Suppose I have a system that wants to take an input signal (audio in this case) and wants to output a Discrete Fourier Transform of it in real time (ie every sample).
My initial thought is that if you are just every sample adding a new sample and bumping off a the oldest sample you could reuse the some of the computation from the last sample.
After googling around I wasn't able to find anything like that on the web.
So my question is this:
Does an algorithm like this exist and what is it called?