Z Transform and Matched Filters.

Cuthbert Nyack
A matched filter has an impulse response which is the reverse of the signal to be detected. This filter is optimum in the sense that it produces the maximum signal to noise ratio. Because of the relation between convolution and correlation, then using the matched filter is equivalent to correlating the signal plus noise with a replica of the signal to be detected.

In the applet below x1(n) is the signal to be processed, x2(n) is the impulse response of the matched filter and y(n) is the convolution of x1(n) with x2(n).

The image below shows an example.

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COPYRIGHT 2008 Cuthbert Nyack.