An intuitive explanation as to why a matched filter is time reversed? It easy enough to study correlation, and matched filters. But the challenge I see unmet anywhere to date and which I struggle to meet myself is a simpler presentation, to with more difficult task I suspect.
Can you explain, in lay terms, to satisfy the intuitions of a listener, why the matched filter is a time reversed copy of the signal we hope to detect? It is not a mathematical proof, or explanation I'm after (they abound) but other some way of explaining it (to lay listeners) that generates a &quot;a ha&quot; experience, a feeling that it makes sense, and I get why we time reverse the signal for a matched filter ...
This is something I have yet to find, read or master myself.
Picture the transmitted signal as a «signature». You want to find some process that maximize the probability of detecting that signature even when there is noise.
What do you do to find some signature buried in noise? You make a template that exactly match the known signature, and you slide it back or forth in time, noting how much the actual signal deviates from the ideal template in any one spot. The time-shift that gives a «large enough» correspondence is your assumed signal location.
The time-reversal of the template is just about reversing the reversal of that argument in the convolution operation. Think of it as non-reversed correlation if you prefer (leaving out complex numbers right now).
-k