stem/Speech/Speech Processing/Vocal Tract.md

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

Frequency Response

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

Magnitude Response

\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