This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Pipeline Design for the Realization of the Prime Factor Algorithm Using the Extended Diagonal Structure
October 1994 (vol. 43 no. 10)
pp. 1232-1237

In this brief contribution, an efficient pipeline architecture is proposed for the realization of the Prime Factor Algorithm (PFA) for digital signal processing. By using the extended diagonal feature of the Chinese Remainder Theorem (CRT) mapping, we show that the input data sequence can be directly loaded into a multidimensional array for the PFA computation without any permutation. Short length modules are modified such that an in-place and in-order computation is allowed. The computed results can then be directly restored back to the memory array without the need for further reordering. More importantly, the CRT mapping can also be used to represent the output data, hence we can utilize the extended diagonal feature of the CRT mapping to directly send the computed results to the outside world. As compared to the previous approaches, the present approach requires no shifting or rotation during the data loading and retrieval processes. In the case of multidimensional PFA computation, it does not require the computation to be split up into a number of two-dimensional computations. Hence, the overhead required for data loading and retrieval in each two-dimensional stage can be saved.

[1] D. P. Kolba and T. W. Parks, "A prime factor FFT algorithm using high-speed convolution,"IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-25, Aug. 1977.
[2] I. J. Good, "The relationship between two fast Fourier transforms,"IEEE Trans. Comput., vol. 20, pp. 310-317, Mar. 1971.
[3] R. E. Blahut,Fast Algorithms for Digital Signal Processing. Reading: MA: Addison-Wesley, 1985.
[4] M. A. Mehalic, P. L. Rustan, and G. P. Route, "Effects of architecture implementation on DFT algorithm performance,"IEEE Trans. Acoust. Speech Signal Processing, vol. ASSP-33, pp. 684-693, June 1985.
[5] P. Duhamel and H. Hollmann, "Split-radix FFT algorithm,"Electronics Lett., vol. 20, no. 1, pp. 14-16, Jan. 5, 1984.
[6] G. Aloisio, G. C. Fox, J. S. Kim, and N. Veneziani, "A concurrent implementation of the time factor algorithm on hypercube,"IEEE Trans. Acoust. Speech Signal Processing, vol. 39, no: 1, pp. 160-171, Jan. 1991.
[7] K. L. Wong and W. C. Siu, "Data routing networks for systolic/pipeline realisation of prime factor mapping,"IEEE Trans. Comput., vol. 40, no. 9, Sept. 1991.
[8] H. C. Shyu, T. K. Truong, I. S. Reed, and I. S. Hsu, "Pipeline primefactor DFT for VLSI using cyclic shuffling,"IEE Proc., vol. 134, pt. E, no. 5, pp. 247-253, Sept. 1987.
[9] T. K. Truong, I. S. Reed. I. S. Hsu. H. C. Shyu, and H. M. Shao, "A pipeline design of a fast prime factor DFT on a finite field,"IEEE Trans. Comput, vol. 37, no. 3, pp. 266-273, Mar. 1988.
[10] D. P. K. Lun, R. Chan, and W. C. Siu, "Yet a faster address generation scheme for the computation of prime factor algorithms," inProc. IEEE Int. Conf. Acoust. Speech Signal Processing, Albuquerque, New Mexico, April 36, 1990, pp. 1499-1502.
[11] C. S. Burrus, "Index mappings for multidimensional formulation of the DFT and convolution,"IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-29, pp. 806-817, Aug. 1981.
[12] Z. D. Wang, "Index mapping for one to multidimensions,"Electronics Lett., vol. 25, pp. 239-242, June 1977.
[13] C. Temperton, "Implementation of a self-sorting in-place prime factor FFT algorithm,"J. Computat. Phys., vol. 58, pp. 238-299, 1985.
[14] A. V. Oppenheim and R. W. Schafer,Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.

Index Terms:
signal processing; parallel algorithms; parallel architectures; pipeline design; prime factor algorithm; pipeline architecture; digital signal processing; Chinese Remainder Theorem; input data sequenc; multidimensional array; data loading; retrieval.
Citation:
D.P.-K. Lun, Wan-Chi Siu, "A Pipeline Design for the Realization of the Prime Factor Algorithm Using the Extended Diagonal Structure," IEEE Transactions on Computers, vol. 43, no. 10, pp. 1232-1237, Oct. 1994, doi:10.1109/12.324549
Usage of this product signifies your acceptance of the Terms of Use.