Question

I am using Goertzel algorithm to get the amplitude of a certain frequency.
I am trying now to get the phase from it, and I don’t know how.

Can some one explain, and show me how to get the phase of a certain-f from this code?

Also, I am using it to 16khz, with sample rate 44.1. What’s the smallest length of samples that I can run it on?

double AlgorithmGoertzel( int16_t *sample,int sampleRate, double Freq, int len )
{
    double realW = 2.0 * cos(2.0 * M_PI * Freq / sampleRate);
    double imagW = 2.0 * sin(2.0 * M_PI * Freq / sampleRate);
    double d1 = 0;
    double d2 = 0;
    double y;
    for (int i = 0; i < len; i++) {
        y=(double)(signed short)sample[i] +realW * d1 - d2;
        d2 = d1;
        d1 = y;
    }
    double rR = 0.5 * realW *d1-d2;
    double rI = 0.5 * imagW *d1-d2;

    return (sqrt(pow(rR, 2)+pow(rI,2)))/len;
}

Answer 1

I don’t think the algorithm consists of multiplying the sequence by a constant, but by the complex signal exp(n*i*2pi*freq/samplerate); 0<=n<=length, and getting the average magnitude (or power of the signal).

As the complex output is R*exp(i theta), R gives the power at the given frequency and theta gives the phase. (theta == atan2 ( imag, real))