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/*
* Copyright (c) 2014 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.
*/
#define _USE_MATH_DEFINES
#include "webrtc/modules/audio_processing/beamformer/nonlinear_beamformer.h"
#include <algorithm>
#include <cmath>
#include <numeric>
#include <vector>
#include "webrtc/common_audio/window_generator.h"
#include "webrtc/modules/audio_processing/beamformer/covariance_matrix_generator.h"
#include "webrtc/rtc_base/arraysize.h"
namespace webrtc {
namespace {
// Alpha for the Kaiser Bessel Derived window.
const float kKbdAlpha = 1.5f;
const float kSpeedOfSoundMeterSeconds = 343;
// The minimum separation in radians between the target direction and an
// interferer scenario.
const float kMinAwayRadians = 0.2f;
// The separation between the target direction and the closest interferer
// scenario is proportional to this constant.
const float kAwaySlope = 0.008f;
// When calculating the interference covariance matrix, this is the weight for
// the weighted average between the uniform covariance matrix and the angled
// covariance matrix.
// Rpsi = Rpsi_angled * kBalance + Rpsi_uniform * (1 - kBalance)
const float kBalance = 0.95f;
// Alpha coefficients for mask smoothing.
const float kMaskTimeSmoothAlpha = 0.2f;
const float kMaskFrequencySmoothAlpha = 0.6f;
// The average mask is computed from masks in this mid-frequency range. If these
// ranges are changed |kMaskQuantile| might need to be adjusted.
const int kLowMeanStartHz = 200;
const int kLowMeanEndHz = 400;
// Range limiter for subtractive terms in the nominator and denominator of the
// postfilter expression. It handles the scenario mismatch between the true and
// model sources (target and interference).
const float kCutOffConstant = 0.9999f;
// Quantile of mask values which is used to estimate target presence.
const float kMaskQuantile = 0.7f;
// Mask threshold over which the data is considered signal and not interference.
// It has to be updated every time the postfilter calculation is changed
// significantly.
// TODO(aluebs): Write a tool to tune the target threshold automatically based
// on files annotated with target and interference ground truth.
const float kMaskTargetThreshold = 0.01f;
// Time in seconds after which the data is considered interference if the mask
// does not pass |kMaskTargetThreshold|.
const float kHoldTargetSeconds = 0.25f;
// To compensate for the attenuation this algorithm introduces to the target
// signal. It was estimated empirically from a low-noise low-reverberation
// recording from broadside.
const float kCompensationGain = 2.f;
// Does conjugate(|norm_mat|) * |mat| * transpose(|norm_mat|). No extra space is
// used; to accomplish this, we compute both multiplications in the same loop.
// The returned norm is clamped to be non-negative.
float Norm(const ComplexMatrix<float>& mat,
const ComplexMatrix<float>& norm_mat) {
RTC_CHECK_EQ(1, norm_mat.num_rows());
RTC_CHECK_EQ(norm_mat.num_columns(), mat.num_rows());
RTC_CHECK_EQ(norm_mat.num_columns(), mat.num_columns());
complex<float> first_product = complex<float>(0.f, 0.f);
complex<float> second_product = complex<float>(0.f, 0.f);
const complex<float>* const* mat_els = mat.elements();
const complex<float>* const* norm_mat_els = norm_mat.elements();
for (size_t i = 0; i < norm_mat.num_columns(); ++i) {
for (size_t j = 0; j < norm_mat.num_columns(); ++j) {
first_product += conj(norm_mat_els[0][j]) * mat_els[j][i];
}
second_product += first_product * norm_mat_els[0][i];
first_product = 0.f;
}
return std::max(second_product.real(), 0.f);
}
// Does conjugate(|lhs|) * |rhs| for row vectors |lhs| and |rhs|.
complex<float> ConjugateDotProduct(const ComplexMatrix<float>& lhs,
const ComplexMatrix<float>& rhs) {
RTC_CHECK_EQ(1, lhs.num_rows());
RTC_CHECK_EQ(1, rhs.num_rows());
RTC_CHECK_EQ(lhs.num_columns(), rhs.num_columns());
const complex<float>* const* lhs_elements = lhs.elements();
const complex<float>* const* rhs_elements = rhs.elements();
complex<float> result = complex<float>(0.f, 0.f);
for (size_t i = 0; i < lhs.num_columns(); ++i) {
result += conj(lhs_elements[0][i]) * rhs_elements[0][i];
}
return result;
}
// Works for positive numbers only.
size_t Round(float x) {
return static_cast<size_t>(std::floor(x + 0.5f));
}
// Calculates the sum of squares of a complex matrix.
float SumSquares(const ComplexMatrix<float>& mat) {
float sum_squares = 0.f;
const complex<float>* const* mat_els = mat.elements();
for (size_t i = 0; i < mat.num_rows(); ++i) {
for (size_t j = 0; j < mat.num_columns(); ++j) {
float abs_value = std::abs(mat_els[i][j]);
sum_squares += abs_value * abs_value;
}
}
return sum_squares;
}
// Does |out| = |in|.' * conj(|in|) for row vector |in|.
void TransposedConjugatedProduct(const ComplexMatrix<float>& in,
ComplexMatrix<float>* out) {
RTC_CHECK_EQ(1, in.num_rows());
RTC_CHECK_EQ(out->num_rows(), in.num_columns());
RTC_CHECK_EQ(out->num_columns(), in.num_columns());
const complex<float>* in_elements = in.elements()[0];
complex<float>* const* out_elements = out->elements();
for (size_t i = 0; i < out->num_rows(); ++i) {
for (size_t j = 0; j < out->num_columns(); ++j) {
out_elements[i][j] = in_elements[i] * conj(in_elements[j]);
}
}
}
std::vector<Point> GetCenteredArray(std::vector<Point> array_geometry) {
for (size_t dim = 0; dim < 3; ++dim) {
float center = 0.f;
for (size_t i = 0; i < array_geometry.size(); ++i) {
center += array_geometry[i].c[dim];
}
center /= array_geometry.size();
for (size_t i = 0; i < array_geometry.size(); ++i) {
array_geometry[i].c[dim] -= center;
}
}
return array_geometry;
}
} // namespace
const float NonlinearBeamformer::kHalfBeamWidthRadians = DegreesToRadians(20.f);
// static
const size_t NonlinearBeamformer::kNumFreqBins;
PostFilterTransform::PostFilterTransform(size_t num_channels,
size_t chunk_length,
float* window,
size_t fft_size)
: transform_(num_channels,
num_channels,
chunk_length,
window,
fft_size,
fft_size / 2,
this),
num_freq_bins_(fft_size / 2 + 1) {}
void PostFilterTransform::ProcessChunk(float* const* data, float* final_mask) {
final_mask_ = final_mask;
transform_.ProcessChunk(data, data);
}
void PostFilterTransform::ProcessAudioBlock(const complex<float>* const* input,
size_t num_input_channels,
size_t num_freq_bins,
size_t num_output_channels,
complex<float>* const* output) {
RTC_DCHECK_EQ(num_freq_bins_, num_freq_bins);
RTC_DCHECK_EQ(num_input_channels, num_output_channels);
for (size_t ch = 0; ch < num_input_channels; ++ch) {
for (size_t f_ix = 0; f_ix < num_freq_bins_; ++f_ix) {
output[ch][f_ix] =
kCompensationGain * final_mask_[f_ix] * input[ch][f_ix];
}
}
}
NonlinearBeamformer::NonlinearBeamformer(
const std::vector<Point>& array_geometry,
size_t num_postfilter_channels,
SphericalPointf target_direction)
: num_input_channels_(array_geometry.size()),
num_postfilter_channels_(num_postfilter_channels),
array_geometry_(GetCenteredArray(array_geometry)),
array_normal_(GetArrayNormalIfExists(array_geometry)),
min_mic_spacing_(GetMinimumSpacing(array_geometry)),
target_angle_radians_(target_direction.azimuth()),
away_radians_(std::min(
static_cast<float>(M_PI),
std::max(kMinAwayRadians,
kAwaySlope * static_cast<float>(M_PI) / min_mic_spacing_))) {
WindowGenerator::KaiserBesselDerived(kKbdAlpha, kFftSize, window_);
}
NonlinearBeamformer::~NonlinearBeamformer() = default;
void NonlinearBeamformer::Initialize(int chunk_size_ms, int sample_rate_hz) {
chunk_length_ =
static_cast<size_t>(sample_rate_hz / (1000.f / chunk_size_ms));
sample_rate_hz_ = sample_rate_hz;
high_pass_postfilter_mask_ = 1.f;
is_target_present_ = false;
hold_target_blocks_ = kHoldTargetSeconds * 2 * sample_rate_hz / kFftSize;
interference_blocks_count_ = hold_target_blocks_;
process_transform_.reset(new LappedTransform(num_input_channels_,
0u,
chunk_length_,
window_,
kFftSize,
kFftSize / 2,
this));
postfilter_transform_.reset(new PostFilterTransform(
num_postfilter_channels_, chunk_length_, window_, kFftSize));
const float wave_number_step =
(2.f * M_PI * sample_rate_hz_) / (kFftSize * kSpeedOfSoundMeterSeconds);
for (size_t i = 0; i < kNumFreqBins; ++i) {
time_smooth_mask_[i] = 1.f;
final_mask_[i] = 1.f;
wave_numbers_[i] = i * wave_number_step;
}
InitLowFrequencyCorrectionRanges();
InitDiffuseCovMats();
AimAt(SphericalPointf(target_angle_radians_, 0.f, 1.f));
}
// These bin indexes determine the regions over which a mean is taken. This is
// applied as a constant value over the adjacent end "frequency correction"
// regions.
//
// low_mean_start_bin_ high_mean_start_bin_
// v v constant
// |----------------|--------|----------------|-------|----------------|
// constant ^ ^
// low_mean_end_bin_ high_mean_end_bin_
//
void NonlinearBeamformer::InitLowFrequencyCorrectionRanges() {
low_mean_start_bin_ = Round(static_cast<float>(kLowMeanStartHz) *
kFftSize / sample_rate_hz_);
low_mean_end_bin_ = Round(static_cast<float>(kLowMeanEndHz) *
kFftSize / sample_rate_hz_);
RTC_DCHECK_GT(low_mean_start_bin_, 0U);
RTC_DCHECK_LT(low_mean_start_bin_, low_mean_end_bin_);
}
void NonlinearBeamformer::InitHighFrequencyCorrectionRanges() {
const float kAliasingFreqHz =
kSpeedOfSoundMeterSeconds /
(min_mic_spacing_ * (1.f + std::abs(std::cos(target_angle_radians_))));
const float kHighMeanStartHz = std::min(0.5f * kAliasingFreqHz,
sample_rate_hz_ / 2.f);
const float kHighMeanEndHz = std::min(0.75f * kAliasingFreqHz,
sample_rate_hz_ / 2.f);
high_mean_start_bin_ = Round(kHighMeanStartHz * kFftSize / sample_rate_hz_);
high_mean_end_bin_ = Round(kHighMeanEndHz * kFftSize / sample_rate_hz_);
RTC_DCHECK_LT(low_mean_end_bin_, high_mean_end_bin_);
RTC_DCHECK_LT(high_mean_start_bin_, high_mean_end_bin_);
RTC_DCHECK_LT(high_mean_end_bin_, kNumFreqBins - 1);
}
void NonlinearBeamformer::InitInterfAngles() {
interf_angles_radians_.clear();
const Point target_direction = AzimuthToPoint(target_angle_radians_);
const Point clockwise_interf_direction =
AzimuthToPoint(target_angle_radians_ - away_radians_);
if (!array_normal_ ||
DotProduct(*array_normal_, target_direction) *
DotProduct(*array_normal_, clockwise_interf_direction) >=
0.f) {
// The target and clockwise interferer are in the same half-plane defined
// by the array.
interf_angles_radians_.push_back(target_angle_radians_ - away_radians_);
} else {
// Otherwise, the interferer will begin reflecting back at the target.
// Instead rotate it away 180 degrees.
interf_angles_radians_.push_back(target_angle_radians_ - away_radians_ +
M_PI);
}
const Point counterclock_interf_direction =
AzimuthToPoint(target_angle_radians_ + away_radians_);
if (!array_normal_ ||
DotProduct(*array_normal_, target_direction) *
DotProduct(*array_normal_, counterclock_interf_direction) >=
0.f) {
// The target and counter-clockwise interferer are in the same half-plane
// defined by the array.
interf_angles_radians_.push_back(target_angle_radians_ + away_radians_);
} else {
// Otherwise, the interferer will begin reflecting back at the target.
// Instead rotate it away 180 degrees.
interf_angles_radians_.push_back(target_angle_radians_ + away_radians_ -
M_PI);
}
}
void NonlinearBeamformer::InitDelaySumMasks() {
for (size_t f_ix = 0; f_ix < kNumFreqBins; ++f_ix) {
delay_sum_masks_[f_ix].Resize(1, num_input_channels_);
CovarianceMatrixGenerator::PhaseAlignmentMasks(
f_ix, kFftSize, sample_rate_hz_, kSpeedOfSoundMeterSeconds,
array_geometry_, target_angle_radians_, &delay_sum_masks_[f_ix]);
complex_f norm_factor = sqrt(
ConjugateDotProduct(delay_sum_masks_[f_ix], delay_sum_masks_[f_ix]));
delay_sum_masks_[f_ix].Scale(1.f / norm_factor);
}
}
void NonlinearBeamformer::InitTargetCovMats() {
for (size_t i = 0; i < kNumFreqBins; ++i) {
target_cov_mats_[i].Resize(num_input_channels_, num_input_channels_);
TransposedConjugatedProduct(delay_sum_masks_[i], &target_cov_mats_[i]);
}
}
void NonlinearBeamformer::InitDiffuseCovMats() {
for (size_t i = 0; i < kNumFreqBins; ++i) {
uniform_cov_mat_[i].Resize(num_input_channels_, num_input_channels_);
CovarianceMatrixGenerator::UniformCovarianceMatrix(
wave_numbers_[i], array_geometry_, &uniform_cov_mat_[i]);
complex_f normalization_factor = uniform_cov_mat_[i].elements()[0][0];
uniform_cov_mat_[i].Scale(1.f / normalization_factor);
uniform_cov_mat_[i].Scale(1 - kBalance);
}
}
void NonlinearBeamformer::InitInterfCovMats() {
for (size_t i = 0; i < kNumFreqBins; ++i) {
interf_cov_mats_[i].clear();
for (size_t j = 0; j < interf_angles_radians_.size(); ++j) {
interf_cov_mats_[i].push_back(std::unique_ptr<ComplexMatrixF>(
new ComplexMatrixF(num_input_channels_, num_input_channels_)));
ComplexMatrixF angled_cov_mat(num_input_channels_, num_input_channels_);
CovarianceMatrixGenerator::AngledCovarianceMatrix(
kSpeedOfSoundMeterSeconds,
interf_angles_radians_[j],
i,
kFftSize,
kNumFreqBins,
sample_rate_hz_,
array_geometry_,
&angled_cov_mat);
// Normalize matrices before averaging them.
complex_f normalization_factor = angled_cov_mat.elements()[0][0];
angled_cov_mat.Scale(1.f / normalization_factor);
// Weighted average of matrices.
angled_cov_mat.Scale(kBalance);
interf_cov_mats_[i][j]->Add(uniform_cov_mat_[i], angled_cov_mat);
}
}
}
void NonlinearBeamformer::NormalizeCovMats() {
for (size_t i = 0; i < kNumFreqBins; ++i) {
rxiws_[i] = Norm(target_cov_mats_[i], delay_sum_masks_[i]);
rpsiws_[i].clear();
for (size_t j = 0; j < interf_angles_radians_.size(); ++j) {
rpsiws_[i].push_back(Norm(*interf_cov_mats_[i][j], delay_sum_masks_[i]));
}
}
}
void NonlinearBeamformer::AnalyzeChunk(const ChannelBuffer<float>& data) {
RTC_DCHECK_EQ(data.num_channels(), num_input_channels_);
RTC_DCHECK_EQ(data.num_frames_per_band(), chunk_length_);
old_high_pass_mask_ = high_pass_postfilter_mask_;
process_transform_->ProcessChunk(data.channels(0), nullptr);
}
void NonlinearBeamformer::PostFilter(ChannelBuffer<float>* data) {
RTC_DCHECK_EQ(data->num_frames_per_band(), chunk_length_);
// TODO(aluebs): Change to RTC_CHECK_EQ once the ChannelBuffer is updated.
RTC_DCHECK_GE(data->num_channels(), num_postfilter_channels_);
postfilter_transform_->ProcessChunk(data->channels(0), final_mask_);
// Ramp up/down for smoothing is needed in order to avoid discontinuities in
// the transitions between 10 ms frames.
const float ramp_increment =
(high_pass_postfilter_mask_ - old_high_pass_mask_) /
data->num_frames_per_band();
for (size_t i = 1; i < data->num_bands(); ++i) {
float smoothed_mask = old_high_pass_mask_;
for (size_t j = 0; j < data->num_frames_per_band(); ++j) {
smoothed_mask += ramp_increment;
for (size_t k = 0; k < num_postfilter_channels_; ++k) {
data->channels(i)[k][j] *= smoothed_mask;
}
}
}
}
void NonlinearBeamformer::AimAt(const SphericalPointf& target_direction) {
target_angle_radians_ = target_direction.azimuth();
InitHighFrequencyCorrectionRanges();
InitInterfAngles();
InitDelaySumMasks();
InitTargetCovMats();
InitInterfCovMats();
NormalizeCovMats();
}
bool NonlinearBeamformer::IsInBeam(const SphericalPointf& spherical_point) {
// If more than half-beamwidth degrees away from the beam's center,
// you are out of the beam.
return fabs(spherical_point.azimuth() - target_angle_radians_) <
kHalfBeamWidthRadians;
}
bool NonlinearBeamformer::is_target_present() { return is_target_present_; }
void NonlinearBeamformer::ProcessAudioBlock(const complex_f* const* input,
size_t num_input_channels,
size_t num_freq_bins,
size_t num_output_channels,
complex_f* const* output) {
RTC_CHECK_EQ(kNumFreqBins, num_freq_bins);
RTC_CHECK_EQ(num_input_channels_, num_input_channels);
RTC_CHECK_EQ(0, num_output_channels);
// Calculating the post-filter masks. Note that we need two for each
// frequency bin to account for the positive and negative interferer
// angle.
for (size_t i = low_mean_start_bin_; i <= high_mean_end_bin_; ++i) {
eig_m_.CopyFromColumn(input, i, num_input_channels_);
float eig_m_norm_factor = std::sqrt(SumSquares(eig_m_));
if (eig_m_norm_factor != 0.f) {
eig_m_.Scale(1.f / eig_m_norm_factor);
}
float rxim = Norm(target_cov_mats_[i], eig_m_);
float ratio_rxiw_rxim = 0.f;
if (rxim > 0.f) {
ratio_rxiw_rxim = rxiws_[i] / rxim;
}
complex_f rmw = abs(ConjugateDotProduct(delay_sum_masks_[i], eig_m_));
rmw *= rmw;
float rmw_r = rmw.real();
new_mask_[i] = CalculatePostfilterMask(*interf_cov_mats_[i][0],
rpsiws_[i][0],
ratio_rxiw_rxim,
rmw_r);
for (size_t j = 1; j < interf_angles_radians_.size(); ++j) {
float tmp_mask = CalculatePostfilterMask(*interf_cov_mats_[i][j],
rpsiws_[i][j],
ratio_rxiw_rxim,
rmw_r);
if (tmp_mask < new_mask_[i]) {
new_mask_[i] = tmp_mask;
}
}
}
ApplyMaskTimeSmoothing();
EstimateTargetPresence();
ApplyLowFrequencyCorrection();
ApplyHighFrequencyCorrection();
ApplyMaskFrequencySmoothing();
}
float NonlinearBeamformer::CalculatePostfilterMask(
const ComplexMatrixF& interf_cov_mat,
float rpsiw,
float ratio_rxiw_rxim,
float rmw_r) {
float rpsim = Norm(interf_cov_mat, eig_m_);
float ratio = 0.f;
if (rpsim > 0.f) {
ratio = rpsiw / rpsim;
}
float numerator = 1.f - kCutOffConstant;
if (rmw_r > 0.f) {
numerator = 1.f - std::min(kCutOffConstant, ratio / rmw_r);
}
float denominator = 1.f - kCutOffConstant;
if (ratio_rxiw_rxim > 0.f) {
denominator = 1.f - std::min(kCutOffConstant, ratio / ratio_rxiw_rxim);
}
return numerator / denominator;
}
// Smooth new_mask_ into time_smooth_mask_.
void NonlinearBeamformer::ApplyMaskTimeSmoothing() {
for (size_t i = low_mean_start_bin_; i <= high_mean_end_bin_; ++i) {
time_smooth_mask_[i] = kMaskTimeSmoothAlpha * new_mask_[i] +
(1 - kMaskTimeSmoothAlpha) * time_smooth_mask_[i];
}
}
// Copy time_smooth_mask_ to final_mask_ and smooth over frequency.
void NonlinearBeamformer::ApplyMaskFrequencySmoothing() {
// Smooth over frequency in both directions. The "frequency correction"
// regions have constant value, but we enter them to smooth over the jump
// that exists at the boundary. However, this does mean when smoothing "away"
// from the region that we only need to use the last element.
//
// Upward smoothing:
// low_mean_start_bin_
// v
// |------|------------|------|
// ^------------------>^
//
// Downward smoothing:
// high_mean_end_bin_
// v
// |------|------------|------|
// ^<------------------^
std::copy(time_smooth_mask_, time_smooth_mask_ + kNumFreqBins, final_mask_);
for (size_t i = low_mean_start_bin_; i < kNumFreqBins; ++i) {
final_mask_[i] = kMaskFrequencySmoothAlpha * final_mask_[i] +
(1 - kMaskFrequencySmoothAlpha) * final_mask_[i - 1];
}
for (size_t i = high_mean_end_bin_ + 1; i > 0; --i) {
final_mask_[i - 1] = kMaskFrequencySmoothAlpha * final_mask_[i - 1] +
(1 - kMaskFrequencySmoothAlpha) * final_mask_[i];
}
}
// Apply low frequency correction to time_smooth_mask_.
void NonlinearBeamformer::ApplyLowFrequencyCorrection() {
const float low_frequency_mask =
MaskRangeMean(low_mean_start_bin_, low_mean_end_bin_ + 1);
std::fill(time_smooth_mask_, time_smooth_mask_ + low_mean_start_bin_,
low_frequency_mask);
}
// Apply high frequency correction to time_smooth_mask_. Update
// high_pass_postfilter_mask_ to use for the high frequency time-domain bands.
void NonlinearBeamformer::ApplyHighFrequencyCorrection() {
high_pass_postfilter_mask_ =
MaskRangeMean(high_mean_start_bin_, high_mean_end_bin_ + 1);
std::fill(time_smooth_mask_ + high_mean_end_bin_ + 1,
time_smooth_mask_ + kNumFreqBins, high_pass_postfilter_mask_);
}
// Compute mean over the given range of time_smooth_mask_, [first, last).
float NonlinearBeamformer::MaskRangeMean(size_t first, size_t last) {
RTC_DCHECK_GT(last, first);
const float sum = std::accumulate(time_smooth_mask_ + first,
time_smooth_mask_ + last, 0.f);
return sum / (last - first);
}
void NonlinearBeamformer::EstimateTargetPresence() {
const size_t quantile = static_cast<size_t>(
(high_mean_end_bin_ - low_mean_start_bin_) * kMaskQuantile +
low_mean_start_bin_);
std::nth_element(new_mask_ + low_mean_start_bin_, new_mask_ + quantile,
new_mask_ + high_mean_end_bin_ + 1);
if (new_mask_[quantile] > kMaskTargetThreshold) {
is_target_present_ = true;
interference_blocks_count_ = 0;
} else {
is_target_present_ = interference_blocks_count_++ < hold_target_blocks_;
}
}
} // namespace webrtc