Correlation Functions and Power Spectra  Jan Larsen
 Abstract  The 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 discretetime and
continuoustime (analog) signals are pretty similar. Consequently, we confine
the discussion mainly to real discretetime signals. The Appendix contains detailed definitions and properties of correlation functions and spectra for analog as well as discretetime 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.  Keywords  aperiodic, periodic, random signals, cross correlation function, cross power spectrum, estimation, properties, stationary ergodic signals  Type  Lecture note  Year  2009 Month November  Publisher  Section for Cognitive Systems, Department of Informatics and Mathematical Modelling, Tehcnical University of Denmark  Address  Richard Petersens Plads, Building 321, DK2800 Kgs. Lyngby, Denmark  Note  8th edition  Electronic version(s)  [pdf]  BibTeX data  [bibtex]  IMM Group(s)  Intelligent Signal Processing 
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