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

Author

Moura, Jose M F ; Bruno, Marcelo G S

Author_Institution

Dept. of Electr. & Comput. Eng., Carnegie Mellon Univ., Pittsburgh, PA, USA

Volume

46

Issue

9

fYear

1998

fDate

9/1/1998 12:00:00 AM

Firstpage

2571

Lastpage

2574

Abstract

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

Keywords

Gaussian processes; Markov processes; Toeplitz matrices; covariance matrices; discrete cosine transforms; lattice theory; polynomial matrices; random processes; 1D Gauss noncausal Markov random fields; 2D Gauss noncausal Markov random fields; DCT; DST; Gauss-Markov fields; Toeplitz matrix; boundary conditions; covariance matrix; discrete cosine transform; discrete sine transform; equivalence conditions; finite lattices; first-order Gauss causal Markov random processes; homogeneous Gauss noncausal Markov random fields; matrix polynomials; Boundary conditions; Counting circuits; Covariance matrix; Discrete cosine transforms; Discrete transforms; Gaussian processes; Lattices; Markov random fields; Random processes; Symmetric matrices;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.709549

Filename

709549