The WalshHadamard 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 ?
The WalshHadamard 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 ? 


Not in the sense I think you mean it. First of all, the WalshHadamard 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. 

