piclist 2004\04\27\002338a >
Thread: Looking for an AVR FFT tutorial
www.piclist.com/techref/logic/dsps.htm?key=fft
BY : Scott Dattalo email (remove spam text)

On Tue, 20 Apr 2004, Mark Jordan wrote:

> On 20 Apr 2004 at 8:43, Richard.ProsserPOWERWARE.COM wrote:
>
> > I don't have a tutorial, but may be able to assist with sample code. (and
> > other help if required)

<snip>

>         Well, what I'm trying to design is an 8 or 16 tone AFSK modem.
>         Based on what I have read, it seems Goertzel is just one form
> of calculating the FFT. But will it give me the best results?

The Goertzel algorithm and an FFT will produce identical results assuming
of course that the Goertzel algorithm is generating all the frequencies.
The difference is efficiency. If there are N frequencies, then the fft
will take N*log2(N) units of time where as the Goertzel algorithm will
take roughly N*N units. However, as mentioned in other portions of this
frequencies can be tuned.

In some sense, you can view the Goertzel algorithm as a narrow band pass
filter. I strongly suspect that if you use this concept as guide that it
would be possible to design an extremely optimal filter bank for filtering
the 8-DTMF frequencies. For example, the first stage can split the signal
into highs and lows. Each of these streams are then split again. Finally,
those four streams are split. You may wish to look up info on multirate
filtering.

>         Do you know of some page describing the FFT process like that
> one on the Goertzel algorithm?

I guess that depends on what you mean by 'like', but you could look at:

http://www.dattalo.com/technical/theory/dtmf.html

Scott

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