DCT/DST and Gauss-Markov fields: conditions for equivalence

The correspondence addresses the intriguing question of which random models are equivalent to the discrete cosine transform (DCT) and discrete sine transform (DST). Common knowledge states that these transforms are asymptotically equivalent to first-order Gauss causal Markov random processes. We establish that the DCT and the DST are exactly equivalent to homogeneous one-dimensional (1-D) and two-dimensional (2-D) Gauss noncausal Markov random fields defined on finite lattices with appropriate boundary conditions.

[1]  Anil K. Jain.  Fundamentals of Digital Image Processing , 2018, Control of Color Imaging Systems.

[2]  W. Kenneth Jenkins,et al.  Alternate realizations to adaptive IIR filters and properties of their performance surfaces , 1989 .

[3]  G. Bonnerot,et al.  A 60 Channel PCM-ADPCM Converter , 1982, IEEE Trans. Commun..

[4]  Antonio M. Peinado,et al.  Generating matrices for the discrete sine transforms , 1996, IEEE Trans. Signal Process..

[5]  U. Forssen.  Analysis of adaptive FIR filters in cascade form , 1994 .

[6]  Woo-Jin Song,et al.  A complementary pair LMS algorithm for adaptive filtering , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[7]  Nikhil Balram,et al.  Recursive structure of noncausal Gauss-Markov random fields , 1992, IEEE Trans. Inf. Theory.

[8]  George Carayannis,et al.  A fast sequential algorithm for least-squares filtering and prediction , 1983 .

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

[10]  Antonio M. Peinado,et al.  Diagonalizing properties of the discrete cosine transforms , 1995, IEEE Trans. Signal Process..

[11]  L. Jackson,et al.  Linear prediction in cascade form , 1978 .