|
| This Article | ||
| ||
| Share | ||
| Bibliographic References | ||
| Add to: | ||
 Digg  Furl  Spurl  Blink  Simpy  Google  Del.icio.us  Y!MyWeb | ||
| Search | ||
| ||
| ASCII Text | x | ||
| C. Chakrabarti, J. Jaja, "Systolic Architectures for the Computation of the Discrete Hartley and the Discrete Cosine Transforms Based on Prime Factor Decomposition," IEEE Transactions on Computers, vol. 39, no. 11, pp. 1359-1368, November, 1990. | |||
| BibTex | x | ||
| @article{ 10.1109/12.61045, author = {C. Chakrabarti and J. Jaja}, title = {Systolic Architectures for the Computation of the Discrete Hartley and the Discrete Cosine Transforms Based on Prime Factor Decomposition}, journal ={IEEE Transactions on Computers}, volume = {39}, number = {11}, issn = {0018-9340}, year = {1990}, pages = {1359-1368}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.61045}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - Systolic Architectures for the Computation of the Discrete Hartley and the Discrete Cosine Transforms Based on Prime Factor Decomposition IS - 11 SN - 0018-9340 SP1359 EP1368 EPD - 1359-1368 A1 - C. Chakrabarti, A1 - J. Jaja, PY - 1990 KW - systolic architectures; discrete Hartley; discrete cosine transforms; prime factor decomposition; two-dimensional systolic arrays; hardware design; binary arithmetic; fast Fourier transforms; parallel architectures. VL - 39 JA - IEEE Transactions on Computers ER - | |||
Two-dimensional systolic array implementations for computing the discrete Hartley transform (DHT) and the discrete cosine transform (DCT) when the transform size N is decomposable into mutually prime factors are proposed. The existing two-dimensional formulations for DHT and DCT are modified, and the corresponding algorithms are mapped into two-dimensional systolic arrays. The resulting architecture is fully pipelined with no control units. The hardware design is based on bit serial left to right MSB (most significant bit) to LSB (least significant bit) binary arithmetic.
[1] N. Ahmed, T. Natarajan, and K. R. Rao, "Discrete cosine transform,"IEEE Trans. Comput., vol. C-23, pp. 90-93, Jan. 1974.
[2] R.N. Bracewell,The Hartley Transform, Oxford University Press, New York, 1986.
[3] R. N. Bracewell, O. Buneman, H. Hao, and J. Villasenor, "Fast two-dimensional Hartley transform,"Proc. IEEE, vol. 74, no. 9, pp. 1282-1283, Sept. 1986.
[4] C. Chakrabarti and J. JáJá, "Optical systolic designs for computing DHT and DCT," inProc. 1988 IEEE Workshop VLSI Signal Processing, Nov. 1988, pp. 411-422.
[5] C. Chakrabarti and J. JáJá, "A family of optimal architectures for multidimensional transforms," inProc. 26th Annu. Allerton Conf. Commun. Contr. Comput., 1988, pp. 1015-1024.
[6] W.H. Chen, C.H. Smith, and S.C. Fralick, "A Fast Computational Algorithm for the Discrete Cosine Transform,"IEEE Trans. on Comm., Vol. COM-25, 1977, pp. 1,004-1,009.
[7] T. C. Chen, M. T. Sun, and A. M. Gottlieb, "VLSI implementation of a 16×16 DCT," inProc. ICASSP' 88, pp. 1973-1976.
[8] A. M. Chiang, "A video-rate CCD two-dimensional cosine transform processor,"Proc. SPIE, vol. 845, Visual Communications and Image Processing, pp. 2-5, 1987.
[9] D. Elliot and K. Rao,Fast Transforms Algorithms, Analyses, Applications. New York: Academic, 1982.
[10] H. S. Hou, "A fast recursive algorithm for computing the discrete cosine transform,"IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, pp. 1455-1461, Oct. 1987.
[11] H.S. Hou, "The Fast Hartley Transform Algorithm,"IEEE Trans. Computers, Vol. C-36, No. 2, Feb. 1987, pp. 147-156.
[12] F. Jutand, N. Demassieux, and M. Danaet al., "A 13.5 MHz single chip multiformat discrete cosine transform,"Proc. SPIE, vol. 845, Visual Communications and Image Processing, pp. 6-12, 1987.
[13] R. Kumaresan and P. K. Gupta, "Vector-radix algorithm for a 2-D discrete Hartley transform," inProc. ICASSP'85, pp. 40.6.1-40.6.4.
[14] B.G. Lee, "A New Algorithm to Compute the Discrete Cosine Transform,"IEEE Trans. on Acoustics, Speech, and Signal Processing, Vol. ASSP-32, 1984, pp. 1,243-1,245.
[15] B. G. Lee "Input and output index mappings for a prime-factor-decomposed computation of discrete cosine transform,"IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, no. 2, pp. 237-244, Feb. 1989.
[16] R. F. Lyon, "Two's complement pipeline multipliers,"IEEE Trans. Commun., vol. COM-24, no. 4, pp. 418-425, Apr. 1976.
[17] H. Malvar, "Fast computation of discrete cosine transform through fast Hartley transform,"Electron. Lett., vol. 22, pp. 353-354, Mar. 1986.
[18] M. Marchesi, G. Orlandi, and F. Piazza, "A systolic circuit for fast Hartley transform," inProc. IEEE Conf. Circuits Syst., Helsinki, 1988, pp. 2685-2688.
[19] M.J. Narasimha et al., "On the Computation of the Discrete Cosine Transform,"IEEE Trans. Communications, Vol. COM-26, No. 6, June 1978, pp. 934-936.
[20] R. M. Owens and J. Ja'Ja', "VLSI chip for the Winograd/prime factor algorithm to compute the discrete Fourier transform,"IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, no. 4, pp. 979-989, Aug. 1986.
[21] H.V. Sorensen, D.L. Jones, C. S. Burrus, and M.T. Heideman, "On computing the discrete Hartley transform,"IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-33, no. 4, pp. 1231-1238, 1985.
[22] M. Vetterli and H. J. Nussbaumer, "Simple FFT and DCT algorithms with reduced number of operations,"Signal Processing, pp. 267-278, 1984.
[23] P. P. N. Yang and M. J. Narasimha, "Prime factor decomposition of the discrete cosine transform and its hardware realization," inProc. ICASSP' 85, pp. 20.5.1-20.5.4.
[24] S. Winograd, "On computing the discrete Fourier transform,"Math. Comput., vol. 32, pp. 175-195, 1978.