/* * Analyze_fft2048_iq_F32.h Assembled by Bob Larkin 8 Mar 2021 * * Note: Teensy 4.x Only, 3.x not supported * * Does Fast Fourier Transform of a 2048 point complex (I-Q) input. * Output is one of three measures of the power in each of the 2048 * 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 512 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 * * Soon: F32 audio outputs for I & Q * * Conversion Copyright (c) 2021 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 2048 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. * * 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 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 * If there is 180 degree phase shift to I or Q these all get reversed. * * Timing, max is longest update() time: * T4.0 Windowed, dBFS Out, 987 uSec * * 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 2048^2/4 = 1048576 without windowing. * Windowing loss cuts this down. The RMS level can grow to sqrt(1048576) * or 2048. The dBFS has been scaled to make this max value 0 dBFS by * removing 60.2 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. */ #ifndef analyze_fft2048iq_h_ #define analyze_fft2048iq_h_ // *************** TEENSY 4.X ONLY **************** // Use 1024 size, or smaller, for Teensy 3.x #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 AudioWindowHanning2048 1 #define AudioWindowKaiser2048 2 #define AudioWindowBlackmanHarris2048 3 class AudioAnalyzeFFT2048_IQ_F32 : public AudioStream_F32 { //GUI: inputs:2, outputs:4 //this line used for automatic generation of GUI node //GUI: shortName:FFT2048IQ public: AudioAnalyzeFFT2048_IQ_F32() : AudioStream_F32(2, 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 // 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_len2048; // 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>2047 || 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 > 2047) return 0.0; if (binLast > 2047) binLast = 2047; float sum = 0; do { sum += output[binFirst++]; } while (binFirst <= binLast); return sum; } // Sets None, Hann, or Blackman-Harris window with no parameter int windowFunction(int wNum) { if(wNum == AudioWindowKaiser2048) 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 == AudioWindowKaiser2048) { if(_kdb<20.0f) kd = 20.0f; else kd = _kdb; useKaiserWindow(kd); } else if (wNum == AudioWindowBlackmanHarris2048) useBHWindow(); else useHanningWindow(); // Default return 0; } // Fast pointer transfer. Be aware that the data will go away // after the next 256 data points occur. float* getData(void) { // available() sets outputflag false 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<2048; i++) *p++ = *pwin++; // Copy for the FFT } // Number of FFT averaged in the output void setNAverage(int _nAverage) { 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: float output[2048]; float window[2048]; float *pWin = window; float fft_buffer[4096]; float sumsq[2048]; // Avoid re-use of output[] uint8_t state = 0; bool outputflag = false; audio_block_f32_t *inputQueueArray[2]; audio_block_f32_t *blocklist_i[16]; audio_block_f32_t *blocklist_q[16]; // 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; // The Hann window is a good all-around window void useHanningWindow(void) { for (int i=0; i < 2048; i++) { // 2*PI/2047 = 0.00306946 window[i] = 0.5*(1.0 - cosf(0.00306946f*(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 < 2048; i++) { float kx = 0.00306946f; // 2*PI/2047 int ix = (float) i; window[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 (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<512; n++) { xn2 = 0.5f+(float32_t)n; // 4/(1023^2)=0.00000382215877f // 4/(2047^2) = 9.546063E-7; xn2 = 9.546063E-7*xn2*xn2; window[511 - n]=kbes*(mathEqualizer.i0f(beta*sqrtf(1.0-xn2))); window[512 + n] = window[511 - n]; } } }; #endif #endif