Convolution using the undecimated discrete wavelet transform

Abstract

Convolution is one of the most widely used digital signal processing operations. It can be implemented using the fast Fourier transform (FFT) with a computational complexity of O (N log N). The undecimated discrete wavelet transform (UDWT) is linear and shift invariant, so it can also be used to implement convolution. We propose a scheme to implement the convolution using the UDWT, and study its advantages and limitations.