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Recent Progress in Operator Theory and Its Applications pp 197–205Cite as

On the Discrete Cosine Transform of Weakly Stationary Signals

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 220))

Abstract

The Discrete Cosine Transform (DCT) is used in a large variety of applications, due to its near-optimal properties for representing and decorrelating random signals. This paper describes a useful but relatively unknown property of this transform, when applied to weakly stationary signals. The transformed autocorrelation matrix has half of its elements equal to zero. This means that it is possible to improve current DCT signal processing systems by means of more efficient implementation and algorithms.

Mathematics Subject Classification (2000).Primary 60G10; Secondary 47A05.

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Author information

Authors and Affiliations

  1. Escuela de Ingenieria, Universidad La Salle, Benjamin Franklin 47 Col. Hipodromo Condesa, Mexico City, CP 06140, Mexico

    Mauricio Martinez-Garcia

Authors
  1. Mauricio Martinez-Garcia
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Correspondence to Mauricio Martinez-Garcia .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Virginia Polytechnic Institute, McBryde Hall 524, Blacksburg, 24061, Virginia, USA

    Joseph A. Ball

  2. Dept. Mathematics, University of Iowa, MacLean Hall 14, Iowa City, 52242-1419, Iowa, USA

    Raúl E. Curto

  3. , CINVESTAV, IPN - Instituto Politécnico Nacional, Av. IPN 2508, Mexico, D.F., 07360, Distrito Federal, Mexico

    Sergei M. Grudsky

  4. Dept. Mathematics, University of California, San Diego, Gilman Dr. 9500, La Jolla, 92093-0112, California, USA

    J. William Helton

  5. , Departamento di Matemática, Centro de Investigación en Matemáticas, Guanajuato, Gto., 36000, Guanajuato, Mexico

    Raúl Quiroga-Barranco

  6. Departamento de Matemática, CINVESTAV-IPN, Apdo. Postal, México, 07300, Distrito Federal, Mexico

    Nikolai L. Vasilevski

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Martinez-Garcia, M. (2012). On the Discrete Cosine Transform of Weakly Stationary Signals. In: Ball, J., Curto, R., Grudsky, S., Helton, J., Quiroga-Barranco, R., Vasilevski, N. (eds) Recent Progress in Operator Theory and Its Applications. Operator Theory: Advances and Applications(), vol 220. Springer, Basel. https://doi.org/10.1007/978-3-0348-0346-5_12

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