


/*




* 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 (IQ) 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 BlackmanHarris.




* * Multiple binsum 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 nonaudio (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




* inclass 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 Clanguage 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




*




* xAxis 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 BlackmanHarris 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 allaround window




// This can be used with zerobias 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));




}




}








// BlackmanHarris 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*kdb0.0002841*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) = 2.3853504E7




xn2 = 2.3853504E7*xn2*xn2;




*(pWindow + 2047  n) = kbes*(mathEqualizer.i0f(beta*sqrtf(1.0xn2)));




}




}




};




#endif




#endif
