Parametric Homomorphic Deconvolution (Prony, ARMA)

Parametric homomorphic deconvolution using Prony (ARMA) modeling to recover time-delay structure from a single-channel signal

Purpose.

Recover the propagation (time-delay) response from a single-channel analog-summed microphone signal using homomorphic deconvolution followed by Prony (ARMA) modeling. Returns the parametric HD magnitude plus numerator/denominator coefficients and poles—handy for compact feature extraction and AoA regression.

[z22, vp2, Num2, Den2] = cep_prony6(Aord, data0, N, W, MM, novlp, normonoff, plotonoff)

Inputs

• Aord — Prony model order (AR and MA orders both set to Aord).
• data0 — Input vector; length must equal N + novlp*(MM-1).
• N — Frame length (power of two recommended).
• W — Quefrency gate length (samples).
• MM — Ensemble length (# of frames to average).
• novlp — Hop size (overlap = N - novlp).
• normonoff — 1 to normalize z22 to unity max.
• plotonoff — 1 to show HD magnitude and pole/zero plot.

Outputs

• z22 — [N/2+1 × 1] parametric HD magnitude (DC…Nyquist).
• vp2 — Prony poles (roots(Den2)).
• Num2, Den2 — Prony MA/AR coefficients.