Efficient algorithms for computing the 2-D hexagonal Fourier transforms

In this paper, representations of the two-dimensional (2-D) signals are presented that reduce the computation of 2-D discrete hexagonal Fourier transforms (2-D DHFTs). The representations are based on the concept of the covering that reveals the mathematical structure of the transforms. Specifically, a set of unitary paired transforms is derived that splits the 2-D DHFT into a number of smaller one-dimensional (1-D) DFTs. Examples for the 8/spl times/4 and 16/spl times/8 hexagonal lattices are described in detail. The number of multiplications required for computing the 8/spl times/4- and 16/spl times/8-point DHFTs are equal 20 and 136, respectively. In the general N/spl ges/8 case, the number of multiplications required to compute the 2N/spl times/N-point DHFT by the paired transforms equals N/sup 2/ (log N-1)+N.