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Add 12 ksps rate and correct block from receiveReadOnly_f32()

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master
boblark 2 years ago
parent f5d1c01a58
commit 7e6b762374
2 changed files with 166 additions and 122 deletions
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  1. 32
      analyze_CTCSS_F32.cpp
  2. 256
      analyze_CTCSS_F32.h

32
analyze_CTCSS_F32.cpp
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@ -38,9 +38,8 @@
void analyze_CTCSS_F32::update(void) {
audio_block_f32_t *block;
float gs0=0.0;
block = receiveReadOnly_f32();
float32_t gs0=0.0;
block = AudioStream_F32::receiveWritable_f32();
if (!block) return;
if (!gEnabled) {
release(block);
@ -48,8 +47,8 @@ void analyze_CTCSS_F32::update(void) {
}
// This process is working with frequencies of 254 Hz or less. Thus
// it is beneficial to decimate before processing. The chosen
// decimation rate is 16. For example, if the basic sample rate is 44.1 kHz,
// it is beneficial to decimate before processing. The decimation ratio
// is 16 or 8. For example, if the basic sample rate is 44.1 kHz,
// the decimated rate is 44100/16=2756.25 Hz Before decimation, we
// low pass filter to prevent alias problems. Returns 128 pts in block.
arm_biquad_cascade_df1_f32(&iir_lpf_inst, block->data,
@ -58,17 +57,18 @@ void analyze_CTCSS_F32::update(void) {
// And decimate, using the first sample, giving 128/16=8 samples to
// be processed per block.
// Create a small data block, normally 8, d16a[].
for(int i=0; i<8; i++)
d16a[i] = *(block->data + 16*i); // Decimated sample, only every 16
uint16_t nPerBlock2 = 128/nDecimate;
for(int i=0; i<nPerBlock2; i++)
d16a[i] = *(block->data + nDecimate*i); // Decimated sample, only every nDecimate
// Filter down to 67-254Hz band, leaving result in d16a[];
arm_biquad_cascade_df1_f32(&iir_bpf_inst, d16a, d16a, 8);
arm_biquad_cascade_df1_f32(&iir_bpf_inst, d16a, d16a, nPerBlock2);
// For reference measurement, only, null out the tone, creating d16b[].
// This d16b signal path is not used for the Goertzel.
arm_biquad_cascade_df1_f32(&iir_nulls_inst, d16a, d16b, 8);
arm_biquad_cascade_df1_f32(&iir_nulls_inst, d16a, d16b, nPerBlock2);
for(int i=0; i<8; i++)
for(int i=0; i<nPerBlock2; i++)
{
if(gCount++ < gLength) // Main Goertzel calculation
{
@ -88,18 +88,18 @@ void analyze_CTCSS_F32::update(void) {
out2 = - gs1*ccIm;
// At this point the phase is still in need of correction. But we
// only use amplitude so, leave the phase as is.
powerTone = 4.0f*(out1*out1 + out2*out2)/((float)gLength*(float)gLength);
// 2.0f*sqrtf(powerTone)/(float)gLength; <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
powerTone = 4.0f*(out1*out1 + out2*out2)/((float32_t)gLength*(float32_t)gLength);
gs1 = 0.0; // Initialize to start new measurement
gs2 = 0.0;
gCount = 0;
// The 2.04 factor makes the reference for sine waves the same as the Goertzel
powerRef = 2.04f*powerSum/((float)powerSumCount);
powerRef = 2.04f*powerSum/((float32_t)powerSumCount);
powerSum = 0.0f;
powerSumCount = 0;
new_output = true;
}
}
// If the CTCSS tone is detected, the output is the original data block.
// If silenced, zeros are returned.
if(powerTone>threshAbs && powerTone>threshRel*powerRef)
@ -107,15 +107,15 @@ void analyze_CTCSS_F32::update(void) {
else
{
for(int i = 0; i<128; i++)
*(block->data + i) = 0.0;
*(block->data + i) = 0.0f;
transmit(block);
}
release(block);
}
analyze_CTCSS_F32::operator bool() {
float pThresh;
pThresh = ((float)gLength)*threshAbs;
float32_t pThresh;
pThresh = ((float32_t)gLength)*threshAbs;
pThresh *= pThresh;
return (powerTone >= pThresh);
}

256
analyze_CTCSS_F32.h
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@ -3,7 +3,9 @@
* (floating point audio).
* MIT License on changed portions
* Bob Larkin March 2021 original write
* Rev 21 Jan 2022 Major redo and ready to publish. RSL
* Rev 21 Jan 2022 Major redo and ready to publish. Bob L
* Rev 15 March 2023 - Added dynamic sample rate control; added 12 ksps; corrected
* receiveWritable_f32() for block with output. Bob L
*
* This is specific for the CTCSS tone system
* with tones in the 67.0 to 254.1 Hz range.
@ -127,7 +129,7 @@
* filtering and to reduce processing load. The filter parameters of the decimation
* LPF can be used at any sampling rate from 44 to 100 kHz. Other rates will need
* a new design for the LPF. See the discussion below for "iirLpfCoeffs" showing
* how to design such a filter.
* how to design such a filter. (Mar 2023: Decimate by 8 for 12 ksps).
*
* The bandpass filter to cover 67 to 254 Hz is predesigned for sample rates near
* 44, 48, 96 or 100 kHz. The discussion below "BPF iir Coefficients" has
@ -138,7 +140,7 @@
*
* Note - Pieces of this support block sizes other than 128, but not all.
* Work needs to be done to implement and test variable block size. The same is
* true for sample rates outside the 44.1 to 100 kHz range.
* true for sample rates outside the 12 and 44.1 to 100 kHz range.
*/
#ifndef analyze_CTCSS_F32_h_
@ -165,42 +167,83 @@ public:
initCTCSS();
}
// This is called at instantation and also if either freq or sample_rate_Hz is changed
void initCTCSS(void)
{
frequency(103.5f, 300.0f); // Defaults
setNotchX4(103.5f);
// Initialize BiQuad instance (ARM DSP Math Library)
gEnabled = true;
float32_t nDecimatef = (float32_t)nDecimate; // Later use
// INFO: Initialize BiQuad instance (ARM DSP Math Library)
//https://www.keil.com/pack/doc/CMSIS/DSP/html/group__BiquadCascadeDF1.html
arm_biquad_cascade_df1_init_f32(&iir_lpf_inst, 2, &iirLpfCoeffs[0], &StateLpf32[0]);
// First, select the BPF for measuring the noise level
if(iirUserBpfCoeffs != NULL)
iirBpfCoeffs = iirUserBpfCoeffs; // From INO, always use if supplied
//else if(sample_rate_Hz>11000.0f && sample_rate_Hz<11050.0f)
//iirBpfCoeffs = coeff32bp11; Not currently implemented
else if(sample_rate_Hz>11975.0f && sample_rate_Hz<12025.0f)
iirBpfCoeffs = coeff32bp12;
//else if(sample_rate_Hz>23950.0f && sample_rate_Hz<24050.0f)
//iirBpfCoeffs = coeff32bp24; Not currently implemented
else if(sample_rate_Hz>43900.0f && sample_rate_Hz<44200.0f)
iirBpfCoeffs = coeff32bp44;
else if(sample_rate_Hz>47900.0f && sample_rate_Hz<48100.0f)
iirBpfCoeffs = coeff32bp48;
else if(sample_rate_Hz>95800.0f && sample_rate_Hz<96200.0f)
iirBpfCoeffs = coeff32bp96;
else if(sample_rate_Hz>99800.0f && sample_rate_Hz<100200.0f)
iirBpfCoeffs = coeff32bp100;
else gEnabled = false;
arm_biquad_cascade_df1_init_f32(&iir_bpf_inst, 4, iirBpfCoeffs, &StateBpf32[0]);
for (int i=0; i<8; i++)
if(sample_rate_Hz>11900 && sample_rate_Hz<24100) // Now choose a pre-decimation LPF
{
d16a[i] = 0.0f;
d16b[i] = 0.0f;
nDecimate = 8;
arm_biquad_cascade_df1_init_f32(&iir_lpf_inst, 4, &iirLpfCoeffs12[0], &StateLpf32[0]);
}
arm_biquad_cascade_df1_init_f32(&iir_nulls_inst, 4, &iirNullsCoeffs[0], &StateNullsF32[0]);
thresholds(0.1f, 1.0f);
gEnabled = true;
setCTCSS_BP(NULL); // May be invalid if Sample rate is not provided for here.
else if (sample_rate_Hz>44000 && sample_rate_Hz<100100)
{
nDecimate = 16;
arm_biquad_cascade_df1_init_f32(&iir_lpf_inst, 4, &iirLpfCoeffs44[0], &StateLpf32[0]);
}
else gEnabled = false;
nDecimatef = (float32_t)nDecimate;
sampleRate2 = sample_rate_Hz / nDecimatef;
// Set frequency and length of Goertzel in Hz and milliseconds.
void frequency(float freq) { // Defaults to 300 mSec
frequency(freq, 300.0f);
for (int i=0; i<16; i++) // Need 8 when decimate is 16 or 16 if decimate is 8
{
d16a[i] = 0.0f;
d16b[i] = 0.0f;
}
arm_biquad_cascade_df1_init_f32(&iir_nulls_inst, 4, &iirNullsCoeffs[0], &StateNullsF32[0]);
void frequency(float freq, float tMeas) {
// e.g. freq=103.5, tMeas=250, sample_rate_Hz = 44100, gLength=689
gLength = (uint16_t)(0.5 + sample_rate_Hz*tMeas/(1000.0f*16)); // reinstated
gLength = (uint16_t)(0.5 + sample_rate_Hz*tMeas/(1000.0f*nDecimatef)); // reinstated
// Now set the notch filters for the four-biquad notch filters
setNotchX4(freq);
// and the sub-audible general BP filter
setCTCSS_BP(NULL);
// e.g., freq=103.5, sample_rate_Hz=44100, gCoefficient=2*cos(0.23594)=1.944634
gCoefficient = 2.0f*cosf(6.28318530718f*16.0f*freq/sample_rate_Hz);
gCoefficient = 2.0f*cosf(6.28318530718f*nDecimatef*freq/sample_rate_Hz);
// Another constant for ending calculation is exp(-j 2*pi*16*freq*(glength-1)/sample_rate_Hz)
ccRe = cos(6.28318530718f*16.0f*freq/sample_rate_Hz);
ccIm = -sin(6.28318530718f*16.0f*freq/sample_rate_Hz);
ccRe = cos(6.28318530718f*nDecimatef*freq/sample_rate_Hz);
ccIm = -sin(6.28318530718f*nDecimatef*freq/sample_rate_Hz);
thresholds(0.1f, 1.0f);
}
// Set frequency and length of Goertzel detect tone in Hz and milliseconds.
void frequency(float32_t _freq) { // Defaults to 300 mSec
frequency(_freq, 300.0f);
}
void frequency(float32_t _freq, float32_t _tMeas) {
freq = _freq;
tMeas = _tMeas;
initCTCSS();
}
// Sample rates 12, 44.1, 48, 96 and 100 ksps are supported.
void setSampleRate_Hz(const float32_t &fs_Hz) {
sample_rate_Hz = fs_Hz;
initCTCSS();
}
bool available(void) {
@ -212,9 +255,9 @@ public:
return flag;
}
float readTonePower(void) { return powerTone; }
float32_t readTonePower(void) { return powerTone; }
float readRefPower(void) { return powerRef; }
float32_t readRefPower(void) { return powerRef; }
const uint16_t isAbsThreshold=1;
const uint16_t isRelThreshold=2;
@ -229,7 +272,7 @@ public:
else return false; // Something was wrong about call
}
void thresholds(float levelAbs, float levelRel) {
void thresholds(float32_t levelAbs, float32_t levelRel) {
// The absolute threshold is compared with tonePower
if (levelAbs < 0.000001f) threshAbs = 0.000001f;
else threshAbs = levelAbs;
@ -244,29 +287,16 @@ public:
virtual void update(void);
/* The bandpass filter covers 67 to 254 Hz to allow a comparison
* measurement for the tone. This changes with sample rate. Four
* precomputed filters are provided for 44.1, 48, 96 and 100 kHz.
* Supply a NULL for the filterCoeffs to use these 4.
* filterCoeffs points to an array of 20 floats that are IIR
* measurement for the tone. This changes with sample rate. Five
* precomputed filters are provided for 12, 44.1, 48, 96 and 100 kHz.
* Supply a NULL for the filterCoeffs to use these five.
* _filterCoeffs points to an array of 20 floats that are IIR
* coefficients for four BiQuad Stages. To use caller supplied
* filter coefficients, call with a pointer to that 4x BiQuad filter at
* filterCoeffs.
*/
float* setCTCSS_BP(float *filterCoeffs)
{
if(filterCoeffs == NULL)
{
if(sample_rate_Hz>43900.0f && sample_rate_Hz<44200.0f)
iirBpfCoeffs = coeff32bp44;
else if(sample_rate_Hz>47900.0f && sample_rate_Hz<48100.0f)
iirBpfCoeffs = coeff32bp48;
else if(sample_rate_Hz>95800.0f && sample_rate_Hz<96200.0f)
iirBpfCoeffs = coeff32bp96;
else if(sample_rate_Hz>99800.0f && sample_rate_Hz<100200.0f)
iirBpfCoeffs = coeff32bp100;
else return NULL;
}
else iirBpfCoeffs = filterCoeffs; // Caller supplied
float* setCTCSS_BP(float32_t *_filterCoeffs) {
iirUserBpfCoeffs = _filterCoeffs; // Caller supplied
return iirBpfCoeffs;
}
@ -275,7 +305,7 @@ public:
* Call this function with a pointer to that array. To stop windowing,
* call this function with NULL as an argument.
* / Windowing not yet implemented <<<-------------------
void setGWindow(float *pWinCoeff)
void setGWindow(float32_t *pWinCoeff)
{
windowCoeff = pWinCoeff; // Point to the caller supplied window function
if(pWinCoeff != NULL)
@ -287,35 +317,39 @@ public:
private:
int16_t count16 = 0; unsigned long cnt = 0UL;
float ccRe=0.0f;
float ccIm=0.0f;
float freq = 103.5f;
float tMeas = 300.0f;
float d16a[8]; // Small data blocks, after decimation
float d16b[8];
float gCoefficient = 1.9f; // Goertzel algorithm coefficient
float gs1, gs2; // Goertzel algorithm state
float out1, out2; // Goertzel algorithm state output
float powerTone;
float powerRef;
float32_t ccRe=0.0f;
float32_t ccIm=0.0f;
float32_t freq = 103.5f;
float32_t tMeas = 300.0f;
uint16_t nDecimate = 16;
float32_t sampleRate2 = 2756.25f; // 44100/16 etc.
float32_t d16a[16]; // Small data blocks, after decimation
float32_t d16b[16]; // Reference power sum
float32_t gCoefficient = 1.9f; // Goertzel algorithm coefficient
float32_t gs1, gs2; // Goertzel algorithm state
float32_t out1, out2; // Goertzel algorithm state output
float32_t powerTone;
float32_t powerRef;
uint16_t gLength; // number of samples to analyze
uint16_t gCount; // how many left to analyze
float powerSum = 0.0f;
float32_t powerSum = 0.0f;
uint16_t powerSumCount = 0;
float threshAbs = 0.1f; // absolute threshold, 0.01 to 0.99
float threshRel = 1.0f; // noise relative threshold
float32_t threshAbs = 0.1f; // absolute threshold, 0.01 to 0.99
float32_t threshRel = 1.0f; // noise relative threshold
bool gEnabled = false;
volatile bool new_output = false;
audio_block_f32_t *inputQueueArray_f32[1];
float sample_rate_Hz = AUDIO_SAMPLE_RATE;
float32_t sample_rate_Hz = AUDIO_SAMPLE_RATE;
uint16_t block_size = 128;
float iirNullsCoeffs[20];
float *iirBpfCoeffs;
float32_t iirNullsCoeffs[20];
float32_t *iirBpfCoeffs;
float32_t *iirUserBpfCoeffs;
// windowCoeff needs to store half of values (symmetry) for up to
// 0.25 second at 100KHz sample rate, or 0.25*0.5*100000/16=782 pts.
// This is extravagant and needs to be in caller area to allow
// frugality when there is no window at all.
// float *windowCoeff; <<- Windowing is not currently implemented
// float32_t *windowCoeff; <<- Windowing is not currently implemented
// uint16_t nWindow = 0; <<- ditto
/* Info - The structure from arm_biquad_casd_df1_inst_f32 instance consists of
* uint32_t numStages;
@ -336,43 +370,47 @@ private:
* The state variables are updated after each block of data is processed; the
* coefficients are untouched.
*/
float StateLpf32[2*4];
float StateBpf32[4*4];
float StateNullsF32[4*4];
float32_t StateLpf32[4*4];
float32_t StateBpf32[4*4];
float32_t StateNullsF32[4*4];
// The coefficients are stored in the array pCoeffs in the following order:
// {b10, b11, b12, a11, a12, b20, b21, b22, a21, a22, ...}
// where b1x and a1x are the coefficients for the first stage, b2x and a2x are
// the coefficients for the second stage, and so on. The pCoeffs array
// contains a total of 5*numStages values.
// a10, a20, etc are all 1.000 and not listed.
/*
* LPF for decimation before CTCSS tone detector.
* Pick cutoff frequency to pass 254 Hz with fs=44.1kHz
* or fc=2*254/44100=0.01152. This passes highest tone
* frequency at the lowest sample rate. Octave code:
* FSample = 44100;
* halfFSample = 0.5 * FSample
* [z,p,g] = ellip(4,0.1,60,254/halfFSample);
* sos = zp2sos(z,p,g);
* sos1 = sos(1:1,:) % 1st row
* sos2 = sos(2:2,:) % 2nd row
* % This puts the stop band at 0.02*fs or for fs=100 KHz
* % at 2 kHz. This, in turn, supports an 4 kHz
* % sampling rate after decimation. Thus a single LPF design
* % can be used for sample rates from 44.1 to 100 kHz.
* % See notes below on how to convert Octave output to coefficients:
* frequency at the lowest sample rate. These
* were calculated by Iowa Hills routines.
*/
float iirLpfCoeffs[10] = // See lp1ForCtcss.gif
{9.937058251573265e-04f, -1.898847656031816e-03f, 9.937058251573265e-04f,
1.953233139252097e+00f, -9.540781328043288e-01f,
1.000000000000000e+00f, -1.983872743032985e+00f, 9.999999999999998e-01f,
1.980584507653506e+00f, -9.822943824311938e-01f};
//12000 260Hz -60 dB double elliptic 8 pole -60 dB at 300 Hz
float32_t iirLpfCoeffs12[20] = {
0.182145523f,-0.359763551f, 0.182145523f, 1.888598461f,-0.893125955f,
0.350161286f,-0.689819799f, 0.350161286f, 1.922991947f,-0.933494720f,
0.293698317f,-0.571683303f, 0.293698317f, 1.954562781f,-0.970276113f,
0.053599924f,-0.089098167f, 0.053599924f, 1.973912800f,-0.992014481f };
float32_t iirLpfCoeffs44[20] = {
0.188636212f,-0.376924253f, 0.188636212f, 1.969403901f,-0.969752071f,
0.357249908f,-0.713703189f, 0.357249908f, 1.980638291f,-0.981434917f,
0.294316431f,-0.587455758f, 0.294316431f, 1.990628020f,-0.991805124f,
0.049761875f,-0.098177786f, 0.049761875f, 1.996468755f,-0.997814718f};
/* There is a band pass filter that is used after decimation to limit the
* spectrum that is seen by the CTCSS detector to (67, 254) Hz. This
* provides the entire CTCSS band to compare against to see if any other
* tones are present. It also restricts the amount of voice spectrum
* presented to the CTCSS detector. This filter is sample rate dependent
* this routine allows for four different "built-in" rates.
* this routine allows for five different "built-in" rates.
*
* Sample LPF Decimation CTCSS BPF
* Rate Fco Ratio Samp Rate Name
* ------- ------ -------- -------- -----
* 12.0kHz 260Hz 8 1500.0Hz BP12
* 44.1kHz 254Hz 16 2756.2Hz BP44
* 48.0kHz 276Hz 16 3000.0Hz BP48
* 96.0kHz 553Hz 16 6000.0Hz BP96
@ -381,7 +419,7 @@ private:
* The following allow computing a bandpass filter for any sample rate in
* the 44 to 100 kHz range (gnu octave script).
*
% ===================== BPF iir Coefficients =============================
% ========== Sidebar: BPF iir Coefficients =============================
% This GNU Octave m script will generate the BPF iir coefficients
% for other sample rates than the four listed here. It will probably
% run under Matlab, but that is untested.
@ -430,11 +468,19 @@ private:
% 1.797650895821358e+00, -8.356641238925192e-01,
% 1.000000000000000e+00, -1.999398698654737e+00, 1.000000000000000e+00,
% 1.941833848024410e+00, -9.614543316508065e-01};
%
*/
// The four predefined bandpass filters:
% ===================================================================== */
// The five predefined bandpass filters:
// BP12 Decimated fSample = 1500 sps
// 65 to 260, 0.1 dB rip, -60 dB elliptic, -7.5 dB at 300 Hz, -60 at 475
float32_t coeff32bp12[20] = {
0.386816925f,-0.769638284f, 0.386816925f, 1.586751090f,-0.706113049f,
0.265346713f, 0.247789162f, 0.265346713f, 0.996735842f,-0.484375851f,
0.461314461f,-0.921736474f, 0.461314461f, 1.864126624f,-0.928392720f,
0.380685155f, 0.664524969f, 0.380685155f, 0.720627184f,-0.766126702f};
// BP44 Decimated fSample = 2756.2 Hz
float coeff32bp44[20] = {
float32_t coeff32bp44[20] = {
4.386558177463118e-03f, 4.835083945591431e-03f, 4.386558177463117e-03f,
1.503280453219001e+00f, -8.498498588788136e-01f,
1.000000000000000e+00f, -4.234328155653108e-01f, 1.000000000000000e+00f,
@ -445,17 +491,15 @@ private:
1.941833848024410e+00f, -9.614543316508065e-01f};
// BP48 Decimated fSample = 3000 Hz
float coeff32bp48[20] = {
3.764439090680418e-03f, 3.650362666517592e-03f, 3.764439090680417e-03f,
1.000000000000000e+00f, -5.926113222413726e-01f, 1.000000000000000e+00f,
1.569400123464342e+00f, -7.055760636246757e-01f,
1.000000000000000e+00f, -1.997300534603388e+00f, 9.999999999999998e-01f,
1.816002936969042e+00f, -8.483092827984080e-01f,
1.000000000000000e+00f, -1.999491318923814e+00f, 1.000000000000000e+00f,
1.947984087804752e+00f, -9.645809301964445e-01f};
// 67 to 254 Band Pass 60 dB reject elliptic -7.5 at 300 Hz -35 at 450 Hz
float32_t coeff32bp48[20] = {
0.272147027f,-0.543594385f, 0.272147027f, 1.819349787f,-0.850367415f,
0.226417971f,-0.138869864f, 0.226417971f, 1.574952243f,-0.707479581f,
0.261002559f,-0.521878771f, 0.261002559f, 1.949332941f,-0.965207141f,
0.232822864f, 0.221820730f, 0.232822864f, 1.572088740f, -0.860996505};
// BP96 Decimated fSample = 6000 Hz
float coeff32bp96[20] = {
float32_t coeff32bp96[20] = {
1.554430361573611e-03f, 5.765630035510897e-04f, 1.554430361573611e-03f,
1.803990601116592e+00f, -8.406882700444890e-01f,
1.000000000000000e+00f, -1.541034615722940e+00f, 9.999999999999998e-01f,
@ -466,7 +510,7 @@ private:
1.978038062492293e+00f, -9.822341038950552e-01f};
// BP100 Decimated fSample = 6250 Hz
float coeff32bp100[20] = {
float32_t coeff32bp100[20] = {
1.504180063396739e-03f, -6.773089598829345e-04f, 1.504180063396738e-03f,
1.812635069874353e+00f, -8.465624856328144e-01f,
1.000000000000000e+00f, -1.573630872142354e+00f, 1.000000000000000e+00f,
@ -482,14 +526,14 @@ private:
* filter is always designed here and there is no need for
* caller-designed filters.
*/
void setNotchX4(float frequency)
void setNotchX4(float32_t frequency)
{
float kf[] = {0.9955f, 0.9982f, 1.0018f, 1.0045f}; // Offset ratios
float Q = 60.0f;
float w0, sinW0, alpha, cosW0, scale;
float32_t kf[] = {0.9955f, 0.9982f, 1.0018f, 1.0045f}; // Offset ratios
float32_t Q = 60.0f;
float32_t w0, sinW0, alpha, cosW0, scale;
for (int ii = 0; ii<4; ii++) // Over 4 cascaded BiQuad filters
{
w0 = kf[ii]*frequency*(2.0f*3.141592654f*16.0f / sample_rate_Hz);
w0 = kf[ii]*frequency*(2.0f*3.141592654f*nDecimate / sample_rate_Hz);
sinW0 = sin(w0);
alpha = sinW0 / (Q * 2.0f);
cosW0 = cos(w0);

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