The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-207

“Design of Optimal FIR Prefilters for Wavelet Coefficient Computation”

by Xiang-Gen Xia, C.-C. Jay Kuo, and Zhen Zhang

June 1992

An algorithm was proposed by Shensa for computing the coefficients of wavelet series transform (WST) or continuous wavelet transform (CWT). With the Shensa algorithm, we first perform filtering on a sampled discrete-time signal and then apply the Mallat's discrete wavelet transform (DWT) algorithm to the filtered sequence, where the prefiltering is used to reduce the approximation error between the computed and desired coefficients. In this research, we consider the design of optimal causal and noncausal FIR prefilters which reduce the approximation error as much as possible with a fixed filter length. Numerical experiments are provided to demonstrate the performance of the designed optimal prefilters.

To download the report in PDF format click here: USC-SIPI-207.pdf (0.4Mb)