Title :
A Split Vector-Radix Algorithm for the 3-D Discrete Hartley Transform
Author :
Bouguezel, Saad ; Ahmad, M. Omair ; Swamy, M.N.S.
Author_Institution :
Center for Signal Process. & Commun., Montreal, Que.
Abstract :
In this paper, we propose a three-dimensional (3-D) split vector-radix fast Hartley transform (FHT) algorithm. The main idea behind the proposed algorithm is that the radix-2/4 approach is introduced in the decomposition of the 3-D discrete Hartley transform by using an appropriate index mapping and the Kronecker product. This provides an algorithm based on a mixture of radix-(2times2times2) and radix-(4times4times4) index maps and has a butterfly that is characterized by simple closed-form expressions. This algorithm offers substantial reductions in the numbers of multiplications, additions, data transfers, and twiddle factor evaluations or accesses to the look-up table, without a significant increase in the structural complexity compared to that of the existing 3-D vector radix FHT algorithm
Keywords :
digital arithmetic; discrete Hartley transforms; signal processing; table lookup; 3D discrete Hartley transform; FHT algorithm; Kronecker product; data transfers; fast Hartley transform algorithm; index mapping; look-up table; split vector-radix algorithm; twiddle factor evaluations; Arithmetic; Closed-form solution; Discrete Fourier transforms; Discrete transforms; Fast Fourier transforms; Fourier transforms; Helium; Multidimensional systems; Signal processing algorithms; Table lookup; 3-D split vector-radix algorithm; Three-dimensional (3-D) discrete Hartley transform (DHT); split radix approach;
Journal_Title :
Circuits and Systems I: Regular Papers, IEEE Transactions on
DOI :
10.1109/TCSI.2006.881185
