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Combined polynomial transform and radix-q algorithm for MD discrete W transform
Yonghong Zheng; Guoan Bi; Kot, A.C.;
Signal Processing, IEEE Transactions on [see also Acoustics, Speech, and Signal Processing, IEEE Transactions on]
Volume 49,
Issue 3,
March 2001
Page(s):634
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641
Abstract:
The type-II r-dimensional discrete W transform (rD-DWT-II) with size ql1×ql2 ×···×lr q where q is an odd prime number, is converted into a series of one-dimensional (1-D) reduced DWT-IIs by using the multidimensional polynomial transform and an index permutation. Then, a radix-q algorithm and a cyclic convolution algorithm are presented for the computation of the 1-D reduced DWT-IIs. The new fast algorithm substantially reduces the overall computational complexity compared with the row-column method. Especially, the number of multiplications required by the proposed algorithm for computing an rD-DWT-II is only 1/r times that needed by the commonly used row-column method
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