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tone detection with Goertzel

Type : Goertzel
References : Posted by espenr[AT]ii[DOT]uib[DOT]no
Linked file :

Notes :
Goertzel is basically DFT of parts of a spectrum not the total spectrum as you normally do with FFT. So if you just want to check out the power for some frequencies this could be better. Is good for DTFM detection I've heard.

The WNk isn't calculated 100% correctly, but it seems to work so ;) Yeah and the code is C++ so you might have to do some small adjustment to compile it as C.

Code :
/** Tone detect by Goertzel algorithm
* This program basically searches for tones (sines) in a sample and reports the different dB it finds for
* different frequencies. Can easily be extended with some thresholding to report true/false on detection.
* I'm far from certain goertzel it implemented 100% correct, but it works :)
* Hint, the SAMPLERATE, BUFFERSIZE, FREQUENCY, NOISE and SIGNALVOLUME all affects the outcome of the reported dB. Tweak
* em to find the settings best for your application. Also, seems to be pretty sensitive to noise (whitenoise anyway) which
* is a bit sad. Also I don't know if the goertzel really likes float values for the frequency ... And using 44100 as
* samplerate for detecting 6000 Hz tone is kinda silly I know :)
* Written by: Espen Riskedal,, july-2002


using std::rand;
// math stuff
using std::cos;
using std::abs;
using std::exp;
using std::log10;
// iostream stuff
using std::cout;
using std::endl;

#define PI 3.14159265358979323844
// change the defines if you want to
#define SAMPLERATE 44100
#define BUFFERSIZE 8820
#define FREQUENCY 6000
#define NOISE 0.05
#define SIGNALVOLUME 0.8

/** The Goertzel algorithm computes the k-th DFT coefficient of the input signal using a second-order filter.
* Basiclly it just does a DFT of the frequency we want to check, and none of the others (FFT calculates for all frequencies).
float goertzel(float *x, int N, float frequency, int samplerate) {
float Skn, Skn1, Skn2;
Skn = Skn1 = Skn2 = 0;

for (int i=0; i Skn2 = Skn1;
Skn1 = Skn;
Skn = 2*cos(2*PI*frequency/samplerate)*Skn1 - Skn2 + x[i];

float WNk = exp(-2*PI*frequency/samplerate); // this one ignores complex stuff
//float WNk = exp(-2*j*PI*k/N);
return (Skn - WNk*Skn1);

/** Generates a tone of the specified frequency
* Gotten from:
float *makeTone(int samplerate, float frequency, int length, float gain=1.0) {
//y(n) = 2 * cos(A) * y(n-1) - y(n-2)
//A= (frequency of interest) * 2 * PI / (sampling frequency)
//A is in radians.
// frequency of interest MUST be <= 1/2 the sampling frequency.
float *tone = new float[length];
float A = frequency*2*PI/samplerate;

for (int i=0; i if (i > 1) tone[i]= 2*cos(A)*tone[i-1] - tone[i-2];
else if (i > 0) tone[i] = 2*cos(A)*tone[i-1] - (cos(A));
else tone[i] = 2*cos(A)*cos(A) - cos(2*A);

for (int i=0; i
return tone;

/** adds whitenoise to a sample */
void *addNoise(float *sample, int length, float gain=1.0) {
for (int i=0; i }

/** returns the signal power/dB */
float power(float value) {
return 20*log10(abs(value));

int main(int argc, const char* argv) {
cout << "Samplerate: " << SAMPLERATE << "Hz\n";
cout << "Buffersize: " << BUFFERSIZE << " samples\n";
cout << "Correct frequency is: " << FREQUENCY << "Hz\n";
cout << " - signal volume: " << SIGNALVOLUME*100 << "%\n";
cout << " - white noise: " << NOISE*100 << "%\n";

addNoise(tone, BUFFERSIZE,NOISE);

int stepsize = FREQUENCY/5;

for (int i=0; i<10; i++) {
int freq = stepsize*i;
cout << "Trying freq: " << freq << "Hz -> dB: " << power(goertzel(tone, BUFFERSIZE, freq, SAMPLERATE)) << endl;
delete tone;

return 0;


Added on : 25/08/02 by ashg[ AT ]eth[ DOT ]net
Comment :
I am interested in knowing that could we  implement the Goertzel algorithm using only integer variables and not using floa at all. Please let me know. I need it urgently.

Added on : 24/02/03 by yunusk[ AT ]telesis[ DOT ]com[ DOT ]tr
Comment :

I will implement DTMF/MFR1/MFR2 generation/detection function using DSP. I have found goertzel algorithm for DTMF. Can I use this algorithm for MFR1 and MFR2? Could you please let me know ?
Best Regards

Added on : 14/04/03 by asaeiaf[ AT ]hotmail[ DOT ]com
Comment :
I'm going to implement a Goertzel algorithm on a Fixed_point DSP .
Could you lead me to the changes I should consider?
I realy appreciate your helping me.

Afsaneh Asaei            

Added on : 12/06/03 by jfishman[ AT ]umsis[ DOT ]miamil[ DOT ]edu
Comment :
Does anybody know if and how this can be done in real time?


Added on : 24/11/03 by no
Comment :
It can.

Added on : 12/12/03 by pabitra_mohan208[ AT ]yahoomail[ DOT ]com
Comment :
i m pabitra.
please help me to understand this program.        

Added on : 12/04/04 by Christian[ AT ]savioursofsoul[ DOT ]de
Comment :
yet untested Delphi translation of the algorithm:

function Goertzel(Buffer:array of Single; frequency, samplerate: single):single;
var Skn, Skn1, Skn2 : Single;
    i               : Integer;
    temp1, temp2    : Single;
for i:=0 to Length(Buffer) do
   Skn2 = Skn1;
   Skn1 = Skn;
   Skn = 2*temp2*Skn1 - Skn2 + Buffer[i];
Result:=(Skn - exp(-temp1)*Skn1);

Maybe someone can use it...


Added on : 16/01/05 by GPOLAT51[ AT ]YAHOO[ DOT ]COM
Comment :

Added on : 06/05/05 by kevin[ AT ]subatomicglue[ DOT ]com
Comment :
why's the 2*cos(2*PI*frequency/samplerate) in that inner loop?  It's all constants...  I'd precompute this outside the for loop.

also.   use the float version of cos and exp... cosf expf... that way you're not wasting time converting and using the more expensive functions.

Added on : 19/06/05 by net_day2004[ AT ]hotmail[ DOT ]com
Comment :
if anyone please can help me, i need a c++ code about the fft.the code should input and array of N rows and 1 column, all set to 1, and also it should input the length of fft(interval from f1 to f2) and output the results.
thank you,
i would appreciate your help,

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