New polynomial transform algorithms for multidimensional DFT´s and convolutions

This paper introduces a new method for the computation of multidimensional DFT´s by polynomial transforms. The method, which maps mtiltidimensional DFT´s into one-dimensional odd-time DFT´s by use of inverse polynomial transforms, is shown to be significantly more efficient than the conventional row-column method from the standpoint of the number of arithmetic operations and quantization noise. The relationship between DFT and convolution algorithms using polynomial transforms is clarified and new convolution algorithms with reduced computational complexities are proposed.