qdsp

Branchless, fixed-point (Q15) DSP primitives for microcontrollers without a floating-point unit.

qdsp is a header-only C99 library of digital-signal-processing building blocks that run on FPU-less MCUs (Cortex-M0/M3, ESP32 in soft-float, RISC-V rv32i). Every quantity is Q15 (int16, value = raw / 32768, range [-1, 1)). All routines are static inline, have no global state, perform no dynamic allocation, and stay branch-light at -O2.

It complements MPTC's sliding-DFT with the classic IIR/FIR primitives that real audio and sensor pipelines need.

Modules

Primitive	What it does
qdsp_biquad_t	2nd-order IIR (low/high/band-pass, notch) — Direct Form II Transposed
qdsp_onepole_t	1st-order one-pole low/high pass
qdsp_goertzel_t	Single-frequency detection (DTMF, tone signalling)
qdsp_envelope_t	Attack/release envelope follower
qdsp_fir_t	Symmetric FIR convolution (caller-owned delay line)
metering	running peak + block RMS (integer sqrt)

Quick start

#include "qdsp.h"

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qdsp_biquad_t bp = { /* coeffs from tools/gen_biquad.py */ };
qdsp_goertzel_t gz = { /* coeffs from tools/gen_goertzel.py */ };

for (int i = 0; i < N; i++) {
    q15_t y = qdsp_biquad_process(&bp, sample[i]);
    qdsp_goertzel_process(&gz, y);
}
q15_t power = qdsp_goertzel_power(&gz);   /* > 0.25*Q15 => tone present */

Generate coefficients:

python tools/gen_biquad.py  --type bandpass --f0 1000 --fs 48000 --q 0.707
python tools/gen_goertzel.py --freq 1000 --fs 48000 --n 256

Demo

examples/demo.c synthesises a 1000 Hz + 5000 Hz mixture, band-passes it, runs the envelope follower and Goertzel detector, and prints the result.

cc -O2 -o demo examples/demo.c && ./demo
# Goertzel power (Q15) = 18551  (threshold 8191)

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# Tone 1000 Hz DETECTED

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examples/reference.py is the floating-point reference used to validate the fixed-point pipeline.

Determinism / WCET

All primitives are straight-line (no loops with data-dependent bounds except the fixed-tap FIR, whose cost is n multiplies regardless of input). Worst- case execution time is therefore constant and computable from the tap count — suitable for the time-triggered, lock-free style of DSO-TRON.

License

Apache 2.0