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Add fft2048_iq_F32 and example INO

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boblark 4 years ago
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  1. 1
      OpenAudio_ArduinoLibrary.h
  2. 238
      analyze_fft2048_iq_F32.cpp
  3. 300
      analyze_fft2048_iq_F32.h
  4. 65
      examples/TestFFT2048iq/TestFFT2048iq.ino

1
OpenAudio_ArduinoLibrary.h
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#include "analyze_fft1024_F32.h" #include "analyze_fft1024_F32.h"
#include "analyze_fft256_iq_F32.h" #include "analyze_fft256_iq_F32.h"
#include "analyze_fft1024_iq_F32.h" #include "analyze_fft1024_iq_F32.h"
#include "analyze_fft2048_iq_F32.h"
#include "analyze_peak_f32.h" #include "analyze_peak_f32.h"
#include "analyze_rms_f32.h" #include "analyze_rms_f32.h"
// #include "control_tlv320aic3206.h" collides much with Teensy Audio // #include "control_tlv320aic3206.h" collides much with Teensy Audio

238
analyze_fft2048_iq_F32.cpp
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/*
* analyze_fft2048_iq_F32.cpp Assembled by Bob Larkin 8 Mar 2021
*
* This class is Teensy 4.x ONLY.
* F32 Bolocks are always 128 floats, and any data rate is OK.
*
* Converted to F32 floating point input and also extended
* for complex I and Q inputs
* * Adapted all I/O to be F32 floating point for OpenAudio_ArduinoLibrary
* * Future: Add outputs for I & Q FFT x2 for overlapped FFT
* * Windowing None, Hann, Kaiser and Blackman-Harris.
*
* Conversion Copyright (c) 2021 Bob Larkin
* Same MIT license as PJRC:
*
* Audio Library for Teensy 3.X
* Copyright (c) 2014, Paul Stoffregen, paul@pjrc.com
*
* Development of this audio library was funded by PJRC.COM, LLC by sales of
* Teensy and Audio Adaptor boards. Please support PJRC's efforts to develop
* open source software by purchasing Teensy or other PJRC products.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice, development funding notice, and this permission
* notice shall be included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
#include <Arduino.h>
#include "analyze_fft2048_iq_F32.h"
// Note: Suppports block size of 128 only. Very "built in."
// Move audio data from audio_block_f32_t to the interleaved FFT instance buffer.
static void copy_to_fft_buffer1(void *destination, const void *sourceI, const void *sourceQ) {
const float *srcI = (const float *)sourceI;
const float *srcQ = (const float *)sourceQ;
float *dst = (float *)destination; // part of fft_buffer array. 256 floats per call
for (int i=0; i < 128; i++) {
*dst++ = *srcI++; // real sample, interleave
*dst++ = *srcQ++; // imag
}
}
static void apply_window_to_fft_buffer1(void *fft_buffer, const void *window) {
float *buf = (float *)fft_buffer; // 0th entry is real (do window) 1st is imag
const float *win = (float *)window;
for (int i=0; i < 2048; i++) {
buf[2*i] *= *win; // real
buf[2*i + 1] *= *win++; // imag
}
}
void AudioAnalyzeFFT2048_IQ_F32::update(void) {
audio_block_f32_t *block_i,*block_q;
int ii;
uint32_t tt;
block_i = receiveReadOnly_f32(0);
if (!block_i) return;
block_q = receiveReadOnly_f32(1);
if (!block_q) {
release(block_i);
return;
}
// Here with two new blocks of data
tt=micros();
switch (state) {
case 0:
blocklist_i[0] = block_i; blocklist_q[0] = block_q;
state = 1;
break;
case 1:
blocklist_i[1] = block_i; blocklist_q[1] = block_q;
state = 2;
break;
case 2:
blocklist_i[2] = block_i; blocklist_q[2] = block_q;
state = 3;
break;
case 3:
blocklist_i[3] = block_i; blocklist_q[3] = block_q;
state = 4;
break;
case 4:
blocklist_i[4] = block_i; blocklist_q[4] = block_q;
state = 5;
break;
case 5:
blocklist_i[5] = block_i; blocklist_q[5] = block_q;
state = 6;
break;
case 6:
blocklist_i[6] = block_i; blocklist_q[6] = block_q;
state = 7;
break;
case 7:
blocklist_i[7] = block_i; blocklist_q[7] = block_q;
state = 8;
break;
case 8:
blocklist_i[8] = block_i; blocklist_q[8] = block_q;
state = 9;
break;
case 9:
blocklist_i[9] = block_i; blocklist_q[9] = block_q;
state = 10;
break;
case 10:
blocklist_i[10] = block_i; blocklist_q[10] = block_q;
state = 11;
break;
case 11:
blocklist_i[11] = block_i; blocklist_q[11] = block_q;
state = 12;
break;
case 12:
blocklist_i[12] = block_i; blocklist_q[12] = block_q;
state = 13;
break;
case 13:
blocklist_i[13] = block_i; blocklist_q[13] = block_q;
state = 14;
break;
case 14:
blocklist_i[14] = block_i; blocklist_q[14] = block_q;
state = 15;
break;
case 15:
blocklist_i[15] = block_i; blocklist_q[15] = block_q;
copy_to_fft_buffer1(fft_buffer+0x000, blocklist_i[0]->data, blocklist_q[0]->data);
copy_to_fft_buffer1(fft_buffer+0x100, blocklist_i[1]->data, blocklist_q[1]->data);
copy_to_fft_buffer1(fft_buffer+0x200, blocklist_i[2]->data, blocklist_q[2]->data);
copy_to_fft_buffer1(fft_buffer+0x300, blocklist_i[3]->data, blocklist_q[3]->data);
copy_to_fft_buffer1(fft_buffer+0x400, blocklist_i[4]->data, blocklist_q[4]->data);
copy_to_fft_buffer1(fft_buffer+0x500, blocklist_i[5]->data, blocklist_q[5]->data);
copy_to_fft_buffer1(fft_buffer+0x600, blocklist_i[6]->data, blocklist_q[6]->data);
copy_to_fft_buffer1(fft_buffer+0x700, blocklist_i[7]->data, blocklist_q[7]->data);
copy_to_fft_buffer1(fft_buffer+0x800, blocklist_i[8]->data, blocklist_q[8]->data);
copy_to_fft_buffer1(fft_buffer+0x900, blocklist_i[9]->data, blocklist_q[9]->data);
copy_to_fft_buffer1(fft_buffer+0xA00, blocklist_i[10]->data, blocklist_q[10]->data);
copy_to_fft_buffer1(fft_buffer+0xB00, blocklist_i[11]->data, blocklist_q[11]->data);
copy_to_fft_buffer1(fft_buffer+0xC00, blocklist_i[12]->data, blocklist_q[12]->data);
copy_to_fft_buffer1(fft_buffer+0xD00, blocklist_i[13]->data, blocklist_q[13]->data);
copy_to_fft_buffer1(fft_buffer+0xE00, blocklist_i[14]->data, blocklist_q[14]->data);
copy_to_fft_buffer1(fft_buffer+0xF00, blocklist_i[15]->data, blocklist_q[15]->data);
if (pWin)
apply_window_to_fft_buffer1(fft_buffer, window);
// Teensyduino core for T4.x supports arm_cfft_f32
// arm_cfft_f32 (const arm_cfft_instance_f32 *S, float32_t *p1, uint8_t ifftFlag, uint8_t bitReverseFlag)
arm_cfft_f32(&Sfft, fft_buffer, 0, 1);
count++;
for (int i = 0; i < 1024; i++) {
// From complex FFT the "negative frequencies" are mirrors of the frequencies above fs/2. So, we get
// frequencies from 0 to fs by re-arranging the coefficients. These are powers (not Volts)
// See DD4WH SDR
float ss0 = fft_buffer[2 * i] * fft_buffer[2 * i] +
fft_buffer[2 * i + 1] * fft_buffer[2 * i + 1];
float ss1 = fft_buffer[2 * (i + 1024)] * fft_buffer[2 * (i + 1024)] +
fft_buffer[2 * (i + 1024) + 1] * fft_buffer[2 * (i + 1024) + 1];
if(count==1) { // Starting new average
sumsq[i+1024] = ss0;
sumsq[i] = ss1;
}
else if (count <= nAverage) { // Adding on to average
sumsq[i+1024] += ss0;
sumsq[i] += ss1;
}
}
if (count >= nAverage) { // Average is finished
count = 0;
float inAf = 1.0f/(float)nAverage;
for (int i=0; i < 2048; i++) {
// xAxis, bit 0 left/right; bit 1 low to high
if(xAxis & 0X02)
ii = i;
else
ii = i^1024;
if(xAxis & 0X01)
ii = (2047 - ii);
if(outputType==FFT_RMS)
output[i] = sqrtf(inAf*sumsq[ii]);
else if(outputType==FFT_POWER)
output[i] = inAf*sumsq[ii];
else if(outputType==FFT_DBFS)
output[i] = 10.0f*log10f(inAf*sumsq[ii])-60.21f; // Scaled to FS sine wave
else
output[i] = 0.0f;
}
} // end of Average is Finished
outputflag = true;
release(blocklist_i[0]); release(blocklist_q[0]);
release(blocklist_i[1]); release(blocklist_q[1]);
release(blocklist_i[2]); release(blocklist_q[2]);
release(blocklist_i[3]); release(blocklist_q[3]);
release(blocklist_i[4]); release(blocklist_q[4]);
release(blocklist_i[5]); release(blocklist_q[5]);
release(blocklist_i[6]); release(blocklist_q[6]);
release(blocklist_i[7]); release(blocklist_q[7]);
blocklist_i[0] = blocklist_i[8];
blocklist_i[1] = blocklist_i[9];
blocklist_i[2] = blocklist_i[10];
blocklist_i[3] = blocklist_i[11];
blocklist_i[4] = blocklist_i[12];
blocklist_i[5] = blocklist_i[13];
blocklist_i[6] = blocklist_i[14];
blocklist_i[7] = blocklist_i[15];
blocklist_q[0] = blocklist_q[8];
blocklist_q[1] = blocklist_q[9];
blocklist_q[2] = blocklist_q[10];
blocklist_q[3] = blocklist_q[11];
blocklist_q[4] = blocklist_q[12];
blocklist_q[5] = blocklist_q[13];
blocklist_q[6] = blocklist_q[14];
blocklist_q[7] = blocklist_q[15];
state = 8; Serial.println(micros()-tt);
break; // From case 15
} // End of switch & case 15
} // End update()

300
analyze_fft2048_iq_F32.h
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/*
* Analyze_fft2048_iq_F32.h Assembled by Bob Larkin 8 Mar 2021
*
* Note: Teensy 4.x Only, 3.x not supported
*
* Does Fast Fourier Transform of a 2048 point complex (I-Q) input.
* Output is one of three measures of the power in each of the 2048
* output bins, Power, RMS level or dB relative to a full scale
* sine wave. Windowing of the input data is provided for to reduce
* spreading of the power in the output bins. All inputs are Teensy
* floating point extension (_F32) and all outputs are floating point.
*
* Features include:
* * I and Q inputs are OpenAudio_Arduino Library F32 compatible.
* * FFT output for every 512 inputs to overlapped FFTs to
* compensate for windowing.
* * Windowing None, Hann, Kaiser and Blackman-Harris.
* * Multiple bin-sum output to simulate wider bins.
* * Power averaging of multiple FFT
* * Soon: F32 audio outputs for I & Q
*
* Conversion Copyright (c) 2021 Bob Larkin
* Same MIT license as PJRC:
*
* From original real FFT:
* Audio Library for Teensy 3.X
* Copyright (c) 2014, Paul Stoffregen, paul@pjrc.com
*
* Development of this audio library was funded by PJRC.COM, LLC by sales of
* Teensy and Audio Adaptor boards. Please support PJRC's efforts to develop
* open source software by purchasing Teensy or other PJRC products.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice, development funding notice, and this permission
* notice shall be included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
/* Does complex input FFT of 2048 points. Multiple non-audio (via functions)
* output formats of RMS (same as I16 version, and default),
* Power or dBFS (full scale). Output can be bin by bin or a pointer to
* the output array is available. Several window functions are provided by
* in-class design, or a custom window can be provided from the INO.
*
* Functions (See comments below and #defines above:
* bool available()
* float read(unsigned int binNumber)
* float read(unsigned int binFirst, unsigned int binLast)
* int windowFunction(int wNum)
* int windowFunction(int wNum, float _kdb) // Kaiser only
* float* getData(void)
* float* getWindow(void)
* void putWindow(float *pwin)
* void setNAverage(int NAve) // >=1
* void setOutputType(int _type)
* void setXAxis(uint8_t _xAxis) // 0, 1, 2, 3
*
* x-Axis direction and offset per setXAxis(xAxis) for sine to I
* and cosine to Q.
* If xAxis=0 f=fs/2 in middle, f=0 on right edge
* If xAxis=1 f=fs/2 in middle, f=0 on left edge
* If xAxis=2 f=fs/2 on left edge, f=0 in middle
* If xAxis=3 f=fs/2 on right edgr, f=0 in middle
* If there is 180 degree phase shift to I or Q these all get reversed.
*
* Timing, max is longest update() time:
* T4.0 Windowed, dBFS Out, 987 uSec
*
* Scaling:
* Full scale for floating point DSP is a nebulous concept. Normally the
* full scale is -1.0 to +1.0. This is an unscaled FFT and for a sine
* wave centered in frequency on a bin and of FS amplitude, the power
* at that center bin will grow by 2048^2/4 = 1048576 without windowing.
* Windowing loss cuts this down. The RMS level can grow to sqrt(1048576)
* or 2048. The dBFS has been scaled to make this max value 0 dBFS by
* removing 60.2 dB. With floating point, the dynamic range is maintained
* no matter how it is scaled, but this factor needs to be considered
* when building the INO.
*/
#ifndef analyze_fft2048iq_h_
#define analyze_fft2048iq_h_
// *************** TEENSY 4.X ONLY ****************
#include "Arduino.h"
#include "AudioStream_F32.h"
#include "arm_math.h"
#include "mathDSP_F32.h"
#include "arm_const_structs.h"
#define FFT_RMS 0
#define FFT_POWER 1
#define FFT_DBFS 2
#define NO_WINDOW 0
#define AudioWindowNone 0
#define AudioWindowHanning2048 1
#define AudioWindowKaiser2048 2
#define AudioWindowBlackmanHarris2048 3
class AudioAnalyzeFFT2048_IQ_F32 : public AudioStream_F32 {
//GUI: inputs:2, outputs:4 //this line used for automatic generation of GUI node
//GUI: shortName:FFT2048IQ
public:
AudioAnalyzeFFT2048_IQ_F32() : AudioStream_F32(2, inputQueueArray) {
// __MK20DX128__ T_LC; __MKL26Z64__ T3.0; __MK20DX256__T3.1 and T3.2
// __MK64FX512__) T3.5; __MK66FX1M0__ T3.6; __IMXRT1062__ T4.0 and T4.1
// Teensy4 core library has the right files for new FFT
// arm CMSIS library has predefined structures of type arm_cfft_instance_f32
Sfft = arm_cfft_sR_f32_len2048; // This is one of the structures
useHanningWindow();
}
// There is no varient for "settings," as blocks other than 128 are
// not supported and, nothing depends on sample rate so we don't need that.
// Returns true when output data is available.
bool available() {
#if defined(__IMXRT1062__)
if (outputflag == true) {
outputflag = false; // No double returns
return true;
}
return false;
#else
// Don't know how you got this far, but....
Serial.println("Teensy 3.x NOT SUPPORTED");
return false;
#endif
}
// Returns a single bin output
float read(unsigned int binNumber) {
if (binNumber>2047 || binNumber<0) return 0.0;
return output[binNumber];
}
// Return sum of several bins. Normally use with power output.
// This produces the equivalent of bigger bins.
float read(unsigned int binFirst, unsigned int binLast) {
if (binFirst > binLast) {
unsigned int tmp = binLast;
binLast = binFirst;
binFirst = tmp;
}
if (binFirst > 2047) return 0.0;
if (binLast > 2047) binLast = 2047;
float sum = 0;
do {
sum += output[binFirst++];
} while (binFirst <= binLast);
return sum;
}
// Sets None, Hann, or Blackman-Harris window with no parameter
int windowFunction(int wNum) {
if(wNum == AudioWindowKaiser2048)
return -1; // Kaiser needs the kdb
windowFunction(wNum, 0.0f);
return 0;
}
int windowFunction(int wNum, float _kdb) {
float kd;
pWin = window;
if(wNum == NO_WINDOW)
pWin = NULL;
else if (wNum == AudioWindowKaiser2048) {
if(_kdb<20.0f)
kd = 20.0f;
else
kd = _kdb;
useKaiserWindow(kd);
}
else if (wNum == AudioWindowBlackmanHarris2048)
useBHWindow();
else
useHanningWindow(); // Default
return 0;
}
// Fast pointer transfer. Be aware that the data will go away
// after the next 256 data points occur.
float* getData(void) {
// available() sets outputflag false
return output;
}
// You can use this to design windows
float* getWindow(void) {
return window;
}
// Bring custom window from the INO
void putWindow(float *pwin) {
float *p = window;
for(int i=0; i<2048; i++)
*p++ = *pwin++; // Copy for the FFT
}
// Number of FFT averaged in the output
void setNAverage(int _nAverage) {
nAverage = _nAverage;
}
// Output RMS (default), power or dBFS (FFT_RMS, FFT_POWER, FFT_DBFS)
void setOutputType(int _type) {
outputType = _type;
}
// xAxis, bit 0 left/right; bit 1 low to high; default 0X03
void setXAxis(uint8_t _xAxis) {
xAxis = _xAxis;
}
virtual void update(void);
private:
float output[2048];
float window[2048];
float *pWin = window;
float fft_buffer[4096];
float sumsq[2048]; // Avoid re-use of output[]
uint8_t state = 0;
bool outputflag = false;
audio_block_f32_t *inputQueueArray[2];
audio_block_f32_t *blocklist_i[16];
audio_block_f32_t *blocklist_q[16];
// For T4.x
// const static arm_cfft_instance_f32 arm_cfft_sR_f32_len1024;
arm_cfft_instance_f32 Sfft;
int outputType = FFT_RMS; //Same type as I16 version init
int count = 0;
int nAverage = 1;
uint8_t xAxis = 0x03;
// The Hann window is a good all-around window
void useHanningWindow(void) {
for (int i=0; i < 2048; i++) {
// 2*PI/2047 = 0.00306946
window[i] = 0.5*(1.0 - cosf(0.00306946f*(float)i));
}
}
// Blackman-Harris produces a first sidelobe more than 90 dB down.
// The price is a bandwidth of about 2 bins. Very useful at times.
void useBHWindow(void) {
for (int i=0; i < 2048; i++) {
float kx = 0.00306946f; // 2*PI/2047
int ix = (float) i;
window[i] = 0.35875 -
0.48829*cosf( kx*ix) +
0.14128*cosf(2.0f*kx*ix) -
0.01168*cosf(3.0f*kx*ix);
}
}
/* The windowing function here is that of James Kaiser. This has a number
* of desirable features. The sidelobes drop off as the frequency away from a transition.
* Also, the tradeoff of sidelobe level versus cutoff rate is variable.
* Here we specify it in terms of kdb, the highest sidelobe, in dB, next to a sharp cutoff. For
* calculating the windowing vector, we need a parameter beta, found as follows:
*/
void useKaiserWindow(float kdb) {
float32_t beta, kbes, xn2;
mathDSP_F32 mathEqualizer; // For Bessel function
if (kdb < 20.0f)
beta = 0.0;
else
beta = -2.17+0.17153*kdb-0.0002841*kdb*kdb; // Within a dB or so
// Note: i0f is the fp zero'th order modified Bessel function (see mathDSP_F32.h)
kbes = 1.0f / mathEqualizer.i0f(beta); // An additional derived parameter used in loop
for (int n=0; n<512; n++) {
xn2 = 0.5f+(float32_t)n;
// 4/(1023^2)=0.00000382215877f
// 4/(2047^2) = 9.546063E-7;
xn2 = 9.546063E-7*xn2*xn2;
window[511 - n]=kbes*(mathEqualizer.i0f(beta*sqrtf(1.0-xn2)));
window[512 + n] = window[511 - n];
}
}
};
#endif

65
examples/TestFFT2048iq/TestFFT2048iq.ino
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// TestFFT2048iq.ino for Teensy 4.x
// Bob Larkin 9 March 2021
// Generate Sin and Cosine pair and input to IQ FFT.
// Serial Print out powers of all 2048 bins in
// dB relative to Sine Wave Full Scale
// Public Domain
#include "OpenAudio_ArduinoLibrary.h"
#include "AudioStream_F32.h"
// GUItool: begin automatically generated code
AudioSynthSineCosine_F32 sine_cos1; //xy=76,532
AudioAnalyzeFFT2048_IQ_F32 FFT2048iq1; //xy=243,532
AudioOutputI2S_F32 audioOutI2S1; //xy=246,591
AudioConnection_F32 patchCord1(sine_cos1, 0, FFT2048iq1, 0);
AudioConnection_F32 patchCord2(sine_cos1, 1, FFT2048iq1, 1);
// GUItool: end automatically generated code
void setup(void) {
float* pPwr;
Serial.begin(9600);
delay(1000);
AudioMemory_F32(50);
Serial.println("FFT2048IQ Test");
sine_cos1.amplitude(1.0f); // Initialize Waveform Generator
// Pick T4.x bin center
sine_cos1.frequency(689.0625f);
// or pick any old frequency
//sine_cos1.frequency(7100.0);
// elect the output format
FFT2048iq1.setOutputType(FFT_DBFS);
// Select the wndow function
//FFT2048iq1.windowFunction(AudioWindowNone);
//FFT2048iq1.windowFunction(AudioWindowHanning2048);
//FFT2048iq1.windowFunction(AudioWindowKaiser2048, 55.0f);
FFT2048iq1.windowFunction(AudioWindowBlackmanHarris2048);
// Uncomment to Serial print window function
//float* pw = FFT2048iq1.getWindow(); // Print window
//for (int i=0; i<2048; i++) Serial.println(pw[i], 4);
// xAxis, bit 0 left/right; bit 1 low to high; default 0X03
FFT2048iq1.setXAxis(0X03);
delay(1000);
// Print output, once
if( FFT2048iq1.available() ) {
pPwr = FFT2048iq1.getData();
for(int i=0; i<2048; i++)
Serial.println(*(pPwr + i), 8 );
}
Serial.println("");
}
void loop(void) {
}
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