8 ms·
I've come to internalize the Fourier transform as a type of sparse matrix algorithm. I.e. something that implements a particular matrix-vector product without r
by thearn4 5y ago
I've come to internalize the Fourier transform as a type of sparse matrix algorithm. I.e. something that implements a particular matrix-vector product without requiring explicit construction of said matrix.
- srean 5y agoAnd pushing the parantheses to factor out common subexpressions. Essentially exploiting the distributive law
- enchiridion 5y agoDo you mean the FFT? I've been trying to wrap my head around the Fourier transform lately, and I can see the matrix connection to an FFT, but not the Fourier transform in general.
- bonoboTP 5y agoThe Fourier transform performs a change of basis into the eigenbasis of convolution. It's linear and so in the discrete case can be expressed as matrix multiplication (every discrete linear operation is expressible as matmul).