Assume you have a signal, and within it, some pulses are present. A pulse is a simple tone. You know the pulses' duration and shape. (Let us assume that a pulse is made of a couple of cycles, and then to which all those cycles are multiplied by a hamming window. So the final pulse may look like the blue plot below:
What we do not know are its frequency. (You know its frequency to within $\pm 100\textrm{ Hz}$).
The question is:
Does performing a match-filtering of a signals' absolute magnitude spectrogram with a 2-D version of your pulse in the time-frequency domain, confer upon you any advantages, versus performing a match-filtering of the signals' (shown in red as an example), against the known envelope of the pulse, in the time-domain?
]2*
For the TF-domain method, assume:
- STFT analysis.
- I am using an analysis window equal to the expected pulse length.
- Percent Overlap: Whatever you want, I do not think it matters for this case.
I am really on the fence on this one because on the one hand, you cannot create information out of nothing, so taking your problem to the time-frequency space seems redundant, while on the other hand, going into the time-frequency space allows you to, perhaps, create 2-D filters that better match your pulse, and/or, ignore noise from other bands which are (perhaps?) not ignored in the time-domain match-filtering case?
My biggest point of confusion is that, inherent to going into the TF domain, we now have both time and frequency localization ambiguity, (based on our choice of the analysis window we use). In contrast, in the time domain, we are $100\%$ sure of our time localization. How - or why - would trading in $100\%$ time-locatlization unambiguity for some joint time-frequency ambiguity help? I am not seeing it.
EDIT:
Another way to look at the problem is with this rephrase: When would one want to do match filtering in only the time-domain ($0\%$ time ambiguity, $100\%$ frequency ambiguity), vs doing it in the joint TF-domain, (x% time ambiguity, (1-x)% frequency ambiguity).
I had a broader question but broke it down into this one first.