Beginning Statistical Signal Processing

The subject of statistical signal processing requires a background in probability theory, random variables, and stochastic processes [185]. However, only a small subset of these topics is really necessary to carry out practical spectrum analysis of noise-like signals (Chapter 5) and to fit deterministic models to noisy data. For a full textbook devoted to statistical signal processing, see, e.g., [107]. In this appendix, we will provide definitions for some of the most commonly encountered terms.

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Subsections

• Stochastic Processes
  • Probability Distribution
  • Independent Events
  • Random Variable
  • Stochastic Process
  • Stationary Stochastic Process
  • Expected Value
  • Mean
  • Sample Mean
  • Variance
  • Sample Variance
  
  
• Correlation Analysis
  • Cross-Correlation
  • Cross-Power Spectral Density
  • Autocorrelation
  • Sample Autocorrelation
  • Power Spectral Density
  • Sample Power Spectral Density
  
  
• White Noise
  • Making White Noise with Dice
  • Independent Implies Uncorrelated

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.