On Mon, 24 Feb 2003, Peter L. Peres wrote:

> Correlation: A simple way is to XOR incoming data with data-to-be-tested
> and count the 1's in the result. The fewer 1's the better the correlation.
> XOR is modulo-2 multiply without carry out (or in) and one (the?)
> correlation function is Fc=SumOf|Ai*Bi|. XOR produces this result when Ai
> and Bi are binary bits, but the sum is zero for high correlation because
> the carry in the XOR multiply is lost. In this case Fc=0 means 'all bits
> caused carry' (which was lost). Otherwise one would use an analog
> multiplier to check for correlation with analog signals, and aim for high
> Fc (not zero). Notice that in a binary XOR correlator an all 1's result
> means input and reference are 180 degrees out of phase, or complementary.

See:

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

Here the pulse stream "decoded" is a 50% duty cycle square wave. In the
real code implementation, it's actually faster to perform sequences of:

    BTFSC   port,bit
     INCF   Fc

Instead of performing a sequence of XOR's

For frequency decoders, you really need quadrature sampling.
Fortunately, only 3/4'ths of the time is spent sampling and 1/4'th spent
processing. (Sampling all 8 DTMF freqeuncies simultaneously is
challenging!)

Scott

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