An Introduction to Statistical Signal Processing
This book describes the essential tools and techniques of statistical signal processing. At every stage theoretical ideas are linked to specific applications in communications and signal processing using a range of carefully chosen examples. The book begins with a development of basic probability, random objects, expectation, and second order moment theory followed by a wide variety of examples of the most popular random process models and their basic uses and properties. Specific applications to the analysis of random signals and systems for communicating, estimating, detecting, modulating, and other processing of signals are interspersed throughout the book. Hundreds of homework problems are included and the book is ideal for graduate students of electrical engineering and applied mathematics. It is also a useful reference for researchers in signal processing and communications.
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abstract space assume autocorrelation function autoregressive binary Borel called characteristic function compute conditional pmf conditional probability consider convergence countable counting process covariance function Define the random deﬁned definition denote described discrete time random equation ergodic estimate evaluate event F event space example expectation Find the mean finite formula Fourier transform given hence iid process iid random implies interval intuitive joint pmf large numbers law of large Lemma limit linear filter linear system marginal Markov matrix mean squared error modulation noise nonnegative notation Observe output process parameter pdf’s pmf’s points Poisson power spectral density probability measure probability space problem process Xn proof properties random process random variable random vector real line real numbers result Riemann integral sample space second-order sequence sigma-field signal processing subsets Suppose theorem theory uncorrelated variance waveforms weakly stationary yields zero zero-mean