Crossposted from https://mbin.potato-guy.space/m/videos@sopuli.xyz/t/214837

From the description:

Fourier transforms are widely understood, allowing a signal to be decomposed into its constituent frequencies. Fractional Fourier transforms are much less well known.

I look at this interesting topic in the video, and see how Fourier transforms are very much like rotations and, just as we can rotate by any angle, you can Fourier transform to any degree. These are like powers of Fourier transform operations, so multiplying two ‘square root Fourier transforms’ gives the standard transform.