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351 lines
14 KiB
351 lines
14 KiB
/*


* 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


