Principles of Signal Detection and Parameter Estimation by Bernard C. Levy

By Bernard C. Levy

This new textbook is for modern sign detection and parameter estimation classes provided on the complicated undergraduate and graduate degrees. It offers a unified remedy of detection difficulties coming up in radar/sonar sign processing and glossy electronic verbal exchange platforms. the cloth is complete in scope and addresses sign processing and conversation functions with an emphasis on basic ideas. as well as common issues often lined in this kind of direction, the writer accommodates contemporary advances, resembling the asymptotic functionality of detectors, sequential detection, generalized chance ratio exams (GLRTs), strong detection, the detection of Gaussian indications in noise, the expectancy maximization set of rules, and the detection of Markov chain indications. a variety of examples and certain derivations besides homework difficulties following every one bankruptcy are included.

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4 Receiver Operating Characteristic 31 FL ( |H0 ) 1 1 − α3 1 − α2 f0 1 − α1 λ1 = 0 λ2 λ3 Fig. 2. Selection of the Neyman-Pearson threshold λ by using the cumulative probability distribution FL ( |H0 ). 58) where FL (λ− |H0 ) denotes the left limit of FL ( |H0 ) at = λ. This case corresponds to the values 1−α3 and λ3 of Fig. 2. Then if we consider the LRT δL,λ , it has the probability of false alarm PF (δL,λ ) = 1−FL (λ|H0 ) < α. Similarly the test δU,λ has probability of false alarm PF (δU,λ ) = 1 − FL (λ− |H0 ) > α.

125). 114) should ¯j be interpreted as the Euclidean distance between the transformed signals m after the noise has been whitened and scaled so its variance is unity. 2 Detection of a Zero-Mean Gaussian Signal in Noise Suppose the means m0 = m1 = 0 and K1 > K0 .

Up to this point, the sufficient statistics we have encountered have been scalar, but vector sufficient statistics can also arise. In general, we say that S(Y) ∈ Rk is a sufficient statistic for the binary hypothesis testing problem if the conditional density fY|S (y|s, Hj ) is independent of hypothesis Hj . 41) is one-to-one, where g and h denote respectively the forward and reverse mappings. 42) where J(y) denotes the Jacobian of the transformation h. Note that J is the same for H0 and H1 , as it depends only on h.

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