Correlation Functions and Power Spectra

Jan Larsen

AbstractThe present lecture note is a supplement to the textbook Digital Signal Processing by J. Proakis and D.G. Manolakis used in the DTU Informatics course 02451 Digital Signal Processing and provides an extended discussion of correlation functions and power spectra.

The definitions of correlation functions and spectra for discrete-time and
continuous-time (analog) signals are pretty similar. Consequently, we confine
the discussion mainly to real discrete-time signals. The Appendix contains detailed definitions and properties of correlation functions and spectra for analog as well as discrete-time signals.

It is possible to define correlation functions and associated spectra for aperiodic, periodic and random signals although the interpretation is
different. Moreover, we will discuss correlation functions when mixing these basic signal types.

In addition, the note include several examples for the purpose of illustrating the discussed methods.
Keywordsaperiodic, periodic, random signals, cross correlation function, cross power spectrum, estimation, properties, stationary ergodic signals
TypeLecture note
Year2009    Month November
PublisherSection for Cognitive Systems, Department of Informatics and Mathematical Modelling, Tehcnical University of Denmark
AddressRichard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby, Denmark
Note8th edition
Electronic version(s)[pdf]
BibTeX data [bibtex]
IMM Group(s)Intelligent Signal Processing

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