text: /*
   *  Copyright (c) 2015 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.
   */
  
  // An implementation of a 3-band FIR filter-bank with DCT modulation, similar to
  // the proposed in "Multirate Signal Processing for Communication Systems" by
  // Fredric J Harris.
  //
  // The idea is to take a heterodyne system and change the order of the
  // components to get something which is efficient to implement digitally.
  //
  // It is possible to separate the filter using the noble identity as follows:
  //
  // H(z) = H0(z^3) + z^-1 * H1(z^3) + z^-2 * H2(z^3)
  //
  // This is used in the analysis stage to first downsample serial to parallel
  // and then filter each branch with one of these polyphase decompositions of the
  // lowpass prototype. Because each filter is only a modulation of the prototype,
  // it is enough to multiply each coefficient by the respective cosine value to
  // shift it to the desired band. But because the cosine period is 12 samples,
  // it requires separating the prototype even further using the noble identity.
  // After filtering and modulating for each band, the output of all filters is
  // accumulated to get the downsampled bands.
  //
  // A similar logic can be applied to the synthesis stage.
  
  // MSVC++ requires this to be set before any other includes to get M_PI.
  #define _USE_MATH_DEFINES
  
  #include BOSS_WEBRTC_U_modules__audio_processing__three_band_filter_bank_h //original-code:"modules/audio_processing/three_band_filter_bank.h"
  
  #include <cmath>
  
  #include BOSS_WEBRTC_U_rtc_base__checks_h //original-code:"rtc_base/checks.h"
  
  namespace webrtc {
  namespace {
  
  const size_t kNumBands = 3;
  const size_t kSparsity = 4;
  
  // Factors to take into account when choosing |kNumCoeffs|:
  //   1. Higher |kNumCoeffs|, means faster transition, which ensures less
  //      aliasing. This is especially important when there is non-linear
  //      processing between the splitting and merging.
  //   2. The delay that this filter bank introduces is
  //      |kNumBands| * |kSparsity| * |kNumCoeffs| / 2, so it increases linearly
  //      with |kNumCoeffs|.
  //   3. The computation complexity also increases linearly with |kNumCoeffs|.
  const size_t kNumCoeffs = 4;
  
  // The Matlab code to generate these |kLowpassCoeffs| is:
  //
  // N = kNumBands * kSparsity * kNumCoeffs - 1;
  // h = fir1(N, 1 / (2 * kNumBands), kaiser(N + 1, 3.5));
  // reshape(h, kNumBands * kSparsity, kNumCoeffs);
  //
  // Because the total bandwidth of the lower and higher band is double the middle
  // one (because of the spectrum parity), the low-pass prototype is half the
  // bandwidth of 1 / (2 * |kNumBands|) and is then shifted with cosine modulation
  // to the right places.
  // A Kaiser window is used because of its flexibility and the alpha is set to
  // 3.5, since that sets a stop band attenuation of 40dB ensuring a fast
  // transition.
  const float kLowpassCoeffs[kNumBands * kSparsity][kNumCoeffs] = {
      {-0.00047749f, -0.00496888f, +0.16547118f, +0.00425496f},
      {-0.00173287f, -0.01585778f, +0.14989004f, +0.00994113f},
      {-0.00304815f, -0.02536082f, +0.12154542f, +0.01157993f},
      {-0.00383509f, -0.02982767f, +0.08543175f, +0.00983212f},
      {-0.00346946f, -0.02587886f, +0.04760441f, +0.00607594f},
      {-0.00154717f, -0.01136076f, +0.01387458f, +0.00186353f},
      {+0.00186353f, +0.01387458f, -0.01136076f, -0.00154717f},
      {+0.00607594f, +0.04760441f, -0.02587886f, -0.00346946f},
      {+0.00983212f, +0.08543175f, -0.02982767f, -0.00383509f},
      {+0.01157993f, +0.12154542f, -0.02536082f, -0.00304815f},
      {+0.00994113f, +0.14989004f, -0.01585778f, -0.00173287f},
      {+0.00425496f, +0.16547118f, -0.00496888f, -0.00047749f}};
  
  // Downsamples |in| into |out|, taking one every |kNumbands| starting from
  // |offset|. |split_length| is the |out| length. |in| has to be at least
  // |kNumBands| * |split_length| long.
  void Downsample(const float* in,
                  size_t split_length,
                  size_t offset,
                  float* out) {
    for (size_t i = 0; i < split_length; ++i) {
      out[i] = in[kNumBands * i + offset];
    }
  }
  
  // Upsamples |in| into |out|, scaling by |kNumBands| and accumulating it every
  // |kNumBands| starting from |offset|. |split_length| is the |in| length. |out|
  // has to be at least |kNumBands| * |split_length| long.
  void Upsample(const float* in, size_t split_length, size_t offset, float* out) {
    for (size_t i = 0; i < split_length; ++i) {
      out[kNumBands * i + offset] += kNumBands * in[i];
    }
  }
  
  }  // namespace
  
  // Because the low-pass filter prototype has half bandwidth it is possible to
  // use a DCT to shift it in both directions at the same time, to the center
  // frequencies [1 / 12, 3 / 12, 5 / 12].
  ThreeBandFilterBank::ThreeBandFilterBank(size_t length)
      : in_buffer_(rtc::CheckedDivExact(length, kNumBands)),
        out_buffer_(in_buffer_.size()) {
    for (size_t i = 0; i < kSparsity; ++i) {
      for (size_t j = 0; j < kNumBands; ++j) {
        analysis_filters_.push_back(
            std::unique_ptr<SparseFIRFilter>(new SparseFIRFilter(
                kLowpassCoeffs[i * kNumBands + j], kNumCoeffs, kSparsity, i)));
        synthesis_filters_.push_back(
            std::unique_ptr<SparseFIRFilter>(new SparseFIRFilter(
                kLowpassCoeffs[i * kNumBands + j], kNumCoeffs, kSparsity, i)));
      }
    }
    dct_modulation_.resize(kNumBands * kSparsity);
    for (size_t i = 0; i < dct_modulation_.size(); ++i) {
      dct_modulation_[i].resize(kNumBands);
      for (size_t j = 0; j < kNumBands; ++j) {
        dct_modulation_[i][j] =
            2.f * cos(2.f * M_PI * i * (2.f * j + 1.f) / dct_modulation_.size());
      }
    }
  }
  
  ThreeBandFilterBank::~ThreeBandFilterBank() = default;
  
  // The analysis can be separated in these steps:
  //   1. Serial to parallel downsampling by a factor of |kNumBands|.
  //   2. Filtering of |kSparsity| different delayed signals with polyphase
  //      decomposition of the low-pass prototype filter and upsampled by a factor
  //      of |kSparsity|.
  //   3. Modulating with cosines and accumulating to get the desired band.
  void ThreeBandFilterBank::Analysis(const float* in,
                                     size_t length,
                                     float* const* out) {
    RTC_CHECK_EQ(in_buffer_.size(), rtc::CheckedDivExact(length, kNumBands));
    for (size_t i = 0; i < kNumBands; ++i) {
      memset(out[i], 0, in_buffer_.size() * sizeof(*out[i]));
    }
    for (size_t i = 0; i < kNumBands; ++i) {
      Downsample(in, in_buffer_.size(), kNumBands - i - 1, &in_buffer_[0]);
      for (size_t j = 0; j < kSparsity; ++j) {
        const size_t offset = i + j * kNumBands;
        analysis_filters_[offset]->Filter(&in_buffer_[0], in_buffer_.size(),
                                          &out_buffer_[0]);
        DownModulate(&out_buffer_[0], out_buffer_.size(), offset, out);
      }
    }
  }
  
  // The synthesis can be separated in these steps:
  //   1. Modulating with cosines.
  //   2. Filtering each one with a polyphase decomposition of the low-pass
  //      prototype filter upsampled by a factor of |kSparsity| and accumulating
  //      |kSparsity| signals with different delays.
  //   3. Parallel to serial upsampling by a factor of |kNumBands|.
  void ThreeBandFilterBank::Synthesis(const float* const* in,
                                      size_t split_length,
                                      float* out) {
    RTC_CHECK_EQ(in_buffer_.size(), split_length);
    memset(out, 0, kNumBands * in_buffer_.size() * sizeof(*out));
    for (size_t i = 0; i < kNumBands; ++i) {
      for (size_t j = 0; j < kSparsity; ++j) {
        const size_t offset = i + j * kNumBands;
        UpModulate(in, in_buffer_.size(), offset, &in_buffer_[0]);
        synthesis_filters_[offset]->Filter(&in_buffer_[0], in_buffer_.size(),
                                           &out_buffer_[0]);
        Upsample(&out_buffer_[0], out_buffer_.size(), i, out);
      }
    }
  }
  
  // Modulates |in| by |dct_modulation_| and accumulates it in each of the
  // |kNumBands| bands of |out|. |offset| is the index in the period of the
  // cosines used for modulation. |split_length| is the length of |in| and each
  // band of |out|.
  void ThreeBandFilterBank::DownModulate(const float* in,
                                         size_t split_length,
                                         size_t offset,
                                         float* const* out) {
    for (size_t i = 0; i < kNumBands; ++i) {
      for (size_t j = 0; j < split_length; ++j) {
        out[i][j] += dct_modulation_[offset][i] * in[j];
      }
    }
  }
  
  // Modulates each of the |kNumBands| bands of |in| by |dct_modulation_| and
  // accumulates them in |out|. |out| is cleared before starting to accumulate.
  // |offset| is the index in the period of the cosines used for modulation.
  // |split_length| is the length of each band of |in| and |out|.
  void ThreeBandFilterBank::UpModulate(const float* const* in,
                                       size_t split_length,
                                       size_t offset,
                                       float* out) {
    memset(out, 0, split_length * sizeof(*out));
    for (size_t i = 0; i < kNumBands; ++i) {
      for (size_t j = 0; j < split_length; ++j) {
        out[j] += dct_modulation_[offset][i] * in[i][j];
      }
    }
  }
  
  }  // namespace webrtc
  