Actually, I don't believe that just because three or more frequencies are
not harmonically related that their beat frequencies will all be different.
 At first glance this may _seem_ intuitive, but even a little deeper
consideration hints that there is actually no such relationship.

In fact, I just threw the DTMF frequencies into a simple spreadsheet, and
now I _know_ that the latter doesn't follow from the former

Consider, the DTMF matrix, with beat freqs.:



As you can see, the beat frequency 780 shows up twice, so there goes that
theory.

CIAO - Martin R. Green
elimar@bigfoot.com

----------
From:   Pierce Nichols[SMTP:pn30@COLUMBIA.EDU]
Sent:   Wednesday, September 10, 1997 4:21 PM
To:     PICLIST@mitvma.mit.edu
Subject:        Re: DTMF decoding

On Wed, 10 Sep 1997, Martin R. Green wrote:

> Actually, I thought the frequencies were chosen so no two DTMF
frequencies
> are harmonically related.  Are you sure the beat frequencies are always
> different?  If so, it should be relatively easy to LPF your input (not
BPF

        The first statement (I believe) implies the second. At any rate,
the beat frequencies are always different (the math to demonstrate that is
relatively simple -- anyone here should be able to do it).

> around the DTMF frequencies) so you get ONLY the beat, and check the
> frequency of that instead, as you suggest.  Of course, by using only one
> frequency, you run the risk of noise artificially triggering your
decoder.

        You can deal with the noise problem by measuring the beat
frequency over several cycles -- the DTMF spec also supplies a minimum
pulse length, and it's long enough so that the code is extremely robust.

        Pierce Nichols