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Tang Baoping
Zhong Youming
Qin Shuren
Department of Mechanical Engineering, Chongqing University,
Chongqing 400044, China |
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RESEARCH OF PROBLEMS ON
REALIZING DIRECT ALGORITHM
OF
WAVELET TRANSFORM*
Abstract: Direct algorithm of wavelet transform (WT) is the numerical algorithm obtained from the integral formula of WT by directly digitization. Some problems on realizing the algorithm are studied. Some conclusions on the direct algorithm of discrete wavelet transform (DWT), such as discrete convolution operation formula of wavelet coefficients and wavelet components, sampling principle and technology to wavelets, deciding method for scale range of wavelets, measures to solve edge effect problem, etc, are obtained. The realization of direct algorithm of continuous wavelet transform (CWT) is also studied. The computing cost of direct algorithm and Mallat algorithm of DWT are still studied, and the computing formulae are obtained. These works are beneficial to deeply understand WT and Mallat algorithm. Examples in the end show that direct algorithm can also be applied widely.
Key words:
Wavelet transform Direct algorithm Mallat
algorithm |