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-205

“On The Accuracy Of Computed Wavelet Coefficients”

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

June 1992

Several types of wavelet transforms such as the continuous wavelet transform (CWT), wavelet series transform (WST) and discrete wavelet transform (DWT) have been considered by researchers. Only the DWT coefficients can be computed numerically, and they are often used to approximate the WST and CWT coefficients. Numerical algorithms have been proposed to compute the DWT coefficients such as the Mallat and the Shensa algorithms. In this research, we study the accuracy of the computed DWT coefficients obtained from these algorithms as an approximate of the WST coefficients. Our analysis indicates that the accuracy of the Shensa algorithm can be adjusted by choosing an appropriate prefilter, and the corresponding result is better than that of the Mallat algorithm.

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