Random Signals: Detection, Estimation and Data Analysis
Random Signals, Noise and Filtering develops the theory of random processes and its application to the study of systems and analysis of random data. The text covers three important areas: (1) fundamentals and examples of random process models, (2) applications of probabilistic models: signal detection, and filtering, and (3) statistical estimation--measurement and analysis of random data to determine the structure and parameter values of probabilistic models. This volume by Breipohl and Shanmugan offers the only one-volume treatment of the fundamentals of random process models, their applications, and data analysis.
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Review of Probability and Random Variables
Random Processes and Sequences
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analysis approximately ARMA assume autocorrelation function binary called chapter chi-square communication system conditional correlation decision rule defined degrees of freedom derived discrete empirical distribution function ensemble ergodic example expected value Find finite first-order Fourier transform frequency domain fx(x Gaussian random variable given in Equation hence independent input integral interval joint Kalman filter likelihood function Markov chain matrix maximum likelihood estimator mean squared measurements member function minimize normal random variable Note null hypothesis observations obtain optimum orthogonal output partial autocorrelation periodogram power spectral density probability density function probability mass function Problem pulse quantizer random experiment random process random process X(t random sequence random signals Rxx(k Rxx(m Rxx(t sample function shown in Figure significance level SOLUTION spectral density function squared error statistic sum of squares Sxx(f unbiased unknown parameter vector waveform white noise Wiener filter Wiley & Sons