An efficient prime-factor algorithm for the discrete cosine transform and its hardware implementations
The prime-factor decomposition is a fast computational technique for many important digital signal processing operations, such as the convolution, the discrete Fourier transform, the discrete Hartley transform, and the discrete cosine transform (DCT). The authors present a new prime-factor algorithm...
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| Published in | IEEE transactions on signal processing Vol. 42; no. 8; pp. 1996 - 2005 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
IEEE
01.08.1994
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1053-587X |
| DOI | 10.1109/78.301838 |
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| Abstract | The prime-factor decomposition is a fast computational technique for many important digital signal processing operations, such as the convolution, the discrete Fourier transform, the discrete Hartley transform, and the discrete cosine transform (DCT). The authors present a new prime-factor algorithm for the DCT. They also design a prime-factor algorithm for the discrete sine transform based on the prime-factor DCT algorithm. Hardware implementations for the prime-factor DCT are also studied. They are especially interested in the hardware designs which are suitable for the VLSI implementations. They show three hardware designs for the prime-factor DCT, including a VLSI circuit fabricated directly according to the signal-flow graph, a linear systolic array, and a mesh-connected systolic array. These three designs show the trade-off between cost and performance. The methodology, which deals with general (N/sub 1//spl times/ N/sub 2/)-point DCTs, where N/sub 1/ and N/sub 2/ are mutually prime, is illustrated by converting a 15-point DCT problem into a (3/spl times/5)-point 2D DCT problem.< > |
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| AbstractList | The prime-factor decomposition is a fast computational technique for many important digital signal processing operations, such as the convolution, the discrete Fourier transform, the discrete Hartley transform, and the discrete cosine transform (DCT). The authors present a new prime-factor algorithm for the DCT. They also design a prime-factor algorithm for the discrete sine transform based on the prime-factor DCT algorithm. Hardware implementations for the prime-factor DCT are also studied. They are especially interested in the hardware designs which are suitable for the VLSI implementations. They show three hardware designs for the prime-factor DCT, including a VLSI circuit fabricated directly according to the signal-flow graph, a linear systolic array, and a mesh-connected systolic array. These three designs show the trade-off between cost and performance. The methodology, which deals with general (N/sub 1//spl times/ N/sub 2/)-point DCTs, where N/sub 1/ and N/sub 2/ are mutually prime, is illustrated by converting a 15-point DCT problem into a (3/spl times/5)-point 2D DCT problem.< > The prime-factor decomposition is a fast computational technique for many important digital signal processing operations, such as the convolution, the discrete Fourier transform, the discrete Hartley transform, and the discrete cosine transform (DCT). The authors present a new prime-factor algorithm for the DCT. They also design a prime-factor algorithm for the discrete sine transform based on the prime-factor DCT algorithm. Hardware implementations for the prime-factor DCT are also studied. They are especially interested in the hardware designs which are suitable for the VLSI implementations. They show three hardware designs for the prime-factor DCT, including a VLSI circuit fabricated directly according to the signal-flow graph, a linear systolic array, and a mesh-connected systolic array. These three designs show the trade-off between cost and performance. The methodology, which deals with general (N(1)x N(2))-point DCTs, where N(1) and N(2) are mutually prime, is illustrated by converting a 15-point DCT problem into a (3x5)-point 2D DCT problem |
| Author | Fang-Yu Huang Pei-Zong Lee |
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| Cites_doi | 10.1109/TASSP.1987.1165220 10.1109/78.157181 10.1109/29.60072 10.1109/TASSP.1977.1162973 10.1016/0165-1684(84)90059-8 10.1109/TASSP.1982.1163852 10.2307/2006266 10.1109/ICASSP.1990.115691 10.1109/ICASSP.1985.1168330 10.1109/TASSP.1982.1163963 10.1016/0021-9991(83)90024-4 10.1109/29.1631 10.1109/78.298269 10.1007/978-3-662-00551-4 10.1109/TASSP.1981.1163645 10.1109/12.83654 10.1109/TASSP.1977.1162938 10.1016/0167-8191(88)90008-7 10.1109/78.136537 10.1109/TCOM.1978.1094144 10.1109/12.61045 10.1109/TASSP.1985.1164687 10.1109/71.80125 10.1109/78.139244 10.1109/TASSP.1984.1164399 10.1109/29.21686 10.1016/0021-9991(85)90164-0 10.1109/ICASSP.1989.266622 10.1109/29.45624 |
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| References | ref35 ref13 ref34 ref15 ref14 ref31 ref30 ref33 lee (ref12) 1984; assp 32 ref32 ref10 ref1 ref17 ref16 ref19 ref18 cho (ref7) 1990; 38 chan (ref6) 1992 rao (ref21) 1990 ref24 ref23 ref26 ref25 ref22 ref28 ref27 ref29 hou (ref9) 1987; assp 35 nussbaumer (ref20) 1981 ref8 ref4 ref3 burrus (ref2) 1987 ref5 kung (ref11) 1980 |
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| SubjectTerms | Algorithm design and analysis Convolution Digital signal processing Discrete cosine transforms Discrete Fourier transforms Fast Fourier transforms Hardware Signal processing algorithms Systolic arrays Very large scale integration |
| Title | An efficient prime-factor algorithm for the discrete cosine transform and its hardware implementations |
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