Hello I am writing a report on the difference between Matched filter and Cross correlation in effectiveness of signal detection. i know that they are essentially the same thing with the same results but are the maths behind them different? I've looked at a lot of literature but can't seem to find anything. Thanks james
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The cross correlator does the cross-correlation between the noisy signal and noisless signal. The matched filter does the convolution between the received signal and the time reversed copy of the original signal. The math is the same. In the Proakis book chapter 5 a more detailed description of the math is given. Matched filter maximizes the SNR. The cross correlator is easier to implement in hardware. Hope this helps, Anna
Same thing. Look at the equations for cross-correlation and convolution and you will see that they only differ by a time reversal.
I think the term "matched filter" focuses more on the fact that it maximize the SNR. Cross correlation can be considered as one of the implementations to the matched filter.