Moment-based fast discrete Hartley transform

A novel approach to compute the discrete Hartley transform (DHT) is proposed. By using a modular mapping, DHT is approximated by the sum of a finite sequence of discrete moments. This enables the computational techniques developed for computing moments to be employed in computing DHT efficiently. We demonstrate this by applying ocr earlier systolic solution for computation of discrete moments to DHT. The resulting solution has a superior complexity: the amount of multiplications used in our method is O(N log2 N/log2 log2 N) and is superior to the O(N log2 N) in the classical FHT. The execution time of the systolic array is only O(N log2 N/log2 log2 N) for one-dimensional DHT and O(Nk) for k-dimensional DHT(k ≥ 2). The method is also applicable to DHT inverses.

[1]  F. H. Y. Chan,et al.  An all adder systolic structure for fast computation of moments , 1996, J. VLSI Signal Process..

[2]  O. Buneman.  Multidimensional Hartley transforms , 1987, Proceedings of the IEEE.

[3]  Neng-Chung Hu,et al.  Generalized discrete Hartley transforms , 1992, IEEE Trans. Signal Process..

[4]  Hsieh S. Hou,et al.  The Fast Hartley Transform Algorithm , 1987, IEEE Transactions on Computers.

[5]  Oscar Buneman,et al.  In-situ bit-reversed ordering for Hartley transforms , 1989, IEEE Trans. Acoust. Speech Signal Process..

[6]  Paul J. Zsombor-Murray,et al.  Fast algorithm for the computation of moment invariants , 1987, Pattern Recognit..

[7]  H. E. Rose.  A course in number theory , 1988 .

[8]  Douglas L. Jones,et al.  On computing the discrete Hartley transform , 1985, IEEE Trans. Acoust. Speech Signal Process..

[9]  Soo-Chang Pei,et al.  Computing pseudo-Wigner distribution by the fast Hartley transform , 1992, IEEE Trans. Signal Process..

[10]  Martin Vetterli,et al.  Improved Fourier and Hartley transform algorithms: Application to cyclic convolution of real data , 1987, IEEE Trans. Acoust. Speech Signal Process..

[11]  Francis H. Y. Chan,et al.  A new approach to fast calculation of moments of 3-D gray level images , 2000, Parallel Comput..

[12]  Naoki Suehiro,et al.  Fast algorithms for the DFT and other sinusoidal transforms , 1986, IEEE Trans. Acoust. Speech Signal Process..

[13]  Jun Shen,et al.  Pascal triangle transform approach to the calculation of 3D moments , 1992, CVGIP Graph. Model. Image Process..

[14]  Murray Eden,et al.  Fundamentals of Digital Optics , 1996 .

[15]  Mehdi Hatamian,et al.  A real-time two-dimensional moment generating algorithm and its single chip implementation , 1986, IEEE Trans. Acoust. Speech Signal Process..

[16]  Ronald N. Bracewell.  The Hartley transform , 1986 .

[17]  R. Bracewell.  The fast Hartley transform , 1984, Proceedings of the IEEE.