nx_lpc_synth.nx

nx_lpc_synth.nx -- LPC synthesis filter (Arc 1 Phase A.3). Counterpart to nx_lpc_autocorr + nx_lpc_levinson. Given LPC predictor coefs a[1..p] (Q30) and residual e[0..N-1] (i16 PCM signed), reconstruct the speech signal: s[n] = e[n] + Σ_{k=1..p} a[k] * s[n-k] (Note: prediction was s_pred[n] = -Σ a[k] s[n-k] making residual e[n] = s[n] - s_pred[n] = s[n] + Σ a[k] s[n-k]. Inverting that: s[n] = e[n] - Σ a[k] s[n-k] ... but the standard convention used in Levinson is a[k] satisfying s[n] + Σ a[k] s[n-k] = e[n], so s[n] = e[n] - Σ a[k] s[n-k]. Match our sign convention.) Per [[feedback-bits-up-exceed-never-match]]: integer-only IIR pole filter. Patent-clean foundation for sovereign nx_voice_codec. Inputs: e_pcm: i16 LE residual signal (N * 2 bytes) n: number of samples a_q30: i64 LE LPC coefs (p * 8 bytes) from nx_lpc_levinson p: LPC order s_out: i16 LE reconstructed signal buffer (N * 2 bytes) Caller responsibility: s_out should be zeroed for n < 0 (we use only n >= 0 history; initial taps treated as 0).