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Efficient algorithms for computing the 2-D hexagonal Fourier transforms

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1 Author(s)
Grigoryan, A.M. ; Dept. of Electr. & Comput. Eng., Texas Univ., San Antonio, TX, USA

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 8×4 and 16×8 hexagonal lattices are described in detail. The number of multiplications required for computing the 8×4- and 16×8-point DHFTs are equal 20 and 136, respectively. In the general N⩾8 case, the number of multiplications required to compute the 2N×N-point DHFT by the paired transforms equals N2 (log N-1)+N

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Signal Processing, IEEE Transactions on  (Volume:50 ,  Issue: 6 )