Application Of Wavelet Analysis On Signal Processing

Wavelet analysis was developed in 1980s. Its many good features render itself useful in many dimensions such as signal processing. This paper studies the frequency alias while using fast algorithm of wavelet analysis—Mallat algorithm in the decomposition and reconstruction of signals. The major works can be summarized as follows:Mallat algorithm is a pyramid algorithm based on Multiresolution analysis of wavelet transform, but it exists frequency alias. This paper analyzed the reason of frequency alias in Mallat algorithm, and found it was caused by characteristics of frequency-domain of orthogonal wavelet filter, downsampling of keeping one sample out of two and upsampling of putting one zero between each sample. Both downsample and upsample cause frequency fold-over, but their directions are opposite, the single sideband...