On Wed, 10 Sep 1997 14:18:36 -0400 "Martin R. Green" <elimar@BIGFOOT.COM>
writes:
>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
>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.
>


        But the beat isn't present unless there is some nonlinearity to
cause intermod distortion.  If I take, for example, 1 KHz and 900 Hz,
linearly combine them and run them into an ideal LPF with a cutoff of 500
Hz, nothing will come out.
        Of course, we HEAR a "beat" because the waveform LOOKS very
similar to a 950 Hz carrier with double sideband suppressed carrier
modulation of 50 Hz, throwing sidebands out +/- 50 Hz (of course these
uncorrelated signals don't have the proper phase relationship to be
DSBSC, but our ear doesn't seem to know).  Looking at the envelope of a
DSBSC signal, we have what appears to be a full-wave rectified copy of
the modulation (with a carrier phase reversal at the zero crossing).
This "full wave rectified" envelope has a lot of second harmonic content,
and no fundamental (the original 50 Hz), so, we hear 950 Hz that seems to
be varying in amplitude by 100 Hz (severly distorted 50 Hz).  If we look
at it on a spectrum analyzer, however, only 900 Hz and 1 KHz are really
present, unless we introduce some nonlinearity.  Once we introduce
nonlinearity, lots of frequencies are present! (due to intermod and
harmonic generation).

Harold