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Is there a hypothetical situation where once can use Wiener filter prior Matched filter to get better result? Mostly I am looking for an example or a situation where both the filters are required as ther are doing different thing to the received signal. Under what circumstanctes this would be helpful?

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A matched filter is matched to a noiseless known waveform.

A Weiner Filter is based on the correlation structure of a random waveform.

The signal models are different but often a signal has deterministic and random characteristics.

It would be a stretch to say that a Kalman Filter could reduce to a matched filter, but it does work in models without process noise.

The short answer is that one can mix detection and estimation together but the likelihood function is the better way to think about it than terms like “matched” or “Weiner” filter.

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