/* analyze_fft1024_F32.h Converted from Teensy I16 Audio Library
*
* 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.
*/
/* Translated from I16 to F32. Bob Larkin 16 Feb 2021
* Does real input FFT of 1024 points. Output is not audio, and is magnitude
* only. Multiple 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 setOutputType(int _type)
* void setNAverage(int nAverage)
*
* Timing, max is longest update() time. Comparison is using full complex FFT
* and no load sharing on "states".
* T3.6 Windowed, Power Out, 682 uSec (was 975 w/ 1024 FFT)
* T3.6 Windowed, dBFS out, 834 uSec (was 1591 w/1024 FFT)
* No Window saves 60 uSec on T3.6 for any output.
* T4.0 Windowed, Power Out, 54 uSec (was 156 w/1024 FFT)
* T4.0 Windowed, dBFS Out, 203 uSec (was 302 w/1024 FFT)
* 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 1024^2/4 = 262144 without windowing.
* Windowing loss cuts this down. The RMS level can grow to sqrt(262144)
* or 512. The dBFS has been scaled to make this max value 0 dBFS by
* removing 54.2 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.
*/
// Fixed float/int problem in read(first, last). RSL 3 Mar 21
// Converted to using half-size FFT for real input, with no zero inputs.
// See E. Oran Brigham and many other FFT references. 16 March 2021 RSL
// Moved post-FFT calculations to state 4 to load share. RSL 18 Mar 2021
#ifndef analyze_fft1024_F32_h_
#define analyze_fft1024_F32_h_
#include "Arduino.h"
#include "AudioStream_F32.h"
#include "arm_math.h"
#include "mathDSP_F32.h"
#if defined(__IMXRT1062__)
#include "arm_const_structs.h"
#endif
// Doing an FFT with NFFT real inputs
#define NFFT 1024
#define NFFT_M1 NFFT-1
#define NFFT_D2 NFFT/2
#define NFFT_D2M1 (NFFT/2)-1
#define NFFT_X2 NFFT*2
#define FFT_PI 3.14159265359f
#define FFT_2PI 6.28318530718f
#define FFT_RMS 0
#define FFT_POWER 1
#define FFT_DBFS 2
#define NO_WINDOW 0
#define AudioWindowNone 0
#define AudioWindowHanning1024 1
#define AudioWindowKaiser1024 2
#define AudioWindowBlackmanHarris1024 3
class AudioAnalyzeFFT1024_F32 : public AudioStream_F32 {
//GUI: inputs:1, outputs:0 //this line used for automatic generation of GUI node
//GUI: shortName:FFT1024
public:
AudioAnalyzeFFT1024_F32() : AudioStream_F32(1, 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
#if defined(__IMXRT1062__)
// 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_len512; // Like this. Changes with size <<<
#else
arm_cfft_radix2_init_f32(&fft_inst, NFFT_D2, 0, 1); // for T3.x (check radix2/radix4)<<<
#endif
// This class is always 128 block size. Any sample rate. No use of "settings"
useHanningWindow();
// Factors for using half size complex FFT
for(int n=0; n<NFFT_D2; n++) {
sinN[n] = sinf(FFT_PI*((float)n)/((float)NFFT_D2));
cosN[n] = cosf(FFT_PI*((float)n)/((float)NFFT_D2));
}
}
// Inform that the output is available for read()
bool available() {
if (outputflag == true) {
outputflag = false;
return true;
}
return false;
}
// Output data from a single bin is transferred
float read(unsigned int binNumber) {
if (binNumber>NFFT_D2M1 || 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 > NFFT_D2M1) return 0.0;
if (binLast > NFFT_D2M1) binLast = NFFT_D2M1;
float sum = 0.0f;
do {
sum += output[binFirst++];
} while (binFirst <= binLast);
return sum;
}
int windowFunction(int wNum) {
if(wNum == AudioWindowKaiser1024) // Changes with size <<<
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 == AudioWindowKaiser1024) { // Changes with size <<<
if(_kdb<20.0f)
kd = 20.0f;
else
kd = _kdb;
useKaiserWindow(kd);
}
else if (wNum == AudioWindowBlackmanHarris1024) // Changes with size <<<
useBHWindow();
else
useHanningWindow(); // Default
return 0;
}
// Fast pointer transfer. Be aware that the data will go away
// after the next 512 data points occur.
float* getData(void) {
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<NFFT; i++)
*p++ = *pwin++;
}
// Output RMS (default) Power or dBFS
void setOutputType(int _type) {
outputType = _type;
}
// Output power (non-coherent) averaging
void setNAverage(int _nAverage) {
nAverage = _nAverage;
}
virtual void update(void);
private:
float output[NFFT_D2];
float sumsq[NFFT_D2]; // Accumulates averages of outputs
float window[NFFT];
float *pWin = window;
float fft_buffer[NFFT];
// The cosN and sinN would seem to be twidddle factors. Someday
// look at this and see if they can be stolen from arm math/DSP.
float cosN[NFFT_D2];
float sinN[NFFT_D2];
audio_block_f32_t *blocklist[8];
uint8_t state = 0;
bool outputflag = false;
audio_block_f32_t *inputQueueArray[1];
#if defined(__IMXRT1062__)
// For T4.x, 512 length for real 1024 input, etc.
// const static arm_cfft_instance_f32 arm_cfft_sR_f32_len512;
arm_cfft_instance_f32 Sfft;
#else
arm_cfft_radix2_instance_f32 fft_inst; // Check radix2/radix4 <<<
#endif
int outputType = FFT_RMS; //Same type as I16 version init
int nAverage = 1;
int count = 0; // used to average for nAverage of powers
// The Hann window is a good all-around window
void useHanningWindow(void) {
for (int i=0; i < NFFT; i++) {
float kx = FFT_2PI/((float)NFFT_M1); // 0.006141921 for 1024
window[i] = 0.5f*(1.0f - cosf(kx*(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 < NFFT; i++) {
float kx = FFT_2PI/((float)NFFT_M1); // 0.006141921 for 1024
int ix = (float) i;
window[i] = 0.35875f -
0.48829f*cosf( kx*ix) +
0.14128f*cosf(2.0f*kx*ix) -
0.01168f*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<NFFT_D2; n++) {
xn2 = 0.5f+(float32_t)n;
float kx = 4.0f/(((float)NFFT_M1) * ((float)NFFT_M1)); // 0.00000382215877f for 1024
xn2 = kx*xn2*xn2;
window[NFFT_D2M1 - n]=kbes*(mathEqualizer.i0f(beta*sqrtf(1.0-xn2)));
window[NFFT_D2 + n] = window[NFFT_D2M1 - n];
}
}
};
#endif