Beginning Statistical Signal Processing

The subject of statistical signal processing requires a background in probability theory, random variables, and stochastic processes [201]. However, only a small subset of these topics is really necessary to carry out practical spectrum analysis of noise-like signals (Chapter 6) and to fit deterministic models to noisy data. For a full textbook devoted to statistical signal processing, see, e.g., [121,95]. In this appendix, we will provide definitions for some of the most commonly encountered terms.

• 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
  • Estimator Variance
    • Sample-Mean Variance
    • Sample-Variance Variance