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Typically, when I want to filter a signal with an LTI filter (in this case a low-pass filter), I just convolve the signal with the filter.

However, what do I do if I have a stream of data that I want to filter as it arrives? Do I have to save a certain amount of the signal and filter it? Is there some other approach or theory that applies to this scenario?

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As a quick draft of an answer, it turns out the things I was looking for was:

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