This paper first presents a conversion of the

m

-dimensional discrete Fourier transform(MD-DFT) into a multiple sum involving a number of one-dimensional generalized discrete Fourier transforms (1D-GDFT's) by reordering the input data.An one-dimensional discrete W transform (DWT) and multidimensional polynomialtransform (MD-PT) are then used to compute the

m

-D DFT so that the number of arithmetic operations needed is reduced.The number of multiplications and additions required by the proposed algorithm is only 1/2

m

and (2

m+1)／4m

times that of the usually used row-column DFT algorithm.Besides

compared with the polynomial transform for 2-D DFT developed by Nussbaumer

the multiplications and additions needed by the p

roposed algorithm are reduced by 50% and 40%

respectively.The numerical experiments show that the proposed algorithm is not only simple in computational structure and but also highly efficient.