Parametric Homomorphic Deconvolution (Yule–Walker)

Compute parametric homomorphic deconvolution (Yule–Walker AR) to recover time-delay structure from a single-channel.

Purpose.

Estimate the propagation (time-delay) response from a single-channel signal that was formed by analog-summing multiple microphones. The algorithm performs homomorphic deconvolution to separate delay components and then fits an AR (Yule–Walker) model to obtain a compact, parametric representation. Outputs include the HD magnitude, AR poles, and AR coefficients—ready to be used as features (e.g., for AoA regression).

[z11, vp1, ar1] = cep_yule2(Aord, data0, N, W, MM, novlp, normonoff, plotonoff)

Inputs

• Aord — AR (Yule–Walker) order (e.g., 3–12; problem-dependent).
• data0 — Input vector; length must equal N + novlp*(MM-1).
• N — Frame length (power of two recommended).
• W — Quefrency window length (in samples of the cepstrum) setting the minimum delay to pass.
• MM — Ensemble (number of frames) for averaging.
• novlp — Hop size between frames (overlap = N - novlp).
• normonoff — If 1, normalize z11 to unit max.
• plotonoff — If 1, plot the HD magnitude and poles.

Outputs

• z11 — [N/2+1 × 1] vector, parametric HD magnitude (DC…Nyquist).
• vp1 — AR pole locations (complex roots).
• ar1 — AR coefficients (denominator of A(z)).