For those interested, here is my best illustration of the pureSpectrum filtering. There are two inputs coming from a sine/cosine pair,AudioSynthSineCosine_F32, running at 1000 Hz. This is going to a 4096 point FFT with complex I-Q inputs. The FFT is running with a Blackman-harris window to give as much view off frequency as possible. The complex input FFT distinguishes between positive and negative frequecies and we plot this with zero in the middle.
The dark blue trace is with the regular sine (and cosine) generators and various responses are seen up to about -110 dB below the carrier. Normally this is at a level that no one would care about! In this case, the question was whether these responses were due to the Sine wave process of the FFT one. Turning on the pureSpectrum filtering suggests they were due to the Sine generator, as the magenta trace is down at the windowing level, with the spurs more-or-less gone. Here is the graph:
The INO that was used is
Code:
// TestFFT2048iqEM.ino for Teensy 4.x
// *** EXTERNAL MEMORY VERSION of 4095 FFT ***
// Bob Larkin 9 March 2021
// Generate Sin and Cosine pair and input to IQ FFT.
// Serial Print outputs of all 4096 bins.
//
// Public Domain
#include "OpenAudio_ArduinoLibrary.h"
#include "AudioStream_F32.h"
// Memory for IQ FFT
float32_t fftOutput[4096]; // Array to allow fftBuffer[] to be available for new in data
float32_t window[2048]; // Half size window storage
float32_t fftBuffer[8192]; // Used for FFT, 4096 real, 4096 imag, interleaved
float32_t sumsq[4096]; // Required if power averaging is being done
int jj;
// GUItool: begin automatically generated code
AudioSynthSineCosine_F32 sine_cos1; //xy=76,532
// Optional
// (float32_t* _pOutput, float32_t* _pWindow, float32_t* _pFFT_buffer, float32_t* _pSumsq)
//AudioAnalyzeFFT4096_IQEM_F32 FFT4096iqEM1(fftOutput, window, fftBuffer); //xy=243,532
AudioAnalyzeFFT4096_IQEM_F32 FFT4096iqEM1(fftOutput, window, fftBuffer, sumsq); // w/ power ave
AudioOutputI2S_F32 audioOutI2S1; //xy=246,591
AudioConnection_F32 patchCord1(sine_cos1, 0, FFT4096iqEM1, 0);
AudioConnection_F32 patchCord2(sine_cos1, 1, FFT4096iqEM1, 1);
// GUItool: end automatically generated code
void setup(void) {
Serial.begin(9600);
delay(1000);
// The 4096 complex FFT needs 32 F32 memory for real and 32 for imag.
// Set memory to more than 64, depending on other useage.
AudioMemory_F32(100);
Serial.println("FFT4096IQem Test");
sine_cos1.amplitude(1.0f); // Initialize Waveform Generator
// Engage the identical BP Filters on sine/cosine outputs (true).
sine_cos1.pureSpectrum(true);
// Pick T4.x bin center
// sine_cos1.frequency(689.0625f);
// or pick any old frequency
sine_cos1.frequency(1000.0f);
// elect the output format, FFT_RMS, FFT_POWER, or FFT_DBFS
FFT4096iqEM1.setOutputType(FFT_DBFS);
// Select the wndow function, designed by FFT object
//FFT4096iqEM1.windowFunction(AudioWindowNone);
//FFT4096iqEM1.windowFunction(AudioWindowHanning4096);
//FFT4096iqEM1.windowFunction(AudioWindowKaiser4096, 55.0f);
FFT4096iqEM1.windowFunction(AudioWindowBlackmanHarris4096);
// Uncomment to Serial print window function
// for (int i=0; i<2048; i++) Serial.println(*(window+i), 7);
// xAxis, See leadin discussion at analyze_fft4096_iqem_F32.h
FFT4096iqEM1.setXAxis(0X03); // 0X03 default
// In order to average powers, a buffer for sumsq[4096] must be
// globally declared and that pointer, sumsq, set as the last
// parameter in the object creation. Then the following will
// cause averaging of 4 powers:
FFT4096iqEM1.setNAverage(4);
jj = 0; // This is to delay data gathering to get steady state
}
void loop(void) {
static bool doPrint=true;
float *pPwr;
// Print output, once
if( FFT4096iqEM1.available() && jj++>2 && doPrint ) {
if(jj++ < 3)return;
for(int i=0; i<4096; i++)
{
// Serial.print((int)((float32_t)i * 44100.0/4096.0)); // Print freq
Serial.print(i); // FFT Output index (0, 4095)
Serial.print(" ");
Serial.println(*(fftOutput + i), 8 );
}
doPrint = false;
}
if(doPrint)
{
Serial.print(" Audio MEM Float32 Peak: ");
Serial.println(AudioMemoryUsageMax_F32());
}
delay(100);
}
The magenta response at -1000 Hz is interesting. It is from before the FFT, but only present when the filters are in place. The coefficients for the sine and cos filters are identical. The response is still due to differences in the 90 degree relationship (at the 10^-6 sort of level). Fun!
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