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 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. >

[1]  Weiping Li,et al.  A new algorithm to compute the DCT and its inverse , 1991, IEEE Trans. Signal Process..

[2]  PeiZong Lee,et al.  Restructured recursive DCT and DST algorithms , 1994, IEEE Trans. Signal Process..

[3]  M. J. Narasimha,et al.  On the Computation of the Discrete Cosine Transform , 1978, IEEE Trans. Commun..

[4]  Douglas L. Jones,et al.  Real-valued fast Fourier transform algorithms , 1987, IEEE Trans. Acoust. Speech Signal Process..

[5]  H. Nussbaumer.  Fast Fourier transform and convolution algorithms , 1981 .

[6]  Hsieh S. Hou.  A fast recursive algorithm for computing the discrete cosine transform , 1987, IEEE Trans. Acoust. Speech Signal Process..

[7]  P. Yip,et al.  Discrete Cosine Transform: Algorithms, Advantages, Applications , 1990 .

[8]  B. Lee.  A new algorithm to compute the discrete cosine Transform , 1984 .

[9]  S. Winograd.  On computing the Discrete Fourier Transform. , 1976, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Byeong Gi Lee.  Input and output index mappings for a prime-factor-decomposed computation of discrete cosine transform , 1989, IEEE Trans. Acoust. Speech Signal Process..

[11]  C. S. Burrus.  Bit reverse unscrambling for a radix-2MFFT , 1987, ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[12]  T. Parks,et al.  A prime factor FFT algorithm using high-speed convolution , 1977 .

[13]  Zhongde Wang.  Fast algorithms for the discrete W transform and for the discrete Fourier transform , 1984 .

[14]  D.P.-K. Lun,et al.  Yet a faster address generation scheme for the computation of prime factor algorithms , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[15]  Zvi M. Kedem,et al.  Mapping Nested Loop Algorithms into Multidimensional Systolic Arrays , 2017, IEEE Trans. Parallel Distributed Syst..

[16]  Clive Temperton.  Implementation of a prime factor FFT algorithm on CRAY-1 , 1988, Parallel Comput..

[17]  N. Ahmed,et al.  Discrete Cosine Transform , 1996 .

[18]  P. Yang,et al.  Prime factor decomposition of the discrete cosine transform and its hardware realization , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[19]  Michael T. Heideman,et al.  Computation of an odd-length DCT from a real-valued DFT of the same length , 1992, IEEE Trans. Signal Process..

[20]  Joseph H. Rothweiler.  Implementation of the in-order prime factor transform for variable sizes , 1982 .

[21]  C. Burrus,et al.  An in-place, in-order prime factor FFT algorithm , 1981 .

[22]  C. Burrus.  Index mappings for multidimensional formulation of the DFT and convolution , 1977 .

[23]  Wan-Chi Siu,et al.  Data Routing Networks for Systolic/Pipeline Realization of Prime Factor Mapping , 1991, IEEE Trans. Computers.

[24]  Wan-Chi Siu,et al.  Efficient address generation for prime factor algorithms [digital signal processing] , 1990, IEEE Trans. Acoust. Speech Signal Process..

[25]  Wan-Chi Siu,et al.  On prime factor mapping for the discrete Hartley transform , 1992, IEEE Trans. Signal Process..

[26]  Zhong-De Wang.  A fast algorithm for the discrete sine transform implemented by the fast cosine transform , 1982 .

[27]  C. Sidney Burrus.  Unscrambling for fast DFT algorithms , 1988, IEEE Trans. Acoust. Speech Signal Process..

[28]  Lynn Conway,et al.  Introduction to VLSI systems , 1978 .

[29]  Clive Temperton.  Implementation of a self-sorting in-place prime factor FFT algorithm , 1985 .

[30]  Clive Temperton,et al.  Note a note on prime factor FFT algorithms , 1983 .

[31]  K.-L. Wong,et al.  Fast address generation for the computation of prime factor algorithms , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[32]  Chaitali Chakrabarti,et al.  Systolic Architectures for the Computation of the Discrete Hartley and the Discrete Cosine Transforms Based on Prime Factor Decomposition , 1990, IEEE Trans. Computers.

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

[34]  M. Vetterli,et al.  Simple FFT and DCT algorithms with reduced number of operations , 1984 .

[35]  Nam Ik Cho,et al.  DCT algorithms for VLSI parallel implementations , 1990, IEEE Trans. Acoust. Speech Signal Process..