## Goertzel's Algorithm

This algorithm can be used to detect a frequency from sampled data.

Here is a link (http://www.mstarlabs.com/dsp/goertzel/goertzel.html).

Here is the preliminary code for a spectrum analyzer:

#include <stdio.h> #include <stdlib.h> #include <math.h> // Uses Daniil Guitelson's BGI library #include "graphics.h" // -lBGI -lgdi32 #define SampleFreq 125000 int main(void) { int N=250; double data[N]; double samples[N]; double freq; double s; double s_prev; double s_prev2; double coeff; double magn; int i; int gd=CUSTOM, gm=CUSTOM_MODE(700,700); initgraph(&gd, &gm, ""); setcolor(WHITE); int X1,Y1,X2,Y2; double scale,xmin,ymin,xmax,ymax; // Find the maximum and minimum data range xmin=0; ymin=0; xmax=50000; ymax=N; scale=1.1*(xmax-xmin>ymax-ymin?xmax-xmin:ymax-ymin); // Generate samples for (i=0;i<N;i++) { samples[i]=(50*sin(2*M_PI*i*3300/SampleFreq)+50*sin(2*M_PI*i*5700/SampleFreq)+50*sin(2*M_PI*i*25700/SampleFreq)+100); // Window the data // data[i]=samples[i]; // Straight Goertzel - not great // data[i]=samples[i]*(0.5-0.25*cos(2*M_PI*i/N)); // Hanning Window data[i]=samples[i]*(0.54-0.46*cos(2*M_PI*i/N)); // Hamming Window // data[i]=samples[i]*(0.426551-0.496561*cos(2*M_PI*i/N)+0.076848*cos(4*M_PI*i/N)); // Exact Blackman Window } // Scan frequencies for (freq=100;freq<=50000;freq+=100) { coeff=2*cos(2*M_PI*freq/SampleFreq); s_prev=0.0; s_prev2=0.0; for (i=0;i<N;i++) { // Goertzel s=data[i]+coeff*s_prev-s_prev2; s_prev2=s_prev; s_prev=s; } // Get magnitude magn=2*sqrt(s_prev2*s_prev2+s_prev*s_prev-coeff*s_prev*s_prev2)/N; printf("Freq: %6f Mag: %6.4f\n",freq,magn); // Plot data X1=(int)((freq-(xmin+xmax)/2)*700/scale+350); Y1=(int)((0+(ymin+ymax)/2)*700/scale+650); X2=(int)((freq-(xmin+xmax)/2)*700/scale+350); Y2=(int)((-magn*700/2+(ymin+ymax)/2)*700/scale+650); line(X1,Y1,X2,Y2); } getchar(); closegraph(); return 0; }

I have used Daniil Guitelson's BGI library (https://sourceforge.net/projects/openbgi/) for the graphics.

## Output

Here is the output showing the DC, 3300 Hz, 5700 Hz and 25700 Hz signals:

## Next Step

The next step is to port the code to a suitable Arduino board.

I have a number of DigiSpark (ATTiny85) boards and Nokia graphic displays.

So that is what I will likely use.

The ATTiny85 has an ADC sampling rate of 125 kHz.

A high ADC sampling rate is important.

AlanX

Hi Elliot,

I told my partner that someone thought my Spectrum Analyser was sexy!

She was horrified and responded "another madman".

Regards AlanX