TITLE: Can Walsh-Hadmard transform be used for convolution ?
QUESTION [5 upvotes]: The Walsh-Hadamard transform is very fast to compute. 
Can it be used to compute the convolution of two functions as it can be done with Fourier transform ?

REPLY [4 votes]: Not in the sense I think you mean it.  First of all, the Walsh-Hadamard transform is a Fourier transform - but on the group (Z/2Z)^n instead of on the group Z/NZ.  That means you can use it to compute convolutions with respect to the space of functions (Z/2Z)^n -> C.  Unfortunately, unlike the case with Z/NZ you can't use this to approximate a compactly supported convolution on Z, at least not directly.