/*
* analyze_fft4096_iqem_F32.h Assembled by Bob Larkin 18 Feb 2022
*
* External Memory - INO supplied memory arrays. Windows are half width.
*
* 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) 2022 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 kBytes of 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=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
*
* Timing, maximum microseconds per update() over the 16 updates,
* and the average percent processor use for 44.1 kHz sample rate and Nave=1:
* T4.0 Windowed, dBFS Out (FFT_DBFS), 710 uSec, Ave 4.64%
* T4.0 Windowed, Power Out (FFT_POWER), 530 uSec, Ave 1.7%
* T4.0 Windowed, RMS Out, (FFT_RMS) 530 uSec, Ave 1.92%
* Nave greater than 1 decreases the average processor load.
*
* 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 right 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.
*
* 22 Feb 2022 Fixed xAxis error, twice!
*/
/* 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; // See discussion above
// 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