepstral Analysis to separate
  • Residual allows more accurate estimation of pitch period
Source FilterSpeech Processing