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351 lines
14 KiB
351 lines
14 KiB
/*
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* analyze_fft4096_iqem_F32.h Assembled by Bob Larkin 18 Feb 2022
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*
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* External Memory - INO supplied memory arrays. Windows are half width.
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*
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* Note: Teensy 4.x ONLY, 3.x not supported
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*
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* Does Fast Fourier Transform of a 4096 point complex (I-Q) input.
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* Output is one of three measures of the power in each of the 4096
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* output bins, Power, RMS level or dB relative to a full scale
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* sine wave. Windowing of the input data is provided for to reduce
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* spreading of the power in the output bins. All inputs are Teensy
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* floating point extension (_F32) and all outputs are floating point.
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*
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* Features include:
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* * I and Q inputs are OpenAudio_Arduino Library F32 compatible.
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* * FFT output for every 2048 inputs to overlapped FFTs to
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* compensate for windowing.
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* * Windowing None, Hann, Kaiser and Blackman-Harris.
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* * Multiple bin-sum output to simulate wider bins.
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* * Power averaging of multiple FFT
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*
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* Conversion Copyright (c) 2022 Bob Larkin
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* Same MIT license as PJRC:
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*
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* From original real FFT:
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* Audio Library for Teensy 3.X
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* Copyright (c) 2014, Paul Stoffregen, paul@pjrc.com
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*
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* Development of this audio library was funded by PJRC.COM, LLC by sales of
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* Teensy and Audio Adaptor boards. Please support PJRC's efforts to develop
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* open source software by purchasing Teensy or other PJRC products.
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*
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* Permission is hereby granted, free of charge, to any person obtaining a copy
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* of this software and associated documentation files (the "Software"), to deal
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* in the Software without restriction, including without limitation the rights
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* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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* copies of the Software, and to permit persons to whom the Software is
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* furnished to do so, subject to the following conditions:
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*
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* The above copyright notice, development funding notice, and this permission
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* notice shall be included in all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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* THE SOFTWARE.
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*/
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/* Does complex input FFT of 4096 points. Multiple non-audio (via functions)
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* output formats of RMS (same as I16 version, and default),
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* Power or dBFS (full scale). Output can be bin by bin or a pointer to
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* the output array is available. Several window functions are provided by
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* in-class design, or a custom window can be provided from the INO.
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*
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* Memory for IQem FFT. The large blocks of memory must be declared in the INO.
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* This typically looks like:
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* float32_t fftOutput[4096]; // Array used for FFT Output to the INO program
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* float32_t window[2048]; // Windows reduce sidelobes with FFT's *Half Size*
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* float32_t fftBuffer[8192]; // Used by FFT, 4096 real, 4096 imag, interleaved
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* float32_t sumsq[4096]; // Required ONLY if power averaging is being done
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*
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* These blocks of memory are communicated to the FFT in the object creation, that
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* might look like:
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* AudioAnalyzeFFT4096_IQEM_F32 myFFT(fftOutput, window, fftBuffer);
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* or, if power averaging is used, the extra parameter is needed as:
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* AudioAnalyzeFFT4096_IQEM_F32 myFFT(fftOutput, window, fftBuffer, sumsq);
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*
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* The memory arrays must be declared before the FFT object. About 74 kBytes are
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* required if power averaging is used and about 58 kBytes without power averaging.
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*
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* In addition, this requires 64 AudioMemory_F32 which work out to about an
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* additional 33 kBytes of memory.
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*
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* If several FFT sizes are used, one at a time, the memory can be shared. Probably
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* the simplest way to do this with a Teensy is to set up C-language unions.
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*
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* Functions (See comments below and #defines above:
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* bool available()
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* float read(unsigned int binNumber)
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* float read(unsigned int binFirst, unsigned int binLast)
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* int windowFunction(int wNum)
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* int windowFunction(int wNum, float _kdb) // Kaiser only
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* void setNAverage(int NAve) // >=1
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* void setOutputType(int _type)
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* void setXAxis(uint8_t _xAxis) // 0, 1, 2, 3
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*
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* x-Axis direction and offset per setXAxis(xAxis) for sine to I
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* and cosine to Q:
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*
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* If xAxis=0 f=fs/2 in middle, f=0 on right edge
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* If xAxis=1 f=fs/2 in middle, f=0 on left edge
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* If xAxis=2 f=fs/2 on left edge, f=0 in middle
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* If xAxis=3 f=fs/2 on right edgr, f=0 in middle
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*
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* Timing, maximum microseconds per update() over the 16 updates,
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* and the average percent processor use for 44.1 kHz sample rate and Nave=1:
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* T4.0 Windowed, dBFS Out (FFT_DBFS), 710 uSec, Ave 4.64%
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* T4.0 Windowed, Power Out (FFT_POWER), 530 uSec, Ave 1.7%
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* T4.0 Windowed, RMS Out, (FFT_RMS) 530 uSec, Ave 1.92%
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* Nave greater than 1 decreases the average processor load.
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*
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* Windows: The FFT window array memory is provided by the INO. Three common and
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* useful window functions, plus no window, can be filled into the array by calling
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* one of the following:
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* windowFunction(AudioWindowNone);
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* windowFunction(AudioWindowHanning4096);
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* windowFunction(AudioWindowKaiser4096);
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* windowFunction(AudioWindowBlackmanHarris4096);
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* See: https://en.wikipedia.org/wiki/Window_function
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*
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* To use an alternate window function, just fill it into the array, window, above.
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* It is only half of the window (2048 floats). It looks like a full window
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* function with the right half missing. It should start with small
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* values on the left (near[0]) and go to 1.0 at the right ([2048]).
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*
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* As with all library FFT's this one provides overlapping time series. This
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* tends to compensate for the attenuation at the window edges when doing a sequence
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* of FFT's. For that reason there can be a new FFT result every 2048 time
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* series data points.
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*
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* Scaling:
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* Full scale for floating point DSP is a nebulous concept. Normally the
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* full scale is -1.0 to +1.0. This is an unscaled FFT and for a sine
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* wave centered in frequency on a bin and of FS amplitude, the power
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* at that center bin will grow by 4096^2/4 = about 4 million without windowing.
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* Windowing loss cuts this down. The RMS level can growwithout windowing to
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* 4096. The dBFS has been scaled to make this max value 0 dBFS by
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* removing 66.2 dB. With floating point, the dynamic range is maintained
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* no matter how it is scaled, but this factor needs to be considered
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* when building the INO.
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*
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* 22 Feb 2022 Fixed xAxis error, twice!
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*/
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/* Info:
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* __MK20DX128__ T_LC; __MKL26Z64__ T3.0; __MK20DX256__T3.1 and T3.2
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* __MK64FX512__) T3.5; __MK66FX1M0__ T3.6; __IMXRT1062__ T4.0 and T4.1 */
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#ifndef analyze_fft4096_iqem_h_
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#define analyze_fft4096_iqem_h_
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// *************** TEENSY 4.X ONLY ****************
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#if defined(__IMXRT1062__)
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#include "Arduino.h"
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#include "AudioStream_F32.h"
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#include "arm_math.h"
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#include "mathDSP_F32.h"
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#include "arm_const_structs.h"
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#define FFT_RMS 0
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#define FFT_POWER 1
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#define FFT_DBFS 2
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#define NO_WINDOW 0
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#define AudioWindowNone 0
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#define AudioWindowHanning4096 1
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#define AudioWindowKaiser4096 2
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#define AudioWindowBlackmanHarris4096 3
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class AudioAnalyzeFFT4096_IQEM_F32 : public AudioStream_F32 {
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//GUI: inputs:2, outputs:0 //this line used for automatic generation of GUI node
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//GUI: shortName:FFT4096IQem
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public:
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AudioAnalyzeFFT4096_IQEM_F32 // Without sumsq in call for averaging
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(float32_t* _pOutput, float32_t* _pWindow, float32_t* _pFFT_buffer) :
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AudioStream_F32(2, inputQueueArray) {
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pOutput = _pOutput;
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pWindow = _pWindow;
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pFFT_buffer = _pFFT_buffer;
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pSumsq = NULL;
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// Teensy4 core library has the right files for new FFT
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// arm CMSIS library has predefined structures of type arm_cfft_instance_f32
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Sfft = arm_cfft_sR_f32_len4096; // This is one of the structures
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useHanningWindow();
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}
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AudioAnalyzeFFT4096_IQEM_F32 // Constructor to include sumsq power averaging.
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(float32_t* _pOutput, float32_t* _pWindow, float32_t* _pFFT_buffer,
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float32_t* _pSumsq) :
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AudioStream_F32(2, inputQueueArray) {
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pOutput = _pOutput;
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pWindow = _pWindow;
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pFFT_buffer = _pFFT_buffer;
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pSumsq = _pSumsq;
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// Teensy4 core library has the right files for new FFT
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// arm CMSIS library has predefined structures of type arm_cfft_instance_f32
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Sfft = arm_cfft_sR_f32_len4096; // This is one of the structures
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useHanningWindow();
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}
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// There is no varient for "settings," as blocks other than 128 are
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// not supported and, nothing depends on sample rate so we don't need that.
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// Returns true when output data is available.
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bool available() {
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#if defined(__IMXRT1062__)
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if (outputflag == true) {
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outputflag = false; // No double returns
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return true;
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}
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return false;
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#else
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// Don't know how you got this far, but....
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Serial.println("Teensy 3.x NOT SUPPORTED");
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return false;
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#endif
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}
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// Returns a single bin output
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float read(unsigned int binNumber) {
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if (binNumber>4095 || binNumber<0) return 0.0;
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return *(pOutput + binNumber);
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}
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// Return sum of several bins. Normally use with power output.
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// This produces the equivalent of bigger bins.
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float read(unsigned int binFirst, unsigned int binLast) {
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if (binFirst > binLast) {
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unsigned int tmp = binLast;
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binLast = binFirst;
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binFirst = tmp;
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}
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if (binFirst > 4095) return 0.0;
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if (binLast > 4095) binLast = 4095;
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float sum = 0;
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do {
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sum += *(pOutput + binFirst++);
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} while (binFirst <= binLast);
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return sum;
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}
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// Sets None, Hann, or Blackman-Harris window with no parameter
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int windowFunction(int _wNum) {
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wNum = _wNum;
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if(wNum == AudioWindowKaiser4096)
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return -1; // Kaiser needs the kdb
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windowFunction(wNum, 0.0f);
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return 0;
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}
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int windowFunction(int _wNum, float _kdb) { // Kaiser case
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float kd;
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wNum = _wNum;
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if (wNum == AudioWindowKaiser4096) {
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if(_kdb<20.0f)
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kd = 20.0f;
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else
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kd = _kdb;
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useKaiserWindow(kd);
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}
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else if (wNum == AudioWindowBlackmanHarris4096)
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useBHWindow();
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else
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useHanningWindow(); // Default
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return 0;
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}
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// Number of FFT averaged in the output
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void setNAverage(int _nAverage) {
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if(!(pSumsq==NULL)) // We can average because we have memory.
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nAverage = _nAverage;
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}
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// Output RMS (default), power or dBFS (FFT_RMS, FFT_POWER, FFT_DBFS)
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void setOutputType(int _type) {
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outputType = _type;
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}
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// xAxis, bit 0 left/right; bit 1 low to high; default 0X03
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void setXAxis(uint8_t _xAxis) {
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xAxis = _xAxis;
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}
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virtual void update(void);
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private:
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float32_t *pOutput, *pWindow, *pFFT_buffer;
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float32_t *pSumsq;
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int wNum = AudioWindowHanning4096;
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uint8_t state = 0;
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bool outputflag = false;
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audio_block_f32_t *inputQueueArray[2];
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audio_block_f32_t *blocklist_i[32];
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audio_block_f32_t *blocklist_q[32];
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// For T4.x
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// const static arm_cfft_instance_f32 arm_cfft_sR_f32_len1024;
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arm_cfft_instance_f32 Sfft;
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int outputType = FFT_RMS; //Same type as I16 version init
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int count = 0;
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int nAverage = 1;
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uint8_t xAxis = 0x03; // See discussion above
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// The Hann window is a good all-around window
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// This can be used with zero-bias frequency interpolation.
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// pWidow points to INO supplied buffer. 4096 for now. MAKE 2048 <<<<<<<<<<<<<<<<
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void useHanningWindow(void) {
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if(!pWindow) return; // No placefor a window
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for (int i=0; i < 2048; i++) {
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// 2*PI/4095 = 0.00153435538
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*(pWindow + i) = 0.5*(1.0 - cosf(0.00153435538f*(float)i));
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}
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}
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// Blackman-Harris produces a first sidelobe more than 90 dB down.
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// The price is a bandwidth of about 2 bins. Very useful at times.
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void useBHWindow(void) {
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if(!pWindow) return;
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for (int i=0; i < 2048; i++) {
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float kx = 0.00153435538f; // 2*PI/4095
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int ix = (float) i;
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*(pWindow + i) = 0.35875 -
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0.48829*cosf( kx*ix) +
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0.14128*cosf(2.0f*kx*ix) -
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0.01168*cosf(3.0f*kx*ix);
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}
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}
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/* The windowing function here is that of James Kaiser. This has a number
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* of desirable features. The sidelobes drop off as the frequency away from a transition.
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* Also, the tradeoff of sidelobe level versus cutoff rate is variable.
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* Here we specify it in terms of kdb, the highest sidelobe, in dB, next to a sharp cutoff. For
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* calculating the windowing vector, we need a parameter beta, found as follows:
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*/
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void useKaiserWindow(float kdb) {
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float32_t beta, kbes, xn2;
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mathDSP_F32 mathEqualizer; // For Bessel function
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if(!pWindow) return;
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if (kdb < 20.0f)
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beta = 0.0;
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else
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beta = -2.17+0.17153*kdb-0.0002841*kdb*kdb; // Within a dB or so
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// Note: i0f is the fp zero'th order modified Bessel function (see mathDSP_F32.h)
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kbes = 1.0f / mathEqualizer.i0f(beta); // An additional derived parameter used in loop
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for (int n=0; n<2048; n++) {
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xn2 = 0.5f+(float32_t)n;
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// 4/(4095^2) = 2.3853504E-7
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xn2 = 2.3853504E-7*xn2*xn2;
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*(pWindow + 2047 - n) = kbes*(mathEqualizer.i0f(beta*sqrtf(1.0-xn2)));
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}
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}
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};
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#endif
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#endif
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