The Fourier transform is just a change of basis, if you squint at it properly. So at least some of the time (eg, when you're not mixing frequency and time domai

The Fourier transform is just a change of basis, if you squint at it properly. So at least some of the time (eg, when you're not mixing frequency and time domains like a crazy person) you can convert to frequency space and the functions become much simpler, and usual polynomial operations are relevant again.