# Reconstruction from Convolution

I am trying to implement Wavelet transform in an embedded environment. The problem I face goes like this:

1. Two vectors, A and B. A is input samples. B is vector co-efficients.

2. I take convolution of A and B, call it C.

3. Now I go back to B and up-sample the co-efficients.

4. Multiple C with new up sampled signal of B.

Problem is I am constrained to up-sample only C, and not B. Is there a way that I can obtain a result where

conv(upsample(B,2), C) == conv(upsample(C,2), B)

• Why do you want to do this? If you upsample one signal and not the other, then they will be at different effective sample rates, which means that the result of the convolution will be different. I'm not sure whether that's what you really want. – Jason R Mar 27 '13 at 12:59