fir v0.1.0

Q15 finite-impulse-response filter.

Application scenarios

• Audio tone shaping and anti-alias filtering.
• Sensor smoothing with a designed response.
• A fixed-point DSP chain on an MCU without floating point.

Contract

typedef struct {
    const int16_t *taps;
    int16_t *history;
    uint16_t length;
    uint16_t index;
    uint8_t shift;
} fir_t;

void fir_init(fir_t *filter, const int16_t *taps, int16_t *history,
              uint16_t length, uint8_t shift);
int32_t fir_step(fir_t *filter, int16_t sample);
void fir_reset(fir_t *filter);

• taps and history are caller-owned arrays of length elements.
• Coefficients are Q15; shift divides the accumulator by 2^shift.
• Direct form: y[n] = sum(taps[k] * x[n-k]) / 2^shift.
• No allocation and no floating point.

Parameters

• Design taps offline with SciPy, MATLAB, or CMSIS-DSP.
• shift keeps the accumulator in range; 15 is common.
• A longer filter costs length multiply-accumulates per sample.

Memory and timing

• history is 2 * length bytes; state is about 20 bytes.
• O(length) per sample; a 32-tap filter is 32 MACs.

Integration

static const int16_t taps[3] = {10923, 10923, 10923};
static int16_t history[3];
fir_t average;
fir_init(&average, taps, history, 3, 15);
int32_t filtered = fir_step(&average, sample);

When not to use

• A low-order response is enough; use biquad (constant cost).
• Very long filters or block processing; use an FFT.

Verification

make test covers a two-tap average, a three-tap average, reset, and an

invalid configuration.

Behavior reference: CMSIS-DSP arm_fir_q15 (Apache-2.0); this implementation is original.

const int16_t *taps;
int16_t *history;
uint16_t length;
uint16_t index;
uint8_t shift;