low pass filter

lowpass.h

typedef struct filter_t {
    double a0, a1, a2; // Feedforward coefficients
    double b1, b2;     // Feedback coefficients
    double z1, z2;     // Filter state (history)
} filter_t;

void filter_init(filter_t *filter, double cutoff, double sample_rate) {
	double const PI = 3.14159265358979323846;
    double omega = 2.0 * PI * cutoff / sample_rate;
    double sin_omega = sin( omega );
    double cos_omega = cos( omega );
    double alpha = sin_omega / sqrt( 2.0 ); // Q = 1 / sqrt( 2 ) (Butterworth)
    double a0_inv = 1.0 / ( 1.0 + alpha );
    filter->a0 = ( 1.0 - cos_omega ) / 2.0 * a0_inv;
    filter->a1 = ( 1.0 - cos_omega ) * a0_inv;
    filter->a2 = ( 1.0 - cos_omega ) / 2.0 * a0_inv;
    filter->b1 = -2.0 * cos_omega * a0_inv;
    filter->b2 = ( 1.0 - alpha ) * a0_inv;
    filter->z1 = 0.0;
    filter->z2 = 0.0;
}

double filter_apply(filter_t *filter, double input) {
    double output = filter->a0 * input + filter->a1 * filter->z1 + 
		filter->a2 * filter->z2 - filter->b1 * filter->z1 - filter->b2 * filter->z2;
    filter->z2 = filter->z1;
    filter->z1 = output;
    return output;
}