If I have a signal that I'd like to filter very precisely (say, a few Hz bandwidth), I feel like the "best" one can possibly do is to take a time sample long enough to get a discrete transform frequency resolution of the same width, erase all but the frequency component of interest, and then transform back.(adsbygoogle = window.adsbygoogle || []).push({});

But am I supposing the Fourier transform is more fundamental than it really is? Could I use, say, a recursive filter or other set of basis functions, to have a few Hz passband over timescales much shorter than the transform-limit? Or is the (Fourier) transform limit really a fundamental limit?

Thanks!

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# A filter with a narrower-than-Fourier Transform passband?

Can you offer guidance or do you also need help?

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