Recursive Orthgonal Wavelet Function

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In this research, we propose a design method of 1 and 2 dimensional recursive wavelet functions and examine its applications for digital signal processing. In this method, we use the parallel connection consisted of some delays and 1 and 2-D allpass filter in order to satisfy the orthogonality. Furthemore a maximum number of zeros is put at aliasing frequencies in the lowpass filter to obtain the regularity. IIR transfer function with some degrees of regularity and arbitrary order can be easily obtained by solving the simultaneous equation. 1-D and 2-D recursive wavelet functions based on iterated filter banks are found. Although the obtained wavelet functions are similar to that based on FIR filters, recursive wavelet functions have higher regularity than nonrecursive wavelet.Next, we considered its application for digital signal processing, singularity detection and image compression. In image ompression, image is separated into multiresolution spaces by wavelet transform. Each multiresolution spaces is coded by using IFS (Iterated Function System) . In this time, IFS codes are make based on the characteristics of each spaces. By this method, good reconstruction image can be obtained.