Module dsp::minphase
Minimum-phase reconstruction (real cepstrum method)
Given an impulse response x[n] (e.g. a linear-phase FIR designed purely from a target magnitude response), minimum_phase produces a different impulse response with the same magnitude spectrum but the minimum possible group delay/phase — the standard "minimum-phase equivalent" used to halve a linear-phase filter's latency for the same magnitude response. Classic homomorphic (cepstral) algorithm: take the log- magnitude spectrum, transform it back to a "real cepstrum", fold the anti-causal half onto the causal half (this is what forces the result causal and minimum-phase — a signal is minimum-phase iff its complex cepstrum is zero for n < 0), then exponentiate back through the spectral domain.
Functions
| minimum_phase | 'x' has 'n' samples (n <= fftLen); 'fftLen' must be a power of two (see fft.h) and should be comfortably larger than n for accurate cepstral liftering (a common rule of thumb: at least 4-8x n). 'outMinPhase' must have room for 'fftLen' samples — the full-length minimum-phase impulse response (its energy concentrates near the start; callers typically keep only the first n-ish samples). |