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Is it possible to implement some sort of filter which adapts as a function of time?

Specifically, say I have a "noiseless" model of some signal which has the same frequency components at the same times as the signal I expect to measure, but with different phase and amplitudes (thus invalidating simple matched filtering).

So, in other words, the absolute value spectrograms (built by STFT, though I suppose any other time-frequency analysis such as CWT would be similar) of both signals will be similar in shape, though one of the acquisitions will be noisy, with different phase and amplitudes.

I guess I could do some filtering window by window, but I'm not entirely sure if this won't produce nasty artifacts when reconstructing in the time domain. Also, I wonder if there might be a smarter way of going about this problem.

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