1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
|
// Copyright 2016 The Chromium Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.
#include "IIRFilter.h"
#include "DenormalDisabler.h"
#include "mozilla/FloatingPoint.h"
#include <mozilla/Assertions.h>
#include <complex>
namespace blink {
// The length of the memory buffers for the IIR filter. This MUST be a power of
// two and must be greater than the possible length of the filter coefficients.
const int kBufferLength = 32;
static_assert(kBufferLength >= IIRFilter::kMaxOrder + 1,
"Internal IIR buffer length must be greater than maximum IIR "
"Filter order.");
IIRFilter::IIRFilter(const AudioDoubleArray* feedforwardCoef,
const AudioDoubleArray* feedbackCoef)
: m_bufferIndex(0),
m_feedback(feedbackCoef),
m_feedforward(feedforwardCoef) {
m_xBuffer.SetLength(kBufferLength);
m_yBuffer.SetLength(kBufferLength);
reset();
}
IIRFilter::~IIRFilter() = default;
void IIRFilter::reset() {
memset(m_xBuffer.Elements(), 0, m_xBuffer.Length() * sizeof(double));
memset(m_yBuffer.Elements(), 0, m_yBuffer.Length() * sizeof(double));
}
static std::complex<double> evaluatePolynomial(const double* coef,
std::complex<double> z,
int order) {
// Use Horner's method to evaluate the polynomial P(z) = sum(coef[k]*z^k, k,
// 0, order);
std::complex<double> result = 0;
for (int k = order; k >= 0; --k)
result = result * z + std::complex<double>(coef[k]);
return result;
}
void IIRFilter::process(const float* sourceP, float* destP,
size_t framesToProcess) {
// Compute
//
// y[n] = sum(b[k] * x[n - k], k = 0, M) - sum(a[k] * y[n - k], k = 1, N)
//
// where b[k] are the feedforward coefficients and a[k] are the feedback
// coefficients of the filter.
// This is a Direct Form I implementation of an IIR Filter. Should we
// consider doing a different implementation such as Transposed Direct Form
// II?
const double* feedback = m_feedback->Elements();
const double* feedforward = m_feedforward->Elements();
MOZ_ASSERT(feedback);
MOZ_ASSERT(feedforward);
// Sanity check to see if the feedback coefficients have been scaled
// appropriately. It must be EXACTLY 1!
MOZ_ASSERT(feedback[0] == 1);
int feedbackLength = m_feedback->Length();
int feedforwardLength = m_feedforward->Length();
int minLength = std::min(feedbackLength, feedforwardLength);
double* xBuffer = m_xBuffer.Elements();
double* yBuffer = m_yBuffer.Elements();
for (size_t n = 0; n < framesToProcess; ++n) {
// To help minimize roundoff, we compute using double's, even though the
// filter coefficients only have single precision values.
double yn = feedforward[0] * sourceP[n];
// Run both the feedforward and feedback terms together, when possible.
for (int k = 1; k < minLength; ++k) {
int n = (m_bufferIndex - k) & (kBufferLength - 1);
yn += feedforward[k] * xBuffer[n];
yn -= feedback[k] * yBuffer[n];
}
// Handle any remaining feedforward or feedback terms.
for (int k = minLength; k < feedforwardLength; ++k)
yn += feedforward[k] * xBuffer[(m_bufferIndex - k) & (kBufferLength - 1)];
for (int k = minLength; k < feedbackLength; ++k)
yn -= feedback[k] * yBuffer[(m_bufferIndex - k) & (kBufferLength - 1)];
// Save the current input and output values in the memory buffers for the
// next output.
m_xBuffer[m_bufferIndex] = sourceP[n];
m_yBuffer[m_bufferIndex] = yn;
m_bufferIndex = (m_bufferIndex + 1) & (kBufferLength - 1);
// Avoid introducing a stream of subnormals
destP[n] = WebCore::DenormalDisabler::flushDenormalFloatToZero(yn);
MOZ_ASSERT(destP[n] == 0.0 || std::fabs(destP[n]) > FLT_MIN ||
std::isnan(destP[n]),
"output should not be subnormal, but can be NaN");
}
}
void IIRFilter::getFrequencyResponse(int nFrequencies, const float* frequency,
float* magResponse, float* phaseResponse) {
// Evaluate the z-transform of the filter at the given normalized frequencies
// from 0 to 1. (One corresponds to the Nyquist frequency.)
//
// The z-tranform of the filter is
//
// H(z) = sum(b[k]*z^(-k), k, 0, M) / sum(a[k]*z^(-k), k, 0, N);
//
// The desired frequency response is H(exp(j*omega)), where omega is in
// [0, 1).
//
// Let P(x) = sum(c[k]*x^k, k, 0, P) be a polynomial of order P. Then each of
// the sums in H(z) is equivalent to evaluating a polynomial at the point 1/z.
for (int k = 0; k < nFrequencies; ++k) {
// zRecip = 1/z = exp(-j*frequency)
double omega = -M_PI * frequency[k];
std::complex<double> zRecip = std::complex<double>(cos(omega), sin(omega));
std::complex<double> numerator = evaluatePolynomial(
m_feedforward->Elements(), zRecip, m_feedforward->Length() - 1);
std::complex<double> denominator = evaluatePolynomial(
m_feedback->Elements(), zRecip, m_feedback->Length() - 1);
// Strangely enough, using complex division:
// e.g. Complex response = numerator / denominator;
// fails on our test machines, yielding infinities and NaNs, so we do
// things the long way here.
double n = norm(denominator);
double r = (real(numerator) * real(denominator) +
imag(numerator) * imag(denominator)) /
n;
double i = (imag(numerator) * real(denominator) -
real(numerator) * imag(denominator)) /
n;
std::complex<double> response = std::complex<double>(r, i);
magResponse[k] = static_cast<float>(abs(response));
phaseResponse[k] =
static_cast<float>(atan2(imag(response), real(response)));
}
}
bool IIRFilter::buffersAreZero() {
double* xBuffer = m_xBuffer.Elements();
double* yBuffer = m_yBuffer.Elements();
for (size_t k = 0; k < m_feedforward->Length(); ++k) {
if (xBuffer[(m_bufferIndex - k) & (kBufferLength - 1)] != 0.0) {
return false;
}
}
for (size_t k = 0; k < m_feedback->Length(); ++k) {
if (fabs(yBuffer[(m_bufferIndex - k) & (kBufferLength - 1)]) >= FLT_MIN) {
return false;
}
}
return true;
}
} // namespace blink
|
