common_audio/vad/vad_filterbank.c

/*
 *  Copyright (c) 2012 The WebRTC project authors. All Rights Reserved.
 *
 *  Use of this source code is governed by a BSD-style license
 *  that can be found in the LICENSE file in the root of the source
 *  tree. An additional intellectual property rights grant can be found
 *  in the file PATENTS.  All contributing project authors may
 *  be found in the AUTHORS file in the root of the source tree.
 */

#include "webrtc/common_audio/vad/vad_filterbank.h"

#include <assert.h>

#include "webrtc/common_audio/signal_processing/include/signal_processing_library.h"
#include "webrtc/typedefs.h"

// Constants used in LogOfEnergy().
static const int16_t kLogConst = 24660;  // 160*log10(2) in Q9.
static const int16_t kLogEnergyIntPart = 14336;  // 14 in Q10

// Coefficients used by HighPassFilter, Q14.
static const int16_t kHpZeroCoefs[3] = { 6631, -13262, 6631 };
static const int16_t kHpPoleCoefs[3] = { 16384, -7756, 5620 };

// Allpass filter coefficients, upper and lower, in Q15.
// Upper: 0.64, Lower: 0.17
static const int16_t kAllPassCoefsQ15[2] = { 20972, 5571 };

// Adjustment for division with two in SplitFilter.
static const int16_t kOffsetVector[6] = { 368, 368, 272, 176, 176, 176 };

// High pass filtering, with a cut-off frequency at 80 Hz, if the |data_in| is
// sampled at 500 Hz.
//
// - data_in      [i]   : Input audio data sampled at 500 Hz.
// - data_length  [i]   : Length of input and output data.
// - filter_state [i/o] : State of the filter.
// - data_out     [o]   : Output audio data in the frequency interval
//                        80 - 250 Hz.
static void HighPassFilter(const int16_t* data_in, size_t data_length,
                           int16_t* filter_state, int16_t* data_out) {
  size_t i;
  const int16_t* in_ptr = data_in;
  int16_t* out_ptr = data_out;
  int32_t tmp32 = 0;


  // The sum of the absolute values of the impulse response:
  // The zero/pole-filter has a max amplification of a single sample of: 1.4546
  // Impulse response: 0.4047 -0.6179 -0.0266  0.1993  0.1035  -0.0194
  // The all-zero section has a max amplification of a single sample of: 1.6189
  // Impulse response: 0.4047 -0.8094  0.4047  0       0        0
  // The all-pole section has a max amplification of a single sample of: 1.9931
  // Impulse response: 1.0000  0.4734 -0.1189 -0.2187 -0.0627   0.04532

  for (i = 0; i < data_length; i++) {
    // All-zero section (filter coefficients in Q14).
    tmp32 = kHpZeroCoefs[0] * *in_ptr;
    tmp32 += kHpZeroCoefs[1] * filter_state[0];
    tmp32 += kHpZeroCoefs[2] * filter_state[1];
    filter_state[1] = filter_state[0];
    filter_state[0] = *in_ptr++;

    // All-pole section (filter coefficients in Q14).
    tmp32 -= kHpPoleCoefs[1] * filter_state[2];
    tmp32 -= kHpPoleCoefs[2] * filter_state[3];
    filter_state[3] = filter_state[2];
    filter_state[2] = (int16_t) (tmp32 >> 14);
    *out_ptr++ = filter_state[2];
  }
}

// All pass filtering of |data_in|, used before splitting the signal into two
// frequency bands (low pass vs high pass).
// Note that |data_in| and |data_out| can NOT correspond to the same address.
//
// - data_in            [i]   : Input audio signal given in Q0.
// - data_length        [i]   : Length of input and output data.
// - filter_coefficient [i]   : Given in Q15.
// - filter_state       [i/o] : State of the filter given in Q(-1).
// - data_out           [o]   : Output audio signal given in Q(-1).
static void AllPassFilter(const int16_t* data_in, size_t data_length,
                          int16_t filter_coefficient, int16_t* filter_state,
                          int16_t* data_out) {
  // The filter can only cause overflow (in the w16 output variable)
  // if more than 4 consecutive input numbers are of maximum value and
  // has the the same sign as the impulse responses first taps.
  // First 6 taps of the impulse response:
  // 0.6399 0.5905 -0.3779 0.2418 -0.1547 0.0990

  size_t i;
  int16_t tmp16 = 0;
  int32_t tmp32 = 0;
  int32_t state32 = ((int32_t) (*filter_state) << 16);  // Q15

  for (i = 0; i < data_length; i++) {
    tmp32 = state32 + filter_coefficient * *data_in;
    tmp16 = (int16_t) (tmp32 >> 16);  // Q(-1)
    *data_out++ = tmp16;
    state32 = (*data_in << 14) - filter_coefficient * tmp16;  // Q14
    state32 <<= 1;  // Q15.
    data_in += 2;
  }

  *filter_state = (int16_t) (state32 >> 16);  // Q(-1)
}

// Splits |data_in| into |hp_data_out| and |lp_data_out| corresponding to
// an upper (high pass) part and a lower (low pass) part respectively.
//
// - data_in      [i]   : Input audio data to be split into two frequency bands.
// - data_length  [i]   : Length of |data_in|.
// - upper_state  [i/o] : State of the upper filter, given in Q(-1).
// - lower_state  [i/o] : State of the lower filter, given in Q(-1).
// - hp_data_out  [o]   : Output audio data of the upper half of the spectrum.
//                        The length is |data_length| / 2.
// - lp_data_out  [o]   : Output audio data of the lower half of the spectrum.
//                        The length is |data_length| / 2.
static void SplitFilter(const int16_t* data_in, size_t data_length,
                        int16_t* upper_state, int16_t* lower_state,
                        int16_t* hp_data_out, int16_t* lp_data_out) {
  size_t i;
  size_t half_length = data_length >> 1;  // Downsampling by 2.
  int16_t tmp_out;

  // All-pass filtering upper branch.
  AllPassFilter(&data_in[0], half_length, kAllPassCoefsQ15[0], upper_state,
                hp_data_out);

  // All-pass filtering lower branch.
  AllPassFilter(&data_in[1], half_length, kAllPassCoefsQ15[1], lower_state,
                lp_data_out);

  // Make LP and HP signals.
  for (i = 0; i < half_length; i++) {
    tmp_out = *hp_data_out;
    *hp_data_out++ -= *lp_data_out;
    *lp_data_out++ += tmp_out;
  }
}

// Calculates the energy of |data_in| in dB, and also updates an overall
// |total_energy| if necessary.
//
// - data_in      [i]   : Input audio data for energy calculation.
// - data_length  [i]   : Length of input data.
// - offset       [i]   : Offset value added to |log_energy|.
// - total_energy [i/o] : An external energy updated with the energy of
//                        |data_in|.
//                        NOTE: |total_energy| is only updated if
//                        |total_energy| <= |kMinEnergy|.
// - log_energy   [o]   : 10 * log10("energy of |data_in|") given in Q4.
static void LogOfEnergy(const int16_t* data_in, size_t data_length,
                        int16_t offset, int16_t* total_energy,
                        int16_t* log_energy) {
  // |tot_rshifts| accumulates the number of right shifts performed on |energy|.
  int tot_rshifts = 0;
  // The |energy| will be normalized to 15 bits. We use unsigned integer because
  // we eventually will mask out the fractional part.
  uint32_t energy = 0;

  assert(data_in != NULL);
  assert(data_length > 0);

  energy = (uint32_t) WebRtcSpl_Energy((int16_t*) data_in, data_length,
                                       &tot_rshifts);

  if (energy != 0) {
    // By construction, normalizing to 15 bits is equivalent with 17 leading
    // zeros of an unsigned 32 bit value.
    int normalizing_rshifts = 17 - WebRtcSpl_NormU32(energy);
    // In a 15 bit representation the leading bit is 2^14. log2(2^14) in Q10 is
    // (14 << 10), which is what we initialize |log2_energy| with. For a more
    // detailed derivations, see below.
    int16_t log2_energy = kLogEnergyIntPart;

    tot_rshifts += normalizing_rshifts;
    // Normalize |energy| to 15 bits.
    // |tot_rshifts| is now the total number of right shifts performed on
    // |energy| after normalization. This means that |energy| is in
    // Q(-tot_rshifts).
    if (normalizing_rshifts < 0) {
      energy <<= -normalizing_rshifts;
    } else {
      energy >>= normalizing_rshifts;
    }

    // Calculate the energy of |data_in| in dB, in Q4.
    //
    // 10 * log10("true energy") in Q4 = 2^4 * 10 * log10("true energy") =
    // 160 * log10(|energy| * 2^|tot_rshifts|) =
    // 160 * log10(2) * log2(|energy| * 2^|tot_rshifts|) =
    // 160 * log10(2) * (log2(|energy|) + log2(2^|tot_rshifts|)) =
    // (160 * log10(2)) * (log2(|energy|) + |tot_rshifts|) =
    // |kLogConst| * (|log2_energy| + |tot_rshifts|)
    //
    // We know by construction that |energy| is normalized to 15 bits. Hence,
    // |energy| = 2^14 + frac_Q15, where frac_Q15 is a fractional part in Q15.
    // Further, we'd like |log2_energy| in Q10
    // log2(|energy|) in Q10 = 2^10 * log2(2^14 + frac_Q15) =
    // 2^10 * log2(2^14 * (1 + frac_Q15 * 2^-14)) =
    // 2^10 * (14 + log2(1 + frac_Q15 * 2^-14)) ~=
    // (14 << 10) + 2^10 * (frac_Q15 * 2^-14) =
    // (14 << 10) + (frac_Q15 * 2^-4) = (14 << 10) + (frac_Q15 >> 4)
    //
    // Note that frac_Q15 = (|energy| & 0x00003FFF)

    // Calculate and add the fractional part to |log2_energy|.
    log2_energy += (int16_t) ((energy & 0x00003FFF) >> 4);

    // |kLogConst| is in Q9, |log2_energy| in Q10 and |tot_rshifts| in Q0.
    // Note that we in our derivation above have accounted for an output in Q4.
    *log_energy = (int16_t)(((kLogConst * log2_energy) >> 19) +
        ((tot_rshifts * kLogConst) >> 9));

    if (*log_energy < 0) {
      *log_energy = 0;
    }
  } else {
    *log_energy = offset;
    return;
  }

  *log_energy += offset;

  // Update the approximate |total_energy| with the energy of |data_in|, if
  // |total_energy| has not exceeded |kMinEnergy|. |total_energy| is used as an
  // energy indicator in WebRtcVad_GmmProbability() in vad_core.c.
  if (*total_energy <= kMinEnergy) {
    if (tot_rshifts >= 0) {
      // We know by construction that the |energy| > |kMinEnergy| in Q0, so add
      // an arbitrary value such that |total_energy| exceeds |kMinEnergy|.
      *total_energy += kMinEnergy + 1;
    } else {
      // By construction |energy| is represented by 15 bits, hence any number of
      // right shifted |energy| will fit in an int16_t. In addition, adding the
      // value to |total_energy| is wrap around safe as long as
      // |kMinEnergy| < 8192.
      *total_energy += (int16_t) (energy >> -tot_rshifts);  // Q0.
    }
  }
}

int16_t WebRtcVad_CalculateFeatures(VadInstT* self, const int16_t* data_in,
                                    size_t data_length, int16_t* features) {
  int16_t total_energy = 0;
  // We expect |data_length| to be 80, 160 or 240 samples, which corresponds to
  // 10, 20 or 30 ms in 8 kHz. Therefore, the intermediate downsampled data will
  // have at most 120 samples after the first split and at most 60 samples after
  // the second split.
  int16_t hp_120[120], lp_120[120];
  int16_t hp_60[60], lp_60[60];
  const size_t half_data_length = data_length >> 1;
  size_t length = half_data_length;  // |data_length| / 2, corresponds to
                                     // bandwidth = 2000 Hz after downsampling.

  // Initialize variables for the first SplitFilter().
  int frequency_band = 0;
  const int16_t* in_ptr = data_in;  // [0 - 4000] Hz.
  int16_t* hp_out_ptr = hp_120;  // [2000 - 4000] Hz.
  int16_t* lp_out_ptr = lp_120;  // [0 - 2000] Hz.

  assert(data_length <= 240);
  assert(4 < kNumChannels - 1);  // Checking maximum |frequency_band|.

  // Split at 2000 Hz and downsample.
  SplitFilter(in_ptr, data_length, &self->upper_state[frequency_band],
              &self->lower_state[frequency_band], hp_out_ptr, lp_out_ptr);

  // For the upper band (2000 Hz - 4000 Hz) split at 3000 Hz and downsample.
  frequency_band = 1;
  in_ptr = hp_120;  // [2000 - 4000] Hz.
  hp_out_ptr = hp_60;  // [3000 - 4000] Hz.
  lp_out_ptr = lp_60;  // [2000 - 3000] Hz.
  SplitFilter(in_ptr, length, &self->upper_state[frequency_band],
              &self->lower_state[frequency_band], hp_out_ptr, lp_out_ptr);

  // Energy in 3000 Hz - 4000 Hz.
  length >>= 1;  // |data_length| / 4 <=> bandwidth = 1000 Hz.

  LogOfEnergy(hp_60, length, kOffsetVector[5], &total_energy, &features[5]);

  // Energy in 2000 Hz - 3000 Hz.
  LogOfEnergy(lp_60, length, kOffsetVector[4], &total_energy, &features[4]);

  // For the lower band (0 Hz - 2000 Hz) split at 1000 Hz and downsample.
  frequency_band = 2;
  in_ptr = lp_120;  // [0 - 2000] Hz.
  hp_out_ptr = hp_60;  // [1000 - 2000] Hz.
  lp_out_ptr = lp_60;  // [0 - 1000] Hz.
  length = half_data_length;  // |data_length| / 2 <=> bandwidth = 2000 Hz.
  SplitFilter(in_ptr, length, &self->upper_state[frequency_band],
              &self->lower_state[frequency_band], hp_out_ptr, lp_out_ptr);

  // Energy in 1000 Hz - 2000 Hz.
  length >>= 1;  // |data_length| / 4 <=> bandwidth = 1000 Hz.
  LogOfEnergy(hp_60, length, kOffsetVector[3], &total_energy, &features[3]);

  // For the lower band (0 Hz - 1000 Hz) split at 500 Hz and downsample.
  frequency_band = 3;
  in_ptr = lp_60;  // [0 - 1000] Hz.
  hp_out_ptr = hp_120;  // [500 - 1000] Hz.
  lp_out_ptr = lp_120;  // [0 - 500] Hz.
  SplitFilter(in_ptr, length, &self->upper_state[frequency_band],
              &self->lower_state[frequency_band], hp_out_ptr, lp_out_ptr);

  // Energy in 500 Hz - 1000 Hz.
  length >>= 1;  // |data_length| / 8 <=> bandwidth = 500 Hz.
  LogOfEnergy(hp_120, length, kOffsetVector[2], &total_energy, &features[2]);

  // For the lower band (0 Hz - 500 Hz) split at 250 Hz and downsample.
  frequency_band = 4;
  in_ptr = lp_120;  // [0 - 500] Hz.
  hp_out_ptr = hp_60;  // [250 - 500] Hz.
  lp_out_ptr = lp_60;  // [0 - 250] Hz.
  SplitFilter(in_ptr, length, &self->upper_state[frequency_band],
              &self->lower_state[frequency_band], hp_out_ptr, lp_out_ptr);

  // Energy in 250 Hz - 500 Hz.
  length >>= 1;  // |data_length| / 16 <=> bandwidth = 250 Hz.
  LogOfEnergy(hp_60, length, kOffsetVector[1], &total_energy, &features[1]);

  // Remove 0 Hz - 80 Hz, by high pass filtering the lower band.
  HighPassFilter(lp_60, length, self->hp_filter_state, hp_120);

  // Energy in 80 Hz - 250 Hz.
  LogOfEnergy(hp_120, length, kOffsetVector[0], &total_energy, &features[0]);

  return total_energy;
}