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The most upvoted answer to this question suggests to use a "conventional" filter in cascade with a matched filter to first remove out of band noise (with conventional filter) and then optimize signal to noise energy (with matched filter).

Given a sampled signal where it is known that all relevant signal information is located in signal's baseband such as this one (the relevant signal here has a gaussian shape): Example signal

and where additive noise information is not known (I know it is for that specific signal, but let's assume it could have any property (colored, white, correlated, etc)).

Is it always better to use the proposed cascaded filters (conventional and then matched filter) or would it be equivalent to only use a matched filter with a gaussian shape?

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No, it is not “always” better.

One would prefilter in circumstances where it makes sense, like Eckart filtering where the signal is random and the background has a known fixed component.

Filtering, generally introduces correlation in a time series. A simple matched filter is derived under the assumption of a white background noise. If the prefilter is a whitening filter, it is better but each situation requires its own analysis.

Food for thought, if both filters are LTI, a prefilter can be a post filter.

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  • $\begingroup$ Thank you for your answer Stanley! That is what I was expecting but I found the other answer (the one I am referring to in the question) to be a bit confusing regarding 'in which situations' is it better. When you say, "if both filters are LTI, a prefilter can be a post filter", are you referring to the fact that in a cascade the filters order (which one comes first/last) can be inverted without consequence (as pointed out here dspfirst.gatech.edu/chapters/06firfreq/demos/blockd/index.html)? $\endgroup$
    – MAI
    Apr 29, 2019 at 16:44
  • $\begingroup$ theoretically yes, they pre and post can be swapped but there are practical considerations like dynamic range that make one configuration preferred over the other. $\endgroup$
    – user28715
    Apr 29, 2019 at 16:48
  • $\begingroup$ Is the fact that the matched filter requires white background noise a practical consideration? Given a signal with a known fixed component in the out of interest band part, would it be equivalent to have Input Signal > Notch > Matched > Output Signal or Input Signal > Matched > Notch > Output Signal ? $\endgroup$
    – MAI
    Apr 29, 2019 at 16:54
  • $\begingroup$ details matter, you have to do the analysis $\endgroup$
    – user28715
    Apr 29, 2019 at 16:56

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