SoftFM/Filter.cc

#include <cassert>
#include <cmath>
#include <cstdint>
#include <algorithm>
#include <complex>

#include "Filter.h"

using namespace std;


/** Prepare Lanczos FIR filter coefficients. */
template <class T>
static void make_lanczos_coeff(unsigned int filter_order, double cutoff,
                               vector<T>& coeff)
{
    coeff.resize(filter_order + 1);

    // Prepare Lanczos FIR filter.
    //   t[i]     =  (i - order/2)
    //   coeff[i] =  Sinc(2 * cutoff * t[i]) * Sinc(t[i] / (order/2 + 1))
    //   coeff    /= sum(coeff)

    double ysum = 0.0;

    // Calculate filter kernel.
    for (int i = 0; i <= (int)filter_order; i++) {
        int t2 = 2 * i - filter_order;

        double y;
        if (t2 == 0) {
            y = 1.0;
        } else {
            double x1 = cutoff * t2;
            double x2 = t2 / double(filter_order + 2);
            y = ( sin(M_PI * x1) / M_PI / x1 ) *
                ( sin(M_PI * x2) / M_PI / x2 );
        }

        coeff[i] = y;
        ysum += y;
    }

    // Apply correction factor to ensure unit gain at DC.
    for (unsigned i = 0; i <= filter_order; i++) {
        coeff[i] /= ysum;
    }
}


/* ****************  class FineTuner  **************** */

// Construct finetuner.
FineTuner::FineTuner(unsigned int table_size, int freq_shift)
    : m_index(0)
    , m_table(table_size)
{
    double phase_step = 2.0 * M_PI / double(table_size);
    for (unsigned int i = 0; i < table_size; i++) {
        double phi = (((int64_t)freq_shift * i) % table_size) * phase_step;
        double pcos = cos(phi);
        double psin = sin(phi);
        m_table[i] = IQSample(pcos, psin);
    }
}


// Process samples.
void FineTuner::process(const IQSampleVector& samples_in,
                        IQSampleVector& samples_out)
{
    unsigned int tblidx = m_index;
    unsigned int tblsiz = m_table.size();
    unsigned int n = samples_in.size();

    samples_out.resize(n);

    for (unsigned int i = 0; i < n; i++) {
        samples_out[i] = samples_in[i] * m_table[tblidx];
        tblidx++;
        if (tblidx == tblsiz)
            tblidx = 0;
    }

    m_index = tblidx; 
}


/* ****************  class LowPassFilterFirIQ  **************** */

// Construct low-pass filter.
LowPassFilterFirIQ::LowPassFilterFirIQ(unsigned int filter_order, double cutoff)
    : m_state(filter_order)
{
    make_lanczos_coeff(filter_order, cutoff, m_coeff);
}


// Process samples.
void LowPassFilterFirIQ::process(const IQSampleVector& samples_in,
                                 IQSampleVector& samples_out)
{
    unsigned int order = m_state.size();
    unsigned int n = samples_in.size();

    samples_out.resize(n);

    if (n == 0)
        return;

    // NOTE: We use m_coeff the wrong way around because it is slightly
    // faster to scan forward through the array. The result is still correct
    // because the coefficients are symmetric.

    // The first few samples need data from m_state.
    unsigned int i = 0;
    for (; i < n && i < order; i++) {
        IQSample y = 0;
        for (unsigned int j = 0; j < order - i; j++)
            y += m_state[i+j] * m_coeff[j];
        for (unsigned int j = order - i; j <= order; j++)
            y += samples_in[i-order+j] * m_coeff[j];
        samples_out[i] = y;
    }

    // Remaining samples only need data from samples_in.
    for (; i < n; i++) {
        IQSample y = 0;
        IQSampleVector::const_iterator inp = samples_in.begin() + i - order;
        for (unsigned int j = 0; j <= order; j++)
            y += inp[j] * m_coeff[j];
        samples_out[i] = y;
    }

    // Update m_state.
    if (n < order) {
        copy(m_state.begin() + n, m_state.end(), m_state.begin());
        copy(samples_in.begin(), samples_in.end(), m_state.end() - n);
    } else {
        copy(samples_in.end() - order, samples_in.end(), m_state.begin());
    }
}


/* ****************  class DownsampleFilter  **************** */

// Construct low-pass filter with optional downsampling.
DownsampleFilter::DownsampleFilter(unsigned int filter_order, double cutoff,
                                   double downsample, bool integer_factor)
    : m_downsample(downsample)
    , m_downsample_int(integer_factor ? lrint(downsample) : 0)
    , m_pos_int(0)
    , m_pos_frac(0)
    , m_state(filter_order)
{
    assert(downsample >= 1);
    assert(filter_order > 1);

    // Force the first coefficient to zero and append an extra zero at the
    // end of the array. This ensures we can always obtain (filter_order+1)
    // coefficients by linear interpolation between adjacent array elements.
    make_lanczos_coeff(filter_order - 1, cutoff, m_coeff);
    m_coeff.insert(m_coeff.begin(), 0);
    m_coeff.push_back(0);
}


// Process samples.
void DownsampleFilter::process(const SampleVector& samples_in,
                               SampleVector& samples_out)
{
    unsigned int order = m_state.size();
    unsigned int n = samples_in.size();

    if (m_downsample_int != 0) {

        // Integer downsample factor, no linear interpolation.
        // This is relatively simple.

        unsigned int p = m_pos_int;
        unsigned int pstep = m_downsample_int;

        samples_out.resize((n - p + pstep - 1) / pstep);

        // The first few samples need data from m_state.
        unsigned int i = 0;
        for (; p < n && p < order; p += pstep, i++) {
            Sample y = 0;
            for (unsigned int j = 1; j <= p; j++)
                y += samples_in[p-j] * m_coeff[j];
            for (unsigned int j = p + 1; j <= order; j++)
                y += m_state[order+p-j] * m_coeff[j];
            samples_out[i] = y;
        }

        // Remaining samples only need data from samples_in.
        for (; p < n; p += pstep, i++) {
            Sample y = 0;
            for (unsigned int j = 1; j <= order; j++)
                y += samples_in[p-j] * m_coeff[j];
            samples_out[i] = y;
        }

        assert(i == samples_out.size());

        // Update index of start position in text sample block.
        m_pos_int = p - n;

    } else {

        // Fractional downsample factor via linear interpolation of
        // the FIR coefficient table. This is a bitch.

        // Estimate number of output samples we can produce in this run.
        Sample p = m_pos_frac;
        Sample pstep = m_downsample;
        unsigned int n_out = int(2 + n / pstep);

        samples_out.resize(n_out);

        // Produce output samples.
        unsigned int i = 0;
        Sample pf = p;
        unsigned int pi = int(pf);
        while (pi < n) {
            Sample k1 = pf - pi;
            Sample k0 = 1 - k1;

            Sample y = 0;
            for (unsigned int j = 0; j <= order; j++) {
                Sample k = m_coeff[j] * k0 + m_coeff[j+1] * k1;
                Sample s = (j <= pi) ? samples_in[pi-j] : m_state[order+pi-j];
                y += k * s;
            }
            samples_out[i] = y;

            i++;
            pf = p + i * pstep;
            pi = int(pf);
        }

        // We may overestimate the number of samples by 1 or 2.
        assert(i <= n_out && i + 2 >= n_out);
        samples_out.resize(i);

        // Update fractional index of start position in text sample block.
        // Limit to 0 to avoid catastrophic results of rounding errors.
        m_pos_frac = pf - n;
        if (m_pos_frac < 0)
            m_pos_frac = 0;
    }

    // Update m_state.
    if (n < order) {
        copy(m_state.begin() + n, m_state.end(), m_state.begin());
        copy(samples_in.begin(), samples_in.end(), m_state.end() - n);
    } else {
        copy(samples_in.end() - order, samples_in.end(), m_state.begin());
    }

}


/* ****************  class LowPassFilterRC  **************** */

// Construct 1st order low-pass IIR filter.
LowPassFilterRC::LowPassFilterRC(double timeconst)
    : m_timeconst(timeconst)
    , m_y1(0)
{
}


// Process samples.
void LowPassFilterRC::process(const SampleVector& samples_in,
                              SampleVector& samples_out)
{
    /*
     * Continuous domain:
     *   H(s) = 1 / (1 - s * timeconst)
     *
     * Discrete domain:
     *   H(z) = (1 - exp(-1/timeconst)) / (1 - exp(-1/timeconst) / z)
     */
    Sample a1 = - exp(-1/m_timeconst);;
    Sample b0 = 1 + a1;

    unsigned int n = samples_in.size();
    samples_out.resize(n);

    Sample y = m_y1;
    for (unsigned int i = 0; i < n; i++) {
        Sample x = samples_in[i];
        y = b0 * x - a1 * y;
        samples_out[i] = y;
    }

    m_y1 = y;
}


// Process samples in-place.
void LowPassFilterRC::process_inplace(SampleVector& samples)
{
    Sample a1 = - exp(-1/m_timeconst);;
    Sample b0 = 1 + a1;

    unsigned int n = samples.size();

    Sample y = m_y1;
    for (unsigned int i = 0; i < n; i++) {
        Sample x = samples[i];
        y = b0 * x - a1 * y;
        samples[i] = y;
    }

    m_y1 = y;
}


/* ****************  class LowPassFilterIir  **************** */

// Construct 4th order low-pass IIR filter.
LowPassFilterIir::LowPassFilterIir(double cutoff)
    : y1(0), y2(0), y3(0), y4(0)
{
    typedef complex<double> CDbl;

    // Angular cutoff frequency.
    double w = 2 * M_PI * cutoff;

    // Poles 1 and 4 are a conjugate pair, and poles 2 and 3 are another pair.
    // Continuous domain:
    //   p_k = w * exp( (2*k + n - 1) / (2*n) * pi * j)
    CDbl p1s = w * exp((2*1 + 4 - 1) / double(2 * 4) * CDbl(0, M_PI));
    CDbl p2s = w * exp((2*2 + 4 - 1) / double(2 * 4) * CDbl(0, M_PI));

    // Map poles to discrete-domain via matched Z transform.
    CDbl p1z = exp(p1s);
    CDbl p2z = exp(p2s);

    // Discrete-domain transfer function:
    //   H(z) = b0 / ( (1 - p1/z) * (1 - p4/z) * (1 - p2/z) * (1 - p3/z) )
    //        = b0 / ( (1 - (p1+p4)/z + p1*p4/z**2) *
    //                 (1 - (p2+p3)/z + p2*p3/z**2) )
    //        = b0 / (1 - (p1 + p4 + p2 + p3)/z
    //                  + (p1*p4 + p2*p3 + (p1+p4)*(p2+p3))/z**2
    //                  - ((p1+p4)*p2*p3 + (p2+p3)*p1*p4)/z**3
    //                  + p1*p4*p2*p3/z**4
    //
    // Note that p3 = conj(p2), p4 = conj(p1)
    // Therefore p1+p4 == 2*real(p1), p1*p4 == abs(p1*p1)
    //
    a1 = - (2*real(p1z) + 2*real(p2z));
    a2 = (abs(p1z*p1z) + abs(p2z*p2z) + 2*real(p1z) * 2*real(p2z));
    a3 = - (2*real(p1z) * abs(p2z*p2z) + 2*real(p2z) * abs(p1z*p1z));
    a4 = abs(p1z*p1z) * abs(p2z*p2z);

    // Choose b0 to get unit DC gain.
    b0 = 1 + a1 + a2 + a3 + a4;
}


// Process samples.
void LowPassFilterIir::process(const SampleVector& samples_in,
                               SampleVector& samples_out)
{
    unsigned int n = samples_in.size();

    samples_out.resize(n);

    for (unsigned int i = 0; i < n; i++) {
        Sample x = samples_in[i];
        Sample y = b0 * x - a1 * y1 - a2 * y2 - a3 * y3 - a4 * y4;
        y4 = y3; y3 = y2; y2 = y1; y1 = y;
        samples_out[i] = y;
    }
}


/* ****************  class HighPassFilterIir  **************** */

// Construct 2nd order high-pass IIR filter.
HighPassFilterIir::HighPassFilterIir(double cutoff)
    : x1(0), x2(0), y1(0), y2(0)
{
    typedef complex<double> CDbl;

    // Angular cutoff frequency.
    double w = 2 * M_PI * cutoff;

    // Poles 1 and 2 are a conjugate pair.
    // Continuous-domain:
    //   p_k = w / exp( (2*k + n - 1) / (2*n) * pi * j)
    CDbl p1s = w / exp((2*1 + 2 - 1) / double(2 * 2) * CDbl(0, M_PI));

    // Map poles to discrete-domain via matched Z transform.
    CDbl p1z = exp(p1s);

    // Both zeros are located in s = 0, z = 1.

    // Discrete-domain transfer function:
    //   H(z) = g * (1 - 1/z) * (1 - 1/z) / ( (1 - p1/z) * (1 - p2/z) )
    //        = g * (1 - 2/z + 1/z**2) / (1 - (p1+p2)/z + (p1*p2)/z**2)
    //
    // Note that z2 = conj(z1).
    // Therefore p1+p2 == 2*real(p1), p1*2 == abs(p1*p1), z4 = conj(z1)
    //
    b0 = 1;
    b1 = -2;
    b2 = 1;
    a1 = -2 * real(p1z);
    a2 = abs(p1z*p1z);

    // Adjust b coefficients to get unit gain at Nyquist frequency (z=-1).
    double g = (b0 - b1 + b2) / (1 - a1 + a2);
    b0 /= g;
    b1 /= g;
    b2 /= g;
}


// Process samples.
void HighPassFilterIir::process(const SampleVector& samples_in,
                                SampleVector& samples_out)
{
    unsigned int n = samples_in.size();

    samples_out.resize(n);

    for (unsigned int i = 0; i < n; i++) {
        Sample x = samples_in[i];
        Sample y = b0 * x + b1 * x1 + b2 * x2 - a1 * y1 - a2 * y2;
        x2 = x1; x1 = x;
        y2 = y1; y1 = y;
        samples_out[i] = y;
    }
}


// Process samples in-place.
void HighPassFilterIir::process_inplace(SampleVector& samples)
{
    unsigned int n = samples.size();

    for (unsigned int i = 0; i < n; i++) {
        Sample x = samples[i];
        Sample y = b0 * x + b1 * x1 + b2 * x2 - a1 * y1 - a2 * y2;
        x2 = x1; x1 = x;
        y2 = y1; y1 = y;
        samples[i] = y;
    }
}

/* end */