nx_lpc.nx

nx_lpc.nx -- Linear Predictive Coding (LPC) analysis via the Levinson-Durbin recursion. Pure integer Q15 fixed-point; no floats; tier-0 ready (runs on MCUs without an FPU). Phase 4a of the Nishi voice codec (docs/NISHI_COMMS_ROADMAP.md). LPC is the spectral-envelope estimator the codec wraps around the excitation signal. Order 10 covers 8 kHz speech; order 16 covers 16 kHz; order 20 for 24 kHz. Q15 convention: - signed coefficients in [-1.0, +1.0) map to int16 in [-32768, +32767] - multiply: (a * b) >> 15 keeps the Q15 invariant - the LPC reflection coefficients k[i] are bounded |k| < 1 in a stable filter; the recursion's stability check is k^2 < 1 We store everything as i64 to give headroom for autocorrelation sums (which can be O(N) where N is samples in a frame, ~320 at 16 kHz / 20 ms). Output coefficients are bounded to Q15 range. Algorithm (standard Levinson-Durbin): R[k] = autocorr(s, k) for k in 0..M e[0] = R[0] for i in 1..M: k_i = -(R[i] + sum(a[j] * R[i-j] for j in 1..i-1)) / e[i-1] a[i] = k_i for j in 1..i-1: a'[j] = a[j] + k_i * a[i-j] a = a' e[i] = (1 - k_i^2) * e[i-1] genealogy_id: levinson_1947 + durbin_1960 + rfc_3951_ilbc + opus_silk_lpc_tables lineage_id: nishi_voice_lpc_q15