chromium/third_party/webrtc/common_audio/smoothing_filter.cc

/*
 *  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 <math.h>

#include <cmath>

#include "rtc_base/checks.h"
#include "rtc_base/time_utils.h"

namespace webrtc {

SmoothingFilterImpl::SmoothingFilterImpl(int init_time_ms)
    : … { … }

SmoothingFilterImpl::~SmoothingFilterImpl() = default;

void SmoothingFilterImpl::AddSample(float sample) { … }

absl::optional<float> SmoothingFilterImpl::GetAverage() { … }

bool SmoothingFilterImpl::SetTimeConstantMs(int time_constant_ms) { … }

void SmoothingFilterImpl::UpdateAlpha(int time_constant_ms) { … }

void SmoothingFilterImpl::ExtrapolateLastSample(int64_t 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}