From the wavelet series to the discrete wavelet transform-the initialization

The discrete wavelet transform (DWT) is computed by subband filters bank and often used to approximate wavelet series (WS) and continuous wavelet transform (CWT). The approximation is often inaccurate because of improper initialized discretization of the continuous-time signal. In this correspondence, the problem is analyzed, and two simple algorithms for the initialization are introduced. Finally, numerical examples are presented to show that our algorithms are more effective than others