em100 iir filters.c

// variable numbering and array indexing is in reverse chronological order, i.e.
// 0 is the current sample, 1 is the previous sample, etc
//
//  x = filter input samples
//  y = filter output samples


//================== generic biquad filter =====================================================

struct BiquadCoeffs {
    float b2, b1, b0;
    float a2, a1;
};

float filter_biquad( struct BiquadCoeffs const *coeffs,
        float x2, float x1, float x0, float y2, float y1 )
{
    float y0 = coeffs->b2 * x2
             + coeffs->b1 * x1
             + coeffs->b0 * x0

             - coeffs->a2 * y2
             - coeffs->a1 * y1;

    return y0;
}


//================== biquad lowpass filter =====================================================
//
// same as above, but optimized for lowpass filters, for which
//   b2 = b0
//   b1 = b0 * 2

struct LPBiquadCoeffs {
    float b0;
    float a2, a1;
};

void filter_lpbiquad( struct BiquadCoeffs const *coeffs,
        float x2, float x1, float x0, float y2, float y1 )
{
    float y0 = coeffs->b0 * (     x2
                            + 2 * x1
                            +     x0 )

             - coeffs->a2 *       y2
             - coeffs->a1 *       y1;

    return y0;
}


// resample to half the sample rate, using lowpass biquad filter.
// returns one output sample per two input samples
//
float decimate_biquad( struct LPBiquadCoeffs const *coeffs, float state[2],
        float const in[2], float const in_prev[2] )
{
    state[1] = coeffs->b0 * (     in_prev[1]
                            + 2 * in_prev[0]
                            +     in[1] )

             - coeffs->a2 *       state[1]
             - coeffs->a1 *       state[0];


    state[0] = coeffs->b0 * (     in_prev[0]
                            + 2 * in[1]
                            +     in[0] )

             - coeffs->a2 *       state[0]
             - coeffs->a1 *       state[1];

    return state[0];
}


// EM100-G IIR filters:
// (2nd-order Butterworth filters with various cutoff frequencies, 1200 Hz sample rate)
static struct LPBiquadCoeffs const
    em100_iir_1 = { .b0 = 2.11929601e-3, .a2 = 0.910120873, .a1 = -1.90164369 },  // 18 Hz
    em100_iir_2 = { .b0 = 4.29590264e-4, .a2 = 0.958983150, .a1 = -1.95726479 },  // 8 Hz
    em100_iir_3 = { .b0 = 1.08521907e-4, .a2 = 0.979274600, .a1 = -1.97884051 },  // 4 Hz
    em100_iir_4 = { .b0 = 6.12030910e-5, .a2 = 0.984415081, .a1 = -1.98417027 },  // 3 Hz
    em100_iir_5 = { .b0 = 2.72725213e-5, .a2 = 0.989582759, .a1 = -1.98947367 },  // 2 Hz
    em100_iir_6 = { .b0 = 6.83597982e-6, .a2 = 0.994777708, .a1 = -1.99475036 },  // 1 Hz
    em100_iir_7 = { .b0 = 1.71123201e-6, .a2 = 0.997385432, .a1 = -1.99737859 },  // 0.5 Hz
    em100_iir_8 = { .b0 = 4.28088003e-7, .a2 = 0.998691860, .a1 = -1.99869015 };  // 0.25 Hz