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