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Pacific-Asia Workshop on Computational Intelligence and Industrial Application, IEEE (2008)
Dec. 19, 2008 to Dec. 20, 2008
ISBN: 978-0-7695-3490-9
pp: 982-986
Today, almost all of the implementations of the discrete wavelet transforms are based on the recursive way. However, non-recursive wavelet transforms (NRWT) are more effective and more flexible. We extend the NRWT theory in l^2 (Z) and propose a new NRWT theory based on 6 different downsampling modes in l^2 (Z_c^+ ). This extending makes NRWT more practical and can be compatible with the traditional recursive wavelet transform. We study the properties of the NRWT under the 6 downsampling modes, W_(-3≤k≤2), through the analysis of redundancy degree and point out that W_(-2) is optimal and the redundancy degrees of W_(-2) and W_0 are identical. The analysis of redundancy degree offers a method to choose the NRWT mode.

Q. Deyu, L. Xiaoxin and Q. Zhengping, "Non-Recursive Wavelet Transforms in l2(Zc+)," 2008 Pacific-Asia Workshop on Computational Intelligence and Industrial Application. PACIIA 2008(PACIIA), Wuhan, 2008, pp. 982-986.
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