fft - Normalizing the magnitude of Goertzel Filter c#

I'm trying to detect some frequencies of 18Khz with sample rate of 44100 [samples/sec].

When I pass a buffer(~4500 samples) to the algorithm it returns a magnitude in a very strange range. Sometimes i get 0.1, or 7 or 250(!) or 154 or 25000 - very strange. I can't decide on a threshold boundary for the filter. Is there any way noramlizing that result? (My result is the magnitude of the complex calculation of real and image)

This is my Goertzel code:

public float goertzel_mag(float[] data,int numSamples, int TARGET_FREQUENCY, int SAMPLING_RATE,int start,int end)
    {
        int k, i;

        float floatnumSamples;
        float omega, sine, cosine, coeff, q0, q1, q2, magnitude, real, imag;

        float scalingFactor = (float)(numSamples / 2.0);

        floatnumSamples = (float)numSamples;
        k = (int)(0.5 + ((floatnumSamples * TARGET_FREQUENCY) / SAMPLING_RATE));
        omega = (float)(2.0 * Math.PI * k) / floatnumSamples;
        sine = (float)Math.Sin(omega);
        cosine = (float)Math.Cos(omega);

        coeff = (float)2.0 * cosine;
        q0 = 0;
        q1 = 0;
        q2 = 0;

        for (i = start; i < end; i++)
        {
            q0 = coeff * q1 - q2 + data[i];
            q2 = q1;
            q1 = q0;

        }

        // calculate the real and imaginary results
        // scaling appropriately
        real = (q1 - q2 * cosine) / scalingFactor;
        imag = (q2 * sine) / scalingFactor;

        magnitude = (float)Math.Sqrt(real * real + imag * imag);
        return magnitude;
    }

Answer

Your Goertzel code looks okay, the standard fare.

Regarding normalization and thresholds, if you're detecting 18kHz, you should calibrate your signal at different levels and establish a threshold from that data

• Start with full-scale (1.0, 0dBFS) 18kHz tones, as those should give you the highest magnitude over the course of your buffer (4500 samples) and then


• Repeat the Goertzel filter mag measurements on tones all the way down in level, as much as you care but I would measure at least 6dB.


• Finally, run your Goertzel filter over non-tonal material, or buffers of audio that don't contain what you're looking for. This will give you an idea of what the filter will output in the non-tone case. In my application, environmental audio/speech can have incidental tones in the range I'm looking for (400-600Hz) and I want to make sure to understand what Goertzel magnitudes I would get versus Goertzel magnitudes in the presence of a real tone.