Fundamentals of Statistical Signal Processing: Detection theory
The most comprehensive overview of signal detection available. This is a thorough, up-to-date introduction to optimizing detection algorithms for implementation on digital computers. It focuses extensively on real-world signal processing applications, including state-of-the-art speech and communications technology as well as traditional sonar/radar systems. Start with a quick review of the fundamental issues associated with mathematical detection, as well as the most important probability density functions and their properties. Next, review Gaussian, Chi-Squared, F, Rayleigh, and Rician PDFs, quadratic forms of Gaussian random variables, asymptotic Gaussian PDFs, and Monte Carlo Performance Evaluations. Three chapters introduce the basics of detection based on simple hypothesis testing, including the Neyman-Pearson Theorem, handling irrelevant data, Bayes Risk, multiple hypothesis testing, and both deterministic and random signals. The author then presents exceptionally detailed coverage of composite hypothesis testing to accommodate unknown signal and noise parameters. These chapters will be especially useful for those building detectors that must work with real, physical data. Other topics covered include: Detection in nonGaussian noise, including nonGaussian noise characteristics, known deterministic signals, and deterministic signals with unknown parameters Detection of model changes, including maneuver detection and time-varying PSD detection Complex extensions, vector generalization, and array processing The book makes extensive use of MATLAB, and program listings are included wherever appropriate. Designed for practicing electrical engineers, researchers, and advanced students, it is an ideal complement to Steven M. Kay's Fundamentals of Statistical Signal Processing, Vol. 1: Estimation Theory(Prentice Hall PTR, 1993, ISBN: 0-13-345711-7).
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Detection based on simple hypothesis testing is described in Chapters
parameters is the subject of Chapters 69 Other chapters address detection
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2lnLG(x Appendix As[n assume asymptotic PDF asymptotic performance Bayesian Bayesian approach Chapter classical linear model correlation covariance matrix DC level decide H deflection coefficient denoted detection performance detection problem detector decides determine eigenvalues eigenvectors energy detector equivalent estimator estimator-correlator example Fisher information matrix frequency function Gaussian noise Gaussian PDF given GLRT GLRT decides GLRT statistic Hence hypothesis testing hypothesis testing problem Kay-I known signal known variance large data records level in WGN likelihood ratio linear model matched filter maximize N-l N-l nonGaussian noise Note NP detector NP test nuisance parameters output parameter test periodogram prior PDF prior probabilities random signal random variable Rao test Rayleigh fading right-tail probability Section sensor shown in Figure Signal Processing signal with unknown sinusoid sufficient statistic test statistic theorem threshold unknown amplitude unknown parameters variance a2 Wald test WGN with variance Wiener filter