/* * 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