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Audaspace: faster audio resampling #116059

Merged
Aras Pranckevicius merged 2 commits from aras_p/blender:audaspace-resampler-opt into main 2024-01-03 21:23:34 +01:00
Conversation 4 Commits 2 Files Changed 8 +3001 -173
8 changed files with 3001 additions and 173 deletions
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4
extern/audaspace/CMakeLists.txt vendored
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@ -108,7 +108,9 @@ set(SRC
src/respec/ConverterFunctions.cpp
src/respec/ConverterReader.cpp
src/respec/JOSResample.cpp
src/respec/JOSResampleReaderCoeff.cpp
src/respec/JOSResampleReaderCoeffHigh.cpp
src/respec/JOSResampleReaderCoeffLow.cpp
src/respec/JOSResampleReaderCoeffMedium.cpp
src/respec/JOSResampleReader.cpp
src/respec/LinearResample.cpp
src/respec/LinearResampleReader.cpp

6
extern/audaspace/README.blender vendored
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@ -1,5 +1,5 @@
Project: Audaspace
URL: https://audaspace.github.io/
URL: https://github.com/audaspace/audaspace
License: Apache 2.0
Upstream version: 1.3 (Last Release)
Local modifications: None
Upstream version: 1.4+ (0d18fe7, 2024 Jan 2)
Local modifications: JOSResampleReader default quality set to MEDIUM

57
extern/audaspace/include/respec/JOSResampleReader.h vendored
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@ -35,20 +35,57 @@ class AUD_API JOSResampleReader : public ResampleReader
private:
typedef void (JOSResampleReader::*resample_f)(double target_factor, int length, sample_t* buffer);
/**
* The half filter length for Quality::HIGH setting.
*/
static const int m_len_high;
/**
* The half filter length for Quality::MEDIUM setting.
*/
static const int m_len_medium;
/**
* The half filter length for Quality::LOW setting.
*/
static const int m_len_low;
/**
* The filter sample step size for Quality::HIGH setting.
*/
static const int m_L_high;
/**
* The filter sample step size for Quality::MEDIUM setting.
*/
static const int m_L_medium;
/**
* The filter sample step size for Quality::LOW setting.
*/
static const int m_L_low;
/**
* The filter coefficients for Quality::HIGH setting.
*/
static const float m_coeff_high[];
/**
* The filter coefficients for Quality::MEDIUM setting.
*/
static const float m_coeff_medium[];
/**
* The filter coefficients for Quality::LOW setting.
*/
static const float m_coeff_low[];
/**
* The half filter length.
*/
static const int m_len;
int m_len;
/**
* The sample step size for the filter.
*/
static const int m_L;
int m_L;
/**
* The filter coefficients.
*/
static const float m_coeff[];
const float* m_coeff;
/**
* The reader channels.
@ -107,17 +144,27 @@ private:
*/
void AUD_LOCAL updateBuffer(int size, double factor, int samplesize);
void AUD_LOCAL resample(double target_factor, int length, sample_t* buffer);
void AUD_LOCAL resample_generic(double target_factor, int length, sample_t* buffer);
void AUD_LOCAL resample_mono(double target_factor, int length, sample_t* buffer);
void AUD_LOCAL resample_stereo(double target_factor, int length, sample_t* buffer);
template <typename T>
void AUD_LOCAL resample(double target_factor, int length, sample_t* buffer);
public:
enum class Quality
{
LOW = 0,
MEDIUM,
HIGH,
};
/**
* Creates a resampling reader.
* \param reader The reader to mix.
* \param rate The target sampling rate.
*/
JOSResampleReader(std::shared_ptr<IReader> reader, SampleRate rate);
JOSResampleReader(std::shared_ptr<IReader> reader, SampleRate rate, Quality = Quality::MEDIUM);
virtual void seek(int position);
virtual int getLength() const;

385
extern/audaspace/src/respec/JOSResampleReader.cpp vendored
View File

@ -20,9 +20,23 @@
#include <cmath>
#include <cstring>
#if defined(__x86_64__) || defined(_M_X64) || defined(__SSE2__)
#include <immintrin.h>
static inline int lrint_impl(double x)
{
return _mm_cvtsd_si32(_mm_load_sd(&x));
}
#else
static inline int lrint_impl(double x)
{
return lrint(x);
}
#endif
#define RATE_MAX 256
#define SHIFT_BITS 12
#define double_to_fp(x) (lrint(x * double(1 << SHIFT_BITS)))
#define double_to_fp(x) (lrint_impl(x * double(1 << SHIFT_BITS)))
#define int_to_fp(x) (x << SHIFT_BITS)
#define fp_to_int(x) (x >> SHIFT_BITS)
#define fp_to_double(x) (x * 1.0/(1 << SHIFT_BITS))
@ -31,7 +45,7 @@
AUD_NAMESPACE_BEGIN
JOSResampleReader::JOSResampleReader(std::shared_ptr<IReader> reader, SampleRate rate) :
JOSResampleReader::JOSResampleReader(std::shared_ptr<IReader> reader, SampleRate rate, Quality quality) :
ResampleReader(reader, rate),
m_channels(CHANNELS_INVALID),
m_n(0),
@ -39,6 +53,28 @@ JOSResampleReader::JOSResampleReader(std::shared_ptr<IReader> reader, SampleRate
m_cache_valid(0),
m_last_factor(0)
{
switch(quality)
{
case Quality::LOW:
m_len = m_len_low;
m_L = m_L_low;
m_coeff = m_coeff_low;
break;
case Quality::MEDIUM:
m_len = m_len_medium;
m_L = m_L_medium;
m_coeff = m_coeff_medium;
break;
case Quality::HIGH:
m_len = m_len_high;
m_L = m_L_high;
m_coeff = m_coeff_high;
break;
default:
m_len = m_len_low;
m_L = m_L_low;
m_coeff = m_coeff_low;
}
}
void JOSResampleReader::reset()
@ -75,168 +111,195 @@ void JOSResampleReader::updateBuffer(int size, double factor, int samplesize)
m_buffer.assureSize((m_cache_valid + size) * samplesize, true);
}
#define RESAMPLE_METHOD(name, left, right) void JOSResampleReader::name(double target_factor, int length, sample_t* buffer)\
{\
sample_t* buf = m_buffer.getBuffer();\
\
unsigned int P, l;\
int end, channel, i;\
double eta, v, f_increment, factor;\
\
m_sums.assureSize(m_channels * sizeof(double));\
double* sums = reinterpret_cast<double*>(m_sums.getBuffer());\
sample_t* data;\
const float* coeff = m_coeff;\
\
unsigned int P_increment;\
\
for(unsigned int t = 0; t < length; t++)\
{\
factor = (m_last_factor * (length - t - 1) + target_factor * (t + 1)) / length;\
\
std::memset(sums, 0, sizeof(double) * m_channels);\
\
if(factor >= 1)\
{\
P = double_to_fp(m_P * m_L);\
\
end = std::floor(m_len / double(m_L) - m_P) - 1;\
if(m_n < end)\
end = m_n;\
\
data = buf + (m_n - end) * m_channels;\
l = fp_to_int(P);\
eta = fp_rest_to_double(P);\
l += m_L * end;\
\
for(i = 0; i <= end; i++)\
{\
v = coeff[l] + eta * (coeff[l+1] - coeff[l]);\
l -= m_L;\
left\
}\
\
P = int_to_fp(m_L) - P;\
\
end = std::floor((m_len - 1) / double(m_L) + m_P) - 1;\
if(m_cache_valid - int(m_n) - 2 < end)\
end = m_cache_valid - int(m_n) - 2;\
\
data = buf + (m_n + 2 + end) * m_channels - 1;\
l = fp_to_int(P);\
eta = fp_rest_to_double(P);\
l += m_L * end;\
\
for(i = 0; i <= end; i++)\
{\
v = coeff[l] + eta * (coeff[l+1] - coeff[l]);\
l -= m_L;\
right\
}\
\
for(channel = 0; channel < m_channels; channel++)\
{\
*buffer = sums[channel];\
buffer++;\
}\
}\
else\
{\
f_increment = factor * m_L;\
P_increment = double_to_fp(f_increment);\
P = double_to_fp(m_P * f_increment);\
\
end = (int_to_fp(m_len) - P) / P_increment - 1;\
if(m_n < end)\
end = m_n;\
\
P += P_increment * end;\
data = buf + (m_n - end) * m_channels;\
l = fp_to_int(P);\
\
for(i = 0; i <= end; i++)\
{\
eta = fp_rest_to_double(P);\
v = coeff[l] + eta * (coeff[l+1] - coeff[l]);\
P -= P_increment;\
l = fp_to_int(P);\
left\
}\
\
P = 0 - P;\
\
end = (int_to_fp(m_len) - P) / P_increment - 1;\
if(m_cache_valid - int(m_n) - 2 < end)\
end = m_cache_valid - int(m_n) - 2;\
\
P += P_increment * end;\
data = buf + (m_n + 2 + end) * m_channels - 1;\
l = fp_to_int(P);\
\
for(i = 0; i <= end; i++)\
{\
eta = fp_rest_to_double(P);\
v = coeff[l] + eta * (coeff[l+1] - coeff[l]);\
P -= P_increment;\
l = fp_to_int(P);\
right\
}\
\
for(channel = 0; channel < m_channels; channel++)\
{\
*buffer = factor * sums[channel];\
buffer++;\
}\
}\
\
m_P += std::fmod(1.0 / factor, 1.0);\
m_n += std::floor(1.0 / factor);\
\
while(m_P >= 1.0)\
{\
m_P -= 1.0;\
m_n++;\
}\
}\
template<typename T>
void JOSResampleReader::resample(double target_factor, int length, sample_t* buffer)
{
const sample_t* buf = m_buffer.getBuffer();
unsigned int P, l;
int end, i;
double eta, v, f_increment, factor;
m_sums.assureSize(m_channels * sizeof(double));
double* sums = reinterpret_cast<double*>(m_sums.getBuffer());
const sample_t* data;
const float* coeff = m_coeff;
unsigned int P_increment;
for(unsigned int t = 0; t < length; t++)
{
factor = (m_last_factor * (length - t - 1) + target_factor * (t + 1)) / length;
std::memset(sums, 0, sizeof(double) * m_channels);
if(factor >= 1)
{
P = double_to_fp(m_P * m_L);
end = std::floor(m_len / double(m_L) - m_P) - 1;
if(m_n < end)
end = m_n;
data = buf + (m_n - end) * m_channels;
l = fp_to_int(P);
eta = fp_rest_to_double(P);
l += m_L * end;
for(i = 0; i <= end; i++)
{
v = coeff[l] + eta * (coeff[l+1] - coeff[l]);
l -= m_L;
T::left(m_channels, sums, data, v);
}
P = int_to_fp(m_L) - P;
end = std::floor((m_len - 1) / double(m_L) + m_P) - 1;
if(m_cache_valid - int(m_n) - 2 < end)
end = m_cache_valid - int(m_n) - 2;
data = buf + (m_n + 2 + end) * m_channels - 1;
l = fp_to_int(P);
eta = fp_rest_to_double(P);
l += m_L * end;
for(i = 0; i <= end; i++)
{
v = coeff[l] + eta * (coeff[l+1] - coeff[l]);
l -= m_L;
T::right(m_channels, sums, data, v);
}
for(int channel = 0; channel < m_channels; channel++)
{
*buffer = sums[channel];
buffer++;
}
}
else
{
f_increment = factor * m_L;
P_increment = double_to_fp(f_increment);
P = double_to_fp(m_P * f_increment);
end = (int_to_fp(m_len) - P) / P_increment - 1;
if(m_n < end)
end = m_n;
P += P_increment * end;
data = buf + (m_n - end) * m_channels;
l = fp_to_int(P);
for(i = 0; i <= end; i++)
{
eta = fp_rest_to_double(P);
v = coeff[l] + eta * (coeff[l+1] - coeff[l]);
P -= P_increment;
l = fp_to_int(P);
T::left(m_channels, sums, data, v);
}
P = 0 - P;
end = (int_to_fp(m_len) - P) / P_increment - 1;
if(m_cache_valid - int(m_n) - 2 < end)
end = m_cache_valid - int(m_n) - 2;
P += P_increment * end;
data = buf + (m_n + 2 + end) * m_channels - 1;
l = fp_to_int(P);
for(i = 0; i <= end; i++)
{
eta = fp_rest_to_double(P);
v = coeff[l] + eta * (coeff[l+1] - coeff[l]);
P -= P_increment;
l = fp_to_int(P);
T::right(m_channels, sums, data, v);
}
for(int channel = 0; channel < m_channels; channel++)
{
*buffer = factor * sums[channel];
buffer++;
}
}
m_P += std::fmod(1.0 / factor, 1.0);
m_n += std::floor(1.0 / factor);
while(m_P >= 1.0)
{
m_P -= 1.0;
m_n++;
}
}
}
RESAMPLE_METHOD(resample, {
channel = 0;
do
{
sums[channel] += *data * v;
channel++;
data++;
}
while(channel < m_channels);
}, {
channel = m_channels;
do
{
channel--;
sums[channel] += *data * v;
data--;
}
while(channel);
})
RESAMPLE_METHOD(resample_mono, {
*sums += *data * v;
void JOSResampleReader::resample_generic(double target_factor, int length, sample_t* buffer)
{
struct OpGeneric
{
static void left(int channel_count, double *sums, const sample_t*& data, double v)
{
int channel = 0;
do
{
sums[channel] += *data * v;
channel++;
data++;
}, {
*sums += *data * v;
} while(channel < channel_count);
}
static void right(int channel_count, double* sums, const sample_t*& data, double v)
{
int channel = channel_count;
do
{
channel--;
sums[channel] += *data * v;
data--;
})
RESAMPLE_METHOD(resample_stereo, {
sums[0] += data[0] * v;
sums[1] += data[1] * v;
data+=2;
}, {
data-=2;
sums[0] += data[1] * v;
sums[1] += data[2] * v;
})
} while(channel);
}
};
resample<OpGeneric>(target_factor, length, buffer);
}
void JOSResampleReader::resample_mono(double target_factor, int length, sample_t* buffer)
{
struct OpMono
{
static void left(int channel_count, double* sums, const sample_t*& data, double v)
{
*sums += *data * v;
data++;
}
static void right(int channel_count, double* sums, const sample_t*& data, double v)
{
*sums += *data * v;
data--;
}
};
resample<OpMono>(target_factor, length, buffer);
}
void JOSResampleReader::resample_stereo(double target_factor, int length, sample_t* buffer)
{
struct OpStereo
{
static void left(int channel_count, double* sums, const sample_t*& data, double v)
{
sums[0] += data[0] * v;
sums[1] += data[1] * v;
data += 2;
}
static void right(int channel_count, double* sums, const sample_t*& data, double v)
{
data -= 2;
sums[0] += data[1] * v;
sums[1] += data[2] * v;
}
};
resample<OpStereo>(target_factor, length, buffer);
}
void JOSResampleReader::seek(int position)
{
@ -290,7 +353,7 @@ void JOSResampleReader::read(int& length, bool& eos, sample_t* buffer)
m_resample = &JOSResampleReader::resample_stereo;
break;
default:
m_resample = &JOSResampleReader::resample;
m_resample = &JOSResampleReader::resample_generic;
break;
}
}

6
extern/audaspace/src/respec/JOSResampleReaderCoeff.cpp → extern/audaspace/src/respec/JOSResampleReaderCoeffHigh.cpp vendored
View File

@ -20,10 +20,10 @@
AUD_NAMESPACE_BEGIN
const int JOSResampleReader::m_len = 325078;
const int JOSResampleReader::m_L = 2304;
const int JOSResampleReader::m_len_high = 325078;
const int JOSResampleReader::m_L_high = 2304;
const float JOSResampleReader::m_coeff[] = {
const float JOSResampleReader::m_coeff_high[m_len_high + 1] = {
9.639035268e-01f, 9.639032492e-01f, 9.639024165e-01f, 9.639010286e-01f, 9.638990855e-01f, 9.638965872e-01f, 9.638935338e-01f, 9.638899253e-01f, 9.638857615e-01f, 9.638810427e-01f,
9.638757686e-01f, 9.638699395e-01f, 9.638635552e-01f, 9.638566158e-01f, 9.638491212e-01f, 9.638410716e-01f, 9.638324668e-01f, 9.638233070e-01f, 9.638135921e-01f, 9.638033220e-01f,
9.637924970e-01f, 9.637811168e-01f, 9.637691817e-01f, 9.637566915e-01f, 9.637436463e-01f, 9.637300461e-01f, 9.637158908e-01f, 9.637011807e-01f, 9.636859155e-01f, 9.636700955e-01f,

275
extern/audaspace/src/respec/JOSResampleReaderCoeffLow.cpp vendored Normal file
View File

@ -0,0 +1,275 @@
/*******************************************************************************
* Copyright 2009-2023 Jörg Müller
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
******************************************************************************/
#include "respec/JOSResampleReader.h"
// sinc filter coefficients, Nz = 16, L = 128, freq = 0.834068, Kaiser Window B = 10
AUD_NAMESPACE_BEGIN
const int JOSResampleReader::m_len_low = 2455;
const int JOSResampleReader::m_L_low = 128;
const float JOSResampleReader::m_coeff_low[m_len_low + 1] = {
8.340675360e-01f, 8.340086260e-01f, 8.338319113e-01f, 8.335374374e-01f, 8.331252804e-01f, 8.325955465e-01f, 8.319483724e-01f, 8.311839250e-01f, 8.303024016e-01f, 8.293040294e-01f,
8.281890659e-01f, 8.269577985e-01f, 8.256105446e-01f, 8.241476514e-01f, 8.225694958e-01f, 8.208764844e-01f, 8.190690531e-01f, 8.171476673e-01f, 8.151128215e-01f, 8.129650394e-01f,
8.107048733e-01f, 8.083329044e-01f, 8.058497425e-01f, 8.032560255e-01f, 8.005524197e-01f, 7.977396190e-01f, 7.948183455e-01f, 7.917893483e-01f, 7.886534040e-01f, 7.854113162e-01f,
7.820639153e-01f, 7.786120581e-01f, 7.750566278e-01f, 7.713985334e-01f, 7.676387098e-01f, 7.637781170e-01f, 7.598177404e-01f, 7.557585901e-01f, 7.516017006e-01f, 7.473481306e-01f,
7.429989628e-01f, 7.385553031e-01f, 7.340182809e-01f, 7.293890482e-01f, 7.246687795e-01f, 7.198586714e-01f, 7.149599422e-01f, 7.099738317e-01f, 7.049016004e-01f, 6.997445297e-01f,
6.945039210e-01f, 6.891810954e-01f, 6.837773936e-01f, 6.782941751e-01f, 6.727328182e-01f, 6.670947189e-01f, 6.613812914e-01f, 6.555939668e-01f, 6.497341931e-01f, 6.438034349e-01f,
6.378031726e-01f, 6.317349019e-01f, 6.256001340e-01f, 6.194003941e-01f, 6.131372220e-01f, 6.068121709e-01f, 6.004268072e-01f, 5.939827100e-01f, 5.874814706e-01f, 5.809246921e-01f,
5.743139887e-01f, 5.676509855e-01f, 5.609373179e-01f, 5.541746308e-01f, 5.473645787e-01f, 5.405088246e-01f, 5.336090401e-01f, 5.266669041e-01f, 5.196841033e-01f, 5.126623308e-01f,
5.056032861e-01f, 4.985086742e-01f, 4.913802058e-01f, 4.842195959e-01f, 4.770285640e-01f, 4.698088330e-01f, 4.625621292e-01f, 4.552901816e-01f, 4.479947212e-01f, 4.406774808e-01f,
4.333401942e-01f, 4.259845960e-01f, 4.186124207e-01f, 4.112254026e-01f, 4.038252749e-01f, 3.964137695e-01f, 3.889926163e-01f, 3.815635430e-01f, 3.741282740e-01f, 3.666885305e-01f,
3.592460298e-01f, 3.518024845e-01f, 3.443596025e-01f, 3.369190863e-01f, 3.294826322e-01f, 3.220519305e-01f, 3.146286642e-01f, 3.072145092e-01f, 2.998111334e-01f, 2.924201965e-01f,
2.850433492e-01f, 2.776822332e-01f, 2.703384802e-01f, 2.630137118e-01f, 2.557095391e-01f, 2.484275618e-01f, 2.411693682e-01f, 2.339365347e-01f, 2.267306252e-01f, 2.195531905e-01f,
2.124057684e-01f, 2.052898829e-01f, 1.982070438e-01f, 1.911587464e-01f, 1.841464709e-01f, 1.771716824e-01f, 1.702358299e-01f, 1.633403466e-01f, 1.564866489e-01f, 1.496761364e-01f,
1.429101914e-01f, 1.361901786e-01f, 1.295174446e-01f, 1.228933176e-01f, 1.163191072e-01f, 1.097961040e-01f, 1.033255791e-01f, 9.690878384e-02f, 9.054694972e-02f, 8.424128778e-02f,
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1.891150820e-02f, 1.336658241e-02f, 7.891594418e-03f, 2.487442186e-03f, -2.845000411e-03f, -8.104883769e-03f, -1.329138273e-02f, -1.840369674e-02f, -2.344105004e-02f, -2.840269178e-02f,
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};
AUD_NAMESPACE_END

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extern/audaspace/src/respec/JOSResampleReaderCoeffMedium.cpp vendored Normal file
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extern/audaspace/src/respec/filter_design.py vendored Normal file
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@ -0,0 +1,121 @@
#!/usr/bin/python
################################################################################
# Copyright 2009-2023 Jörg Müller
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
################################################################################
# high quality: sinc filter coefficients, Nz = 136, L = 2304, freq = 0.963904, Kaiser Window B = 16
# medium quality: sinc filter coefficients, Nz = 42, L = 500, freq = 0.916636, Kaiser Window B = 12
# low quality: sinc filter coefficients, Nz = 16, L = 128, freq = 0.834068, Kaiser Window B = 10
import numpy as np
import scipy
L = 2304
Nz = 136
B = 16
freq = Nz / (Nz + B / np.pi)
print(f'// sinc filter coefficients, Nz = {Nz}, L = {L}, freq = {freq:.6f}, Kaiser Window B = {B}')
Nz = Nz / freq
a = freq * np.sinc(freq * np.arange(0, Nz, 1/L))
M = len(a)*2-1
b = scipy.signal.windows.kaiser(M, B)
b = b[len(a)-1:]
y = a * b
# print filter coefficients from y
if False:
print(f'AUD_NAMESPACE_BEGIN')
print(f'const int JOSResampleReader::m_len_PRESET = {int(L*Nz)};')
print(f'const int JOSResampleReader::m_L_PRESET = {L};')
print(f'const float JOSResampleReader::m_coeff_PRESET[m_len_PRESET + 1] = {{')
for idx, val in enumerate(y):
print(f'{val:.9e}f', end=', ')
if (idx + 1) % 10 == 0:
print("\n", end='')
print(f'}};')
print(f'AUD_NAMESPACE_END')
# visualize filter
import matplotlib.pyplot as plt
mid = len(y)
res = np.concatenate([y[:0:-1], y])
f1 = L
f2 = 1
Fs1 = L
Fs2 = 2
area = mid - 1
t = (np.arange(1, area*2+1) - area) / (Fs1 * f2)
plt.figure()
plt.plot(t, res[mid - area:mid + area])
plt.xlim([t[0], t[-1]])
plt.ylim(np.array([np.min(res), np.max(res)]) * 1.05)
plt.xlabel('Time [s]')
plt.ylabel('Amplitude')
plt.title('Response')
fftres = np.fft.fft(res / f1)
f = np.arange(len(fftres)) * Fs2 * f1 / len(fftres)
plt.figure()
plt.plot(f, np.log10(np.abs(fftres))*20)
plt.xlim([0, Fs2])
plt.ylim([-200, 0])
plt.xlabel('Frequency [Hz]')
plt.ylabel('Magnitude [dB]')
plt.title('Magnitude')
plt.figure()
plt.plot(f, np.log10(np.abs(fftres)/np.abs(fftres[0]))*20)
plt.xlim(np.array([0, Fs2/2])*1.1)
plt.ylim([-3, 1.5])
plt.xlabel('Frequency [Hz]')
plt.ylabel('Magnitude [dB]')
plt.title('Passband')
plt.figure()
plt.plot(f, np.log10(np.abs(fftres)/np.abs(fftres[0]))*20)
plt.xlim(np.array([0.8, 1.1])*Fs2/2)
plt.ylim([-100, 6])
plt.xlabel('Frequency [Hz]')
plt.ylabel('Magnitude [dB]')
plt.title('Transition')
phi = np.angle(fftres);
phi -= (phi > np.pi / 2) * np.pi;
phi += (phi < -np.pi / 2) * np.pi;
plt.figure()
plt.plot(f, phi * 180 / np.pi)
plt.xlim([0, Fs2/2])
plt.ylim([-180, 180])
plt.xlabel('Frequency [Hz]')
plt.ylabel('Phase [deg]')
plt.title('Phase')
plt.show()