The fast algorithm for the finite length discrete wavelet transform

The paper presents a structured algorithm for the finite length discrete wavelet transform. The analysis and synthesis filter matrices H, G can be decomposed in kronecker product form with cyclic block matrix and lower-triangle block matrix. The cyclic matrix can be implemented using FFT and the lower-triangle matrix is implemented straightforward. The arithmetic complexity of the algorithm is prior to the full-FFT implementation. Since the filter matrix of two-dimensional discrete wavelet transform separated into the kronecker product of the filter matrices of one-dimensional discrete wavelet transform, the algorithm can also be extended to the two-dimensional discrete wavelet transform conveniently.<
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