Matched Filter Correlation

[msabeel]

We were taught that a matched filter performs correlation on the received noisy signal in order to determine the transmitted signal.....but I could not get the idea. Can anyboy explain to me how a matched filter works? Thanks in anticipations.

 

[oyvdahl]

Actually I am looking into this myself.
I think the idea is to take a template (a "perfect" version) of the signal you want to detect and correlate this with the received noisy signal to detect if the signal you are looking for is present in the received signal.
A place to start is wikipedia (Matched filter - Wikipedia, the free encyclopedia).

 

[msabeel]

You are right. But I have one more question.

The response h(t) of the matched filter is the reversed, time delayed version of the signal being transmitted. But if h(t) is dependent on the signal to be transmitted, then it means we'll have to design a seperate matched filter for each signal that we want to transmit. Can't we design a general match filter whose impulse response is independent of one single signal, so that we don't have to design a seperate matched filter for every signal we want to transmit?

 

[oyvdahl]

Are you thinking about a specific scenario or just in general?
Because my initial thought is that a transimitter-receiver system would have a predefined pulse that can be used as the template and that this pulse stays the same all the time.

 

[msabeel]

In general.
Ok the pulse stays the same all the time. But if the pulse changes at any time, we'll have to redesign our matched filter, right?

 

[oyvdahl]

Yes that is correct.

 

[SKS]

Generally, if there are number of transmit signals, matched filters are "matched" to the basis functions of the transmit signal set. So the number of matched filters required is lesser than the transmit signals.

 

[msabeel]

You are talking about the orthonormal bases?

 

[SKS]

You are talking about the orthonormal bases?

Yes thats correct!!