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Initial add of analyze_fft4096_iqem_F32

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boblark 3 years ago
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  1. 1
      OpenAudio_ArduinoLibrary.h
  2. 429
      analyze_fft4096_iqem_F32.cpp
  3. 348
      analyze_fft4096_iqem_F32.h
  4. 94
      examples/TestFFT4096iqEM/TestFFT4096iqEM.ino
  5. 1
      keywords.txt

1
OpenAudio_ArduinoLibrary.h
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#include "analyze_fft1024_iq_F32.h"
#include "analyze_fft2048_iq_F32.h"
#include "analyze_fft4096_iq_F32.h"
#include "analyze_fft4096_iqem_F32.h"
#include "analyze_peak_f32.h"
#include "analyze_rms_f32.h"
#include "analyze_tonedetect_F32.h"

429
analyze_fft4096_iqem_F32.cpp
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/*
* analyze_fft4096_iq_F32.cpp Assembled by Bob Larkin 9 Mar 2021
*
* External Memory **** BETA TEST VERSION - NOT FULLY TESTED **** <<<<<<<<<<
*
* 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.
*/
// *************** TEENSY 4.X ONLY ****************
#if defined(__IMXRT1062__)
#include <Arduino.h>
#include "analyze_fft4096_iqem_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
}
}
void AudioAnalyzeFFT4096_IQEM_F32::update(void) {
audio_block_f32_t *block_i,*block_q;
int i, ii;
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. These are retained until the FFT
// but with new pointers, blocklist_i[] and blocklist_q[].
switch (state) {
case 0:
blocklist_i[0] = block_i; blocklist_q[0] = block_q; // Copy 2 ptrs
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;
state = 16;
break;
// ********************************************************
// Once things are running, the loop comes back to this point
case 16:
blocklist_i[16] = block_i; blocklist_q[16] = block_q;
// Now work on the FFT output data. This was created in case 31.
// This next forming of the sumsq[] takes 48 uSec
count++;
for (int i = 0; i < 2048; i++) {
// Re-arranging the coefficients. These are bin powers (not Volts)
// See DD4WH SDR
float ss0 = *(pFFT_buffer + 2*i) * *(pFFT_buffer + 2*i) +
*(pFFT_buffer + 2*i+1) * *(pFFT_buffer + 2*i+1);
float ss1 = *(pFFT_buffer + 2*(i+2048)) * *(pFFT_buffer + 2*(i+2048)) +
*(pFFT_buffer + 2*(i+2048)+1) * *(pFFT_buffer + 2*(i+2048)+1);
if(!(pSumsq==NULL)) { // We have memory to do averages
if(count==1) { // Starting new average
*(pSumsq+i+2048) = ss0;
*(pSumsq+i) = ss1;
}
else if (count <= nAverage) { // Adding on to average
*(pSumsq+i+2048) += ss0;
*(pSumsq+i) += ss1;
}
}
else // No averaging is used
{
// Parts of pFFT_buffer are becoming available for
// temporary storage, but not all:
*(pFFT_buffer+i) = ss0;
*(pFFT_buffer+4096+i) = ss1;
// Now in pFFT_buffer 0,2047 and 4096,6143
}
}
// sumsq[] is filled. Wait to state==17 to convert to dBFS, etc
state = 17;
break;
case 17:
blocklist_i[17] = block_i; blocklist_q[17] = block_q;
// This state==17 block takes 710 uSec for DBFS, but
// only 65 for POWER. DB conversions do not need to be under
// this interrupt and POWER output should be used if time is short.
if (pSumsq==NULL || count>=nAverage) { // Average is not being done or is finished
outputflag = false; // Avoid starting read() during block 17 to 18
float inAf = 1.0f/(float)nAverage;
for (ii=0; ii < 2048; ii++) {
// xAxis, bit 0 left/right; bit 1 low to high
if(xAxis & 0X02)
i = ii;
else
i = ii^2048;
if(xAxis & 0X01)
i = (4095 - i);
if(!(pSumsq==NULL)) { // We have memory to do averages
if(outputType==FFT_RMS)
*(pOutput+i) = sqrtf(inAf* *(pSumsq+ii));
else if(outputType==FFT_POWER)
*(pOutput+i) = inAf* *(pSumsq+ii);
else if(outputType==FFT_DBFS)
*(pOutput+i) = 10.0f*log10f(inAf* *(pSumsq+ii))-66.23f; // Scaled to FS sine wave
else
*(pOutput+i) = 0.0f;
}
else { // No averaging
if(outputType==FFT_RMS)
*(pOutput+i) = sqrtf(*(pFFT_buffer+ii));
else if(outputType==FFT_POWER)
*(pOutput+i) = *(pFFT_buffer+ii);
else if(outputType==FFT_DBFS)
*(pOutput+i) = 10.0f*log10f(*(pFFT_buffer+ii))-66.23f;
} // End, no averaging
} // End of "over all i"
} // end of Average is Finished
state = 18;
break;
case 18:
blocklist_i[18] = block_i; blocklist_q[18] = block_q;
// Second half of post-FFT processing. dBFS (log10f) is the big user of time.
if (pSumsq==NULL || count>=nAverage) { // Average is finished
Serial.println(count);
count = 0; // CHECK WHERE IS count++ ??? <<<<<<<<<<<<<<
float inAf = 1.0f/(float)nAverage;
// ii is the index to data source, i is for data output
for (int ii=2048; ii < 4096; ii++) {
// xAxis, bit 0 left/right; bit 1 low to high
if(xAxis & 0X02)
i = ii;
else
i = ii^2048;
if(xAxis & 0X01)
i = (4095 - i);
if(!(pSumsq==NULL)) { // We have memory to do averages
if(outputType==FFT_RMS)
*(pOutput+i) = sqrtf(inAf* *(pSumsq+ii));
else if(outputType==FFT_POWER)
*(pOutput+i) = inAf* *(pSumsq+ii);
else if(outputType==FFT_DBFS)
*(pOutput+i) = 10.0f*log10f(inAf* *(pSumsq+ii))-66.23f; // Scaled to FS sine wave
else
*(pOutput+i) = 0.0f;
}
else { // No averaging being done
if(outputType==FFT_RMS)
*(pOutput+i) = sqrtf(*(pFFT_buffer+ii+2048));
else if(outputType==FFT_POWER)
*(pOutput+i) = *(pFFT_buffer+ii+2048);
else if(outputType==FFT_DBFS)
*(pOutput+i) = 10.0f*log10f(*(pFFT_buffer+ii+2048))-66.23f;
else
*(pOutput+i) = 0.0f;
}
}
outputflag = true;
} // end of Average is Finished
state = 19;
break;
case 19:
blocklist_i[19] = block_i; blocklist_q[19] = block_q;
state = 20;
break;
case 20:
blocklist_i[20] = block_i; blocklist_q[20] = block_q;
state = 21;
break;
case 21:
blocklist_i[21] = block_i; blocklist_q[21] = block_q;
state = 22;
break;
case 22:
blocklist_i[22] = block_i; blocklist_q[22] = block_q;
state = 23;
break;
case 23:
blocklist_i[23] = block_i; blocklist_q[23] = block_q;
state = 24;
break;
case 24:
blocklist_i[24] = block_i; blocklist_q[24] = block_q;
state = 25;
break;
case 25:
blocklist_i[25] = block_i; blocklist_q[25] = block_q;
state = 26;
break;
case 26:
blocklist_i[26] = block_i; blocklist_q[26] = block_q;
state = 27;
break;
case 27:
blocklist_i[27] = block_i; blocklist_q[27] = block_q;
state = 28;
break;
case 28:
blocklist_i[28] = block_i; blocklist_q[28] = block_q;
state = 29;
break;
case 29:
blocklist_i[29] = block_i; blocklist_q[29] = block_q;
state = 30;
break;
case 30:
blocklist_i[30] = block_i; blocklist_q[30] = block_q;
state = 31;
break;
case 31:
blocklist_i[31] = block_i; blocklist_q[31] = block_q;
// Copy 8192 data to fft_buffer This state==31 takes about 500 uSec, including the FFT.
// i & q interleaved data.
copy_to_fft_buffer1(pFFT_buffer+0x000, blocklist_i[0]->data, blocklist_q[0]->data);
copy_to_fft_buffer1(pFFT_buffer+0x100, blocklist_i[1]->data, blocklist_q[1]->data);
copy_to_fft_buffer1(pFFT_buffer+0x200, blocklist_i[2]->data, blocklist_q[2]->data);
copy_to_fft_buffer1(pFFT_buffer+0x300, blocklist_i[3]->data, blocklist_q[3]->data);
copy_to_fft_buffer1(pFFT_buffer+0x400, blocklist_i[4]->data, blocklist_q[4]->data);
copy_to_fft_buffer1(pFFT_buffer+0x500, blocklist_i[5]->data, blocklist_q[5]->data);
copy_to_fft_buffer1(pFFT_buffer+0x600, blocklist_i[6]->data, blocklist_q[6]->data);
copy_to_fft_buffer1(pFFT_buffer+0x700, blocklist_i[7]->data, blocklist_q[7]->data);
copy_to_fft_buffer1(pFFT_buffer+0x800, blocklist_i[8]->data, blocklist_q[8]->data);
copy_to_fft_buffer1(pFFT_buffer+0x900, blocklist_i[9]->data, blocklist_q[9]->data);
copy_to_fft_buffer1(pFFT_buffer+0xA00, blocklist_i[10]->data, blocklist_q[10]->data);
copy_to_fft_buffer1(pFFT_buffer+0xB00, blocklist_i[11]->data, blocklist_q[11]->data);
copy_to_fft_buffer1(pFFT_buffer+0xC00, blocklist_i[12]->data, blocklist_q[12]->data);
copy_to_fft_buffer1(pFFT_buffer+0xD00, blocklist_i[13]->data, blocklist_q[13]->data);
copy_to_fft_buffer1(pFFT_buffer+0xE00, blocklist_i[14]->data, blocklist_q[14]->data);
copy_to_fft_buffer1(pFFT_buffer+0xF00, blocklist_i[15]->data, blocklist_q[15]->data);
copy_to_fft_buffer1(pFFT_buffer+0x1000, blocklist_i[16]->data, blocklist_q[16]->data);
copy_to_fft_buffer1(pFFT_buffer+0x1100, blocklist_i[17]->data, blocklist_q[17]->data);
copy_to_fft_buffer1(pFFT_buffer+0x1200, blocklist_i[18]->data, blocklist_q[18]->data);
copy_to_fft_buffer1(pFFT_buffer+0x1300, blocklist_i[19]->data, blocklist_q[19]->data);
copy_to_fft_buffer1(pFFT_buffer+0x1400, blocklist_i[20]->data, blocklist_q[20]->data);
copy_to_fft_buffer1(pFFT_buffer+0x1500, blocklist_i[21]->data, blocklist_q[21]->data);
copy_to_fft_buffer1(pFFT_buffer+0x1600, blocklist_i[22]->data, blocklist_q[22]->data);
copy_to_fft_buffer1(pFFT_buffer+0x1700, blocklist_i[23]->data, blocklist_q[23]->data);
copy_to_fft_buffer1(pFFT_buffer+0x1800, blocklist_i[24]->data, blocklist_q[24]->data);
copy_to_fft_buffer1(pFFT_buffer+0x1900, blocklist_i[25]->data, blocklist_q[25]->data);
copy_to_fft_buffer1(pFFT_buffer+0x1A00, blocklist_i[26]->data, blocklist_q[26]->data);
copy_to_fft_buffer1(pFFT_buffer+0x1B00, blocklist_i[27]->data, blocklist_q[27]->data);
copy_to_fft_buffer1(pFFT_buffer+0x1C00, blocklist_i[28]->data, blocklist_q[28]->data);
copy_to_fft_buffer1(pFFT_buffer+0x1D00, blocklist_i[29]->data, blocklist_q[29]->data);
copy_to_fft_buffer1(pFFT_buffer+0x1E00, blocklist_i[30]->data, blocklist_q[30]->data);
copy_to_fft_buffer1(pFFT_buffer+0x1F00, blocklist_i[31]->data, blocklist_q[31]->data);
// Apply the window function, if any, to the time series. Half size window buffer.
if(wNum!=NULL && pWindow)
{
for (int i=0; i < 2048; i++) {
*(pFFT_buffer + 2*i) *= *(pWindow + i); // real
*(pFFT_buffer + 2*i+1) *= *(pWindow + i); // imag
}
for (int i=0; i < 2048; i++) { // Second half
*(pFFT_buffer + 8191 - 2*i) *= *(pWindow + i);
*(pFFT_buffer + 8190 - 2*i) *= *(pWindow + i);
}
}
// 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)
// I & O are real/imag interleaved in 8192-float point array p1.
arm_cfft_f32(&Sfft, pFFT_buffer, 0, 1);
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]);
release(blocklist_i[8]); release(blocklist_q[8]);
release(blocklist_i[9]); release(blocklist_q[9]);
release(blocklist_i[10]); release(blocklist_q[10]);
release(blocklist_i[11]); release(blocklist_q[11]);
release(blocklist_i[12]); release(blocklist_q[12]);
release(blocklist_i[13]); release(blocklist_q[13]);
release(blocklist_i[14]); release(blocklist_q[14]);
release(blocklist_i[15]); release(blocklist_q[15]);
blocklist_i[0] = blocklist_i[16];
blocklist_i[1] = blocklist_i[17];
blocklist_i[2] = blocklist_i[18];
blocklist_i[3] = blocklist_i[19];
blocklist_i[4] = blocklist_i[20];
blocklist_i[5] = blocklist_i[21];
blocklist_i[6] = blocklist_i[22];
blocklist_i[7] = blocklist_i[23];
blocklist_i[8] = blocklist_i[24];
blocklist_i[9] = blocklist_i[25];
blocklist_i[10] = blocklist_i[26];
blocklist_i[11] = blocklist_i[27];
blocklist_i[12] = blocklist_i[28];
blocklist_i[13] = blocklist_i[29];
blocklist_i[14] = blocklist_i[30];
blocklist_i[15] = blocklist_i[31];
blocklist_q[0] = blocklist_q[16];
blocklist_q[1] = blocklist_q[17];
blocklist_q[2] = blocklist_q[18];
blocklist_q[3] = blocklist_q[19];
blocklist_q[4] = blocklist_q[20];
blocklist_q[5] = blocklist_q[21];
blocklist_q[6] = blocklist_q[22];
blocklist_q[7] = blocklist_q[23];
blocklist_q[8] = blocklist_q[24];
blocklist_q[9] = blocklist_q[25];
blocklist_q[10] = blocklist_q[26];
blocklist_q[11] = blocklist_q[27];
blocklist_q[12] = blocklist_q[28];
blocklist_q[13] = blocklist_q[29];
blocklist_q[14] = blocklist_q[30];
blocklist_q[15] = blocklist_q[31];
state = 16;
break; // From case 31
} // End of switch & case 31
} // End update()
// End, if Teensy 4.x
#endif

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analyze_fft4096_iqem_F32.h
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/*
* analyze_fft4096_iqem_F32.h Assembled by Bob Larkin 9 Mar 2021
*
* External Memory **** BETA TEST VERSION - NOT FULLY TESTED **** <<<<<<<<<<
*
* Note: Teensy 4.x Only, 3.x not supported
*
* Does Fast Fourier Transform of a 4096 point complex (I-Q) input.
* Output is one of three measures of the power in each of the 4096
* 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 2048 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
*
* 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 4096 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.
*
* Memory for IQem FFT. The large blocks of memory must be declared in the INO.
* This typically looks like:
* float32_t fftOutput[4096]; // Array used for FFT Output to the INO program
* float32_t window[2048]; // Windows reduce sidelobes with FFT's *Half Size*
* float32_t fftBuffer[8192]; // Used by FFT, 4096 real, 4096 imag, interleaved
* float32_t sumsq[4096]; // Required ONLY if power averaging is being done
*
* These blocks of memory are communicated to the FFT in the object creation, that
* might look like:
* AudioAnalyzeFFT4096_IQEM_F32 myFFT(fftOutput, window, fftBuffer);
* or, if power averaging is used, the extra parameter is needed as:
* AudioAnalyzeFFT4096_IQEM_F32 myFFT(fftOutput, window, fftBuffer, sumsq);
*
* The memory arrays must be declared before the FFT object. About 74 kBytes are
* required if power averaging is used and about 58 kBytes without power averaging.
*
* In addition, this requires 64 AudioMemory_F32 which work out to about an
* additional 33 kBytesof memory.
*
* If several FFT sizes are used, one at a time, the memory can be shared. Probably
* the simplest way to do this with a Teensy is to set up C-language unions.
*
* 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
* 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=0 in middle, f=fs/2 on left edge
* If xAxis=1 f=0 in middle, f=fs/2 on right edge
* If xAxis=2 f=0 on right edge, f=fs/2 in middle
* If xAxis=3 f=0 on left edge, f=fs/2 in middle
* If there is 180 degree phase shift to I or Q these all get reversed.
* xAxis=1 is a mathemetically consistent method. It has positive frequencies
* on the right and negative ones on the left. The center is half the sample
* rate, both + and -. Uniormly sampled data lives in this circular world.rate.
*
* Timing, max is longest update() time:
* T4.0 Windowed, dBFS Out, 987 uSec <<<<<<CHECK
*
* Windows: The FFT window array memory is provided by the INO. Three common and
* useful window functions, plus no window, can be filled into the array by calling
* one of the following:
* windowFunction(AudioWindowNone);
* windowFunction(AudioWindowHanning4096);
* windowFunction(AudioWindowKaiser4096);
* windowFunction(AudioWindowBlackmanHarris4096);
* See: https://en.wikipedia.org/wiki/Window_function
*
* To use an alternate window function, just fill it into the array, window, above.
* It is only half of the window (2048 floats). It looks like a full window
* function with the righ half missing. It should start with small
* values on the left (near[0]) and go to 1.0 at the right ([2048]).
*
* As with all library FFT's this one provides overlapping time series. This
* tends to compensate for the attenuation at the window edges when doing a sequence
* of FFT's. For that reason there can be a new FFT result every 2048 time
* series data points.
*
* 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 4096^2/4 = about 4 million without windowing.
* Windowing loss cuts this down. The RMS level can growwithout windowing to
* 4096. The dBFS has been scaled to make this max value 0 dBFS by
* removing 66.2 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.
*/
/* Info
* __MK20DX128__ T_LC; __MKL26Z64__ T3.0; __MK20DX256__T3.1 and T3.2
* __MK64FX512__) T3.5; __MK66FX1M0__ T3.6; __IMXRT1062__ T4.0 and T4.1 */
#ifndef analyze_fft4096_iqem_h_
#define analyze_fft4096_iqem_h_
// *************** TEENSY 4.X ONLY ****************
#if defined(__IMXRT1062__)
#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 AudioWindowHanning4096 1
#define AudioWindowKaiser4096 2
#define AudioWindowBlackmanHarris4096 3
class AudioAnalyzeFFT4096_IQEM_F32 : public AudioStream_F32 {
//GUI: inputs:2, outputs:0 //this line used for automatic generation of GUI node
//GUI: shortName:FFT4096IQem
public:
AudioAnalyzeFFT4096_IQEM_F32 // Without sumsq in call for averaging
(float32_t* _pOutput, float32_t* _pWindow, float32_t* _pFFT_buffer) :
AudioStream_F32(2, inputQueueArray) {
pOutput = _pOutput;
pWindow = _pWindow;
pFFT_buffer = _pFFT_buffer;
pSumsq = NULL;
// 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_len4096; // This is one of the structures
useHanningWindow();
}
AudioAnalyzeFFT4096_IQEM_F32 // Constructor to include sumsq power averaging.
(float32_t* _pOutput, float32_t* _pWindow, float32_t* _pFFT_buffer,
float32_t* _pSumsq) :
AudioStream_F32(2, inputQueueArray) {
pOutput = _pOutput;
pWindow = _pWindow;
pFFT_buffer = _pFFT_buffer;
pSumsq = _pSumsq;
// 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_len4096; // 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>4095 || binNumber<0) return 0.0;
return *(pOutput + 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 > 4095) return 0.0;
if (binLast > 4095) binLast = 4095;
float sum = 0;
do {
sum += *(pOutput + binFirst++);
} while (binFirst <= binLast);
return sum;
}
// Sets None, Hann, or Blackman-Harris window with no parameter
int windowFunction(int _wNum) {
wNum = _wNum;
if(wNum == AudioWindowKaiser4096)
return -1; // Kaiser needs the kdb
windowFunction(wNum, 0.0f);
return 0;
}
int windowFunction(int _wNum, float _kdb) { // Kaiser case
float kd;
wNum = _wNum;
if (wNum == AudioWindowKaiser4096) {
if(_kdb<20.0f)
kd = 20.0f;
else
kd = _kdb;
useKaiserWindow(kd);
}
else if (wNum == AudioWindowBlackmanHarris4096)
useBHWindow();
else
useHanningWindow(); // Default
return 0;
}
// Number of FFT averaged in the output
void setNAverage(int _nAverage) {
if(!(pSumsq==NULL)) // We can average because we have memory.
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:
float32_t *pOutput, *pWindow, *pFFT_buffer;
float32_t *pSumsq;
int wNum = AudioWindowHanning4096;
uint8_t state = 0;
bool outputflag = false;
audio_block_f32_t *inputQueueArray[2];
audio_block_f32_t *blocklist_i[32];
audio_block_f32_t *blocklist_q[32];
// 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
// This can be used with zero-bias frequency interpolation.
// pWidow points to INO supplied buffer. 4096 for now. MAKE 2048 <<<<<<<<<<<<<<<<
void useHanningWindow(void) {
if(!pWindow) return; // No placefor a window
for (int i=0; i < 2048; i++) {
// 2*PI/4095 = 0.00153435538
*(pWindow + i) = 0.5*(1.0 - cosf(0.00153435538f*(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) {
if(!pWindow) return;
for (int i=0; i < 2048; i++) {
float kx = 0.00153435538f; // 2*PI/4095
int ix = (float) i;
*(pWindow + 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(!pWindow) return;
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<2048; n++) {
xn2 = 0.5f+(float32_t)n;
// 4/(4095^2) = 2.3853504E-7
xn2 = 2.3853504E-7*xn2*xn2;
*(pWindow + 2047 - n) = kbes*(mathEqualizer.i0f(beta*sqrtf(1.0-xn2)));
}
}
};
#endif
#endif

94
examples/TestFFT4096iqEM/TestFFT4096iqEM.ino
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@ -0,0 +1,94 @@
// TestFFT2048iqEM.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 4096 bins in
// dB relative to Sine Wave Full Scale
// EXTERNAL MEMORY FFT
// Public Domain
#include "OpenAudio_ArduinoLibrary.h"
#include "AudioStream_F32.h"
// Memory for IQ FFT
float32_t fftOutput[4096]; // Array to allow fftBuffer[] to be available for new in data
float32_t window[2048]; // Half size window storage
float32_t fftBuffer[8192]; // Used for FFT, 4096 real, 4096 imag, interleaved
float32_t sumsq[4096]; // Required if power averaging is being done
int jj;
// GUItool: begin automatically generated code
AudioSynthSineCosine_F32 sine_cos1; //xy=76,532
// Optional
// (float32_t* _pOutput, float32_t* _pWindow, float32_t* _pFFT_buffer, float32_t* _pSumsq)
//AudioAnalyzeFFT4096_IQEM_F32 FFT4096iqEM1(fftOutput, window, fftBuffer); //xy=243,532
AudioAnalyzeFFT4096_IQEM_F32 FFT4096iqEM1(fftOutput, window, fftBuffer, sumsq); // w/ power ave
AudioOutputI2S_F32 audioOutI2S1; //xy=246,591
AudioConnection_F32 patchCord1(sine_cos1, 0, FFT4096iqEM1, 0);
AudioConnection_F32 patchCord2(sine_cos1, 1, FFT4096iqEM1, 1);
// GUItool: end automatically generated code
void setup(void) {
Serial.begin(9600);
delay(1000);
// The 4096 complex FFT needs 32 F32 memory for real and 32 for imag.
// Set memory to more than 64, depending on other useage.
AudioMemory_F32(100);
Serial.println("FFT4096IQem 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(1000.0f);
// elect the output format, FFT_RMS, FFT_POWER, or FFT_DBFS
FFT4096iqEM1.setOutputType(FFT_DBFS);
// Select the wndow function, designed by FFT object
//FFT4096iqEM1.windowFunction(AudioWindowNone);
//FFT4096iqEM1.windowFunction(AudioWindowHanning4096);
//FFT4096iqEM1.windowFunction(AudioWindowKaiser4096, 55.0f);
FFT4096iqEM1.windowFunction(AudioWindowBlackmanHarris4096);
// Uncomment to Serial print window function
// for (int i=0; i<2048; i++) Serial.println(*(window+i), 7);
// xAxis, bit 0 left/right; bit 1 low to high; default 0X03
FFT4096iqEM1.setXAxis(0X01);
// In order to average powers, a buffer for sumsq[4096] must be
// globally declared and that pointer, sumsq, set as the last
// parameter in the object creation. Then the following will
// cause averaging of 4 powers:
FFT4096iqEM1.setNAverage(20);
jj = 0; // This is todelay data gathering to get steady state
}
void loop(void) {
static bool doPrint=true;
float *pPwr;
delay(10);
// Print output, once
if( FFT4096iqEM1.available() && doPrint ) {
if(jj++ < 3)return;
for(int i=0; i<4096; i++)
{
Serial.print((int)((float32_t)i * 44100.0/4096.0));
Serial.print(" ");
Serial.println(*(fftOutput + i), 8 );
}
doPrint = false;
}
Serial.print(" Audio MEM Float32 Peak: ");
Serial.println(AudioMemoryUsageMax_F32());
delay(500);
}

1
keywords.txt
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@ -19,6 +19,7 @@ setXAxis KEYWORD2
AudioAnalyzeFFT1024_F32 KEYWORD1
AudioAnalyzeFFT2048_F32 KEYWORD1
AudioAnalyzeFFT4096_F32 KEYWORD1
AudioAnalyzeFFT4096_IQEM_F32 KEYWORD1
AudioAnalyzePeak_F32 KEYWORD1
readPeakToPeak KEYWORD2

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