nx_biquad.nx

nx_biquad.nx -- direct-form-II transposed biquad filter in Q14. Cross-cutting Substrate B primitive per nxc2/docs/NISHI_GAME_ENGINE_ROADMAP.md. Biquad = second-order recursive filter section. Building block for every parametric EQ, low-pass, high-pass, band-pass, band-stop, peak, and shelf. Coefficients computed per Bristow-Johnson's "Audio EQ Cookbook" (W3C public-domain reference). This primitive ships the EVALUATION (the per-sample state-update step + block apply); coefficient DESIGN helpers (computing b0..b2, a1..a2 from filter_kind, cutoff, Q) ship as a follow-up primitive once the in-house Q14 sin/cos helpers are factored out. Caller supplies pre-normalized coefficients (a0 = 1 implicit, all others already divided by a0). Transposed Direct Form II: y[n] = b0 * x[n] + s1 s1' = b1 * x[n] + s2 - a1 * y[n] s2' = b2 * x[n] - a2 * y[n] Two state vars instead of four. Numerically better-behaved for IIR than Direct Form I; standard DSP-textbook recommendation. Fixed-point: Q14 throughout (matches nx_sound's NX_SOUND_Q). Coefficient * signal products are Q28 internally; divided down to Q14 immediately to keep state vars in-range. Loss audit: integer division (/Q) truncates 14 fractional bits per multiply. For stable filters with |poles| << 1 the error is tiny; for filters near the unit circle the error can accumulate (the same limitation any fixed-point biquad has). Documented at the top of every filter design helper that ships against this primitive. genealogy_id: bristow_johnson_eq_cookbook + smith_julius_iir_filters_textbook lineage_id: nx_biquad_tdf2_q14