Extending Goertzel algorithm to 24 kHz, 32 kHz and 48 kHz in python

Question

I'm learning to implement Goertzel's algorithm to detect DTMF tones from recorded wave files. I got one implemented in python from here. It supports audio sampled at 8 kHz and 16 kHz. I would like to extend it to support audio files sampled at 24 kHz, 32 kHz and 48 kHz.

From the code I got from the link above, I see that the author has set the following precondition parameters/constants:

self.MAX_BINS = 8
if pfreq == 16000:
    self.GOERTZEL_N = 210
    self.SAMPLING_RATE = 16000
else:
    self.GOERTZEL_N = 92
    self.SAMPLING_RATE = 8000

According to this article, before one can do the actual Goertzel, two of the preliminary calculations are:

1. Decide on the sampling rate.
2. Choose the block size, N

So, the author has clearly set block size as 210 for 16k sampled inputs and 92 for 8k sampled inputs. Now, I would like to understand:

1. how the author has arrived at this block size?
2. what would be the block size for 24k, 32k and 48k samples?

Answer 1

The block size determines the frequency resolution/selectivity and the time it takes to gather a block of samples.

The bandwidth of your detector is about Fs/N, and of course the time it takes to gather a block is N/Fs.

For equivalent performance, you should keep the ratio between Fs and N roughly the same, so that both of those measurements remain unchanged.

It is also important, though, to adjust your block size to be as close as possible to a multiple of the wave lengths you want to detect. The Goertzel algorithm is basically a quick way to calculate a few selected DFT bins, and this adjustment puts the frequencies you want to see near the center of those bins.

Optimization of the block size according to the last point is probably why Fs/N is not exactly the same in the code you have for 8KHz and 16Khz sampling rates.

You could redo this optimization for the other sampling rates you want to support, but really performance will be equivalent to what you already have if you just use N = 210 * Fs / 16000

You can find a detailed description of the block size choice here: http://www.telfor.rs/telfor2006/Radovi/10_S_18.pdf