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/*
* 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 "webrtc/modules/audio_processing/three_band_filter_bank.h"
#include <cmath>
#include "webrtc/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