Combined polynomial transform and radix-q algorithm for MD discreteW transform

  • Authors:
  • Yonghong Zheng;Guoan Bi;A.C. Kot

  • Affiliations:
  • Sch. of Electr. & Electron. Eng., Nanyang Technol. Inst.;-;-

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2001

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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