A fast recursive algorithm for computing the discrete cosine transform

The discrete cosine transform (DCT) is widely applied in various fields, including image data compression, because it operates like the Karhunen-Loeve transform for stationary random data. This paper presents a recursive algorithm for DCT with a structure that allows the generation of the next higher order DCT from two identical lower order DCT's. As a result, the method for implementing this recursive DCT requires fewer multipliers and adders than other DCT algorithms.

[1]  Mohammed Ghanbari,et al.  Fast cosine transform implementation for television signals , 1982 .

[2]  Anil K. Jain,et al.  A Sinusoidal Family of Unitary Transforms , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[4]  Ali Habibi,et al.  Direct Computation Of Higher-Order Dct Coefficients From Lower-Order Dct Coefficients , 1984, Optics & Photonics.

[5]  J. Pearl,et al.  Comparison of the cosine and Fourier transforms of Markov-1 signals , 1976 .

[6]  Wen-Hsiung Chen,et al.  A Fast Computational Algorithm for the Discrete Cosine Transform , 1977, IEEE Trans. Commun..

[7]  William C. Miller,et al.  On Computing the Discrete Cosine Transform , 1978, IEEE Transactions on Computers.

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

[9]  MUNSI ALAUL HAQUE,et al.  A two-dimensional fast cosine transform , 1985, IEEE Trans. Acoust. Speech Signal Process..

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

[11]  Nasir Ahmed,et al.  On a Real-Time Walsh-Hadamard/Cosine Transform Image Processor , 1978, IEEE Transactions on Electromagnetic Compatibility.

[12]  Robert M. Harlick.  A Storage Efficient Way to Implement the Discrete Cosine Transform , 1976, IEEE Trans. Computers.

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

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

[15]  R. Clarke,et al.  Relation between the Karhunen Loève and cosine transforms , 1981 .

[16]  K. R. Rao,et al.  Fast Computational for the Discrete Cosine Transform , 1985, Nineteeth Asilomar Conference on Circuits, Systems and Computers, 1985..

[17]  M. Chelemal-D,et al.  FAST COMPUTATIONAL ALGORITHMS FOR THE DISCRETE COSINE TRANSFORM , 1986 .

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

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