On the computation of wavelet series transform

Abstract

Because the discrete wavelet transform (DWT) can be computed effectively with a fast algorithm, the DWT is often used to approximate the continuous wavelet transform (CWT) and wavelet series transform (WST). Approximation accuracy is considered as an open problem in wavelet theory. In this paper, we firstly give three parts that affect the approximation accuracy. Based on sampling theory for wavelet subspaces, two kinds of prefilters are given; one can exactly compute the WST for any signal in this wavelet subspace and the other one can effectively approximate the true WST. Finally, numerical examples are given to show that our algorithms are effective.