24: The Fourier Transform and the Convolution Theorem

As we saw in the foregoing, convolution and its partner the Fourier Transform are fundamental ways to understand what’s going on in both Radar (as an example of a sensorial system) and quantum mechanics. I don’t know for sure, but I think the Fourier Transform (FT) is better known to students just getting used to the ideas involved than is the idea of convolution. Historically, the FT provides one with the occupancy in a mathematical frequency space of things in real space, but it is often moot which space is the more real! Here’s one way to express the FT; in one dimension we have