Biquad Filter (biquad)

Biquadratic IIR filter, supporting 8 common filter types, used for frequency response shaping in audio and signal processing.

Principle

The biquad filter is a standard implementation of a second-order IIR filter, with the transfer function:

H(z) = (b0 + b1·z⁻¹ + b2·z⁻²) / (1 + a1·z⁻¹ + a2·z⁻²)

The corresponding difference equation:

y[n] = b0·x[n] + b1·x[n-1] + b2·x[n-2] - a1·y[n-1] - a2·y[n-2]

Coefficients are calculated from the sample rate, cutoff frequency, quality factor Q, and gain based on the filter type, referencing BiQuadDesigner.

Filter Types

Enum Value	Type	Description
BIQUAD_FILTER_TYPE_LOWPASS	Low-pass	Attenuates high frequencies, preserves low frequencies
BIQUAD_FILTER_TYPE_HIGHPASS	High-pass	Attenuates low frequencies, preserves high frequencies
BIQUAD_FILTER_TYPE_BANDPASS	Band-pass	Preserves only the frequency band around the center frequency
BIQUAD_FILTER_TYPE_LOWSHELF	Low shelf	Boosts or cuts low frequencies
BIQUAD_FILTER_TYPE_HIGHSHELF	High shelf	Boosts or cuts high frequencies
BIQUAD_FILTER_TYPE_PEAKING	Peaking	Boosts or cuts a specified frequency
BIQUAD_FILTER_TYPE_NOTCH	Notch	Attenuates a specified frequency (narrow band)
BIQUAD_FILTER_TYPE_ALLPASS	All-pass	Changes phase only, does not alter magnitude

Data Structure

struct biquad_filter_t {
    float b0, b1, b2;   /* Numerator coefficients */
    float a1, a2;       /* Denominator coefficients (a0 normalized to 1) */
    float xn1, xn2;     /* Input history: x[n-1], x[n-2] */
    float yn1, yn2;     /* Output history: y[n-1], y[n-2] */
};

API

struct biquad_filter_t * biquad_alloc(enum biquad_filter_type_t type, float samplerate, float frequency, float quality, float gain);

Allocate and initialize a filter. samplerate is the sample rate (Hz), frequency is the cutoff/center frequency (Hz), quality is the quality factor Q, gain is the gain (dB, valid only for shelf and peaking types). Returns NULL on failure.

void biquad_free(struct biquad_filter_t * filter);

Free the filter.

void biquad_init(struct biquad_filter_t * filter, enum biquad_filter_type_t type, float samplerate, float frequency, float quality, float gain);

Initialize the coefficients of an existing filter structure without allocating memory. After calling, biquad_clear must be called manually to clear the history state.

void biquad_clear(struct biquad_filter_t * filter);

Clear the filter's historical input/output state (zero xn1, xn2, yn1, yn2), does not change coefficients.

void biquad_process(struct biquad_filter_t * filter, float * input, float * output, int len);

Filter len samples from the input buffer and write the result to output. Supports block processing; history state is automatically maintained across calls.

Usage Example

struct biquad_filter_t * f = biquad_alloc(BIQUAD_FILTER_TYPE_LOWPASS, 44100.0f, 1000.0f, 0.707f, 0.0f);

float in[256], out[256];
while(read_audio(in, 256))
{
    biquad_process(f, in, out, 256);
    write_audio(out, 256);
}

biquad_free(f);