146 lines
5.1 KiB
C++
146 lines
5.1 KiB
C++
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/*
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* Copyright (c) 2016 The WebRTC project authors. All Rights Reserved.
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*
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* Use of this source code is governed by a BSD-style license
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* that can be found in the LICENSE file in the root of the source
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* tree. An additional intellectual property rights grant can be found
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* in the file PATENTS. All contributing project authors may
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* be found in the AUTHORS file in the root of the source tree.
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*/
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#include "common_audio/smoothing_filter.h"
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#include <cmath>
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#include "rtc_base/checks.h"
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#include "rtc_base/timeutils.h"
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namespace webrtc {
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SmoothingFilterImpl::SmoothingFilterImpl(int init_time_ms)
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: init_time_ms_(init_time_ms),
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// Duing the initalization time, we use an increasing alpha. Specifically,
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// alpha(n) = exp(-powf(init_factor_, n)),
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// where |init_factor_| is chosen such that
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// alpha(init_time_ms_) = exp(-1.0f / init_time_ms_),
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init_factor_(init_time_ms_ == 0
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? 0.0f
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: powf(init_time_ms_, -1.0f / init_time_ms_)),
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// |init_const_| is to a factor to help the calculation during
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// initialization phase.
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init_const_(init_time_ms_ == 0
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? 0.0f
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: init_time_ms_ -
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powf(init_time_ms_, 1.0f - 1.0f / init_time_ms_)) {
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UpdateAlpha(init_time_ms_);
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}
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SmoothingFilterImpl::~SmoothingFilterImpl() = default;
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void SmoothingFilterImpl::AddSample(float sample) {
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const int64_t now_ms = rtc::TimeMillis();
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if (!init_end_time_ms_) {
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// This is equivalent to assuming the filter has been receiving the same
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// value as the first sample since time -infinity.
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state_ = last_sample_ = sample;
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init_end_time_ms_ = now_ms + init_time_ms_;
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last_state_time_ms_ = now_ms;
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return;
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}
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ExtrapolateLastSample(now_ms);
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last_sample_ = sample;
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}
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absl::optional<float> SmoothingFilterImpl::GetAverage() {
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if (!init_end_time_ms_) {
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// |init_end_time_ms_| undefined since we have not received any sample.
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return absl::nullopt;
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}
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ExtrapolateLastSample(rtc::TimeMillis());
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return state_;
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}
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bool SmoothingFilterImpl::SetTimeConstantMs(int time_constant_ms) {
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if (!init_end_time_ms_ || last_state_time_ms_ < *init_end_time_ms_) {
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return false;
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}
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UpdateAlpha(time_constant_ms);
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return true;
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}
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void SmoothingFilterImpl::UpdateAlpha(int time_constant_ms) {
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alpha_ = time_constant_ms == 0 ? 0.0f : exp(-1.0f / time_constant_ms);
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}
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void SmoothingFilterImpl::ExtrapolateLastSample(int64_t time_ms) {
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RTC_DCHECK_GE(time_ms, last_state_time_ms_);
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RTC_DCHECK(init_end_time_ms_);
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float multiplier = 0.0f;
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if (time_ms <= *init_end_time_ms_) {
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// Current update is to be made during initialization phase.
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// We update the state as if the |alpha| has been increased according
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// alpha(n) = exp(-powf(init_factor_, n)),
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// where n is the time (in millisecond) since the first sample received.
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// With algebraic derivation as shown in the Appendix, we can find that the
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// state can be updated in a similar manner as if alpha is a constant,
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// except for a different multiplier.
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if (init_time_ms_ == 0) {
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// This means |init_factor_| = 0.
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multiplier = 0.0f;
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} else if (init_time_ms_ == 1) {
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// This means |init_factor_| = 1.
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multiplier = exp(last_state_time_ms_ - time_ms);
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} else {
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multiplier =
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exp(-(powf(init_factor_, last_state_time_ms_ - *init_end_time_ms_) -
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powf(init_factor_, time_ms - *init_end_time_ms_)) /
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init_const_);
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}
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} else {
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if (last_state_time_ms_ < *init_end_time_ms_) {
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// The latest state update was made during initialization phase.
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// We first extrapolate to the initialization time.
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ExtrapolateLastSample(*init_end_time_ms_);
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// Then extrapolate the rest by the following.
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}
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multiplier = powf(alpha_, time_ms - last_state_time_ms_);
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}
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state_ = multiplier * state_ + (1.0f - multiplier) * last_sample_;
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last_state_time_ms_ = time_ms;
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}
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} // namespace webrtc
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// Appendix: derivation of extrapolation during initialization phase.
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// (LaTeX syntax)
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// Assuming
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// \begin{align}
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// y(n) &= \alpha_{n-1} y(n-1) + \left(1 - \alpha_{n-1}\right) x(m) \\*
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// &= \left(\prod_{i=m}^{n-1} \alpha_i\right) y(m) +
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// \left(1 - \prod_{i=m}^{n-1} \alpha_i \right) x(m)
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// \end{align}
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// Taking $\alpha_{n} = \exp(-\gamma^n)$, $\gamma$ denotes init\_factor\_, the
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// multiplier becomes
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// \begin{align}
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// \prod_{i=m}^{n-1} \alpha_i
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// &= \exp\left(-\sum_{i=m}^{n-1} \gamma^i \right) \\*
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// &= \begin{cases}
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// \exp\left(-\frac{\gamma^m - \gamma^n}{1 - \gamma} \right)
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// & \gamma \neq 1 \\*
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// m-n & \gamma = 1
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// \end{cases}
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// \end{align}
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// We know $\gamma = T^{-\frac{1}{T}}$, where $T$ denotes init\_time\_ms\_. Then
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// $1 - \gamma$ approaches zero when $T$ increases. This can cause numerical
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// difficulties. We multiply $T$ (if $T > 0$) to both numerator and denominator
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// in the fraction. See.
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// \begin{align}
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// \frac{\gamma^m - \gamma^n}{1 - \gamma}
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// &= \frac{T^\frac{T-m}{T} - T^\frac{T-n}{T}}{T - T^{1-\frac{1}{T}}}
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// \end{align}
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