Probability, Random Variables, and Random Signal PrinciplesToday, any well-designed electrical engineering curriculum must train engineers to account for noise and random signals in systems. The best approach is to emphasize fundamental principles since systems can vary greatly. Professor Peebles's book specifically has this emphasis, offering clear and concise coverage of the theories of probability, random variables, and random signals, including the response of linear networks to random waveforms. By careful organization, the book allows learning to flow naturally from the most elementary to the most advanced subjects. Time domain descriptions of the concepts are first introduced, followed by a thorough description of random signals using frequency domain. Practical applications are not forgotten, and the book includes discussions of practical noises (noise figures and noise temperatures) and an entire special chapter on applications of the theory. Another chapter is devoted to optimum networks when noise is present (matched filters and Wiener filters). This third edition differs from earlier editions mainly in making the book more useful for classroom use. Beside the addition of new topics (Poisson random processes, measurement of power spectra, and computer generation of random variables), the main change involves adding many new end-of-chapter exercises (180 were added for a total of over 800 exercises). The new exercises are all clearly identified for instructors who have used the previous edition. |
From inside the book
Results 1-3 of 12
Page 165
... time . We easily visualize any number of random variables X , derived from a random process X ( t ) at times t1 , i ... discrete random process , corre- sponds to the random variable X having only discrete values while t is continuous ...
... time . We easily visualize any number of random variables X , derived from a random process X ( t ) at times t1 , i ... discrete random process , corre- sponds to the random variable X having only discrete values while t is continuous ...
Page 181
... discrete random process known as the Poisson process . † It describes the number of times that some event has occurred as a function of time ... time and the process amounts to counting the number † For additional reading , some recent books ...
... discrete random process known as the Poisson process . † It describes the number of times that some event has occurred as a function of time ... time and the process amounts to counting the number † For additional reading , some recent books ...
Page 182
... time ( the process ) ; then X ( t ) has integer - valued , nondecreasing sample functions , as illustrated in Figure ... discrete random process , and ( b ) the random times of occurrence of events being counted to form the process .
... time ( the process ) ; then X ( t ) has integer - valued , nondecreasing sample functions , as illustrated in Figure ... discrete random process , and ( b ) the random times of occurrence of events being counted to form the process .
Common terms and phrases
Advanced Book Program antenna applied assume autocorrelation function available power gain average power bandpass covariance cross-correlation cross-correlation function cross-power defined denoted discrete random variable distribution function effective input noise effective noise temperature ergodic event Example expected value find the probability Fourier transform frequency Fx(x gaussian random variables given impulse response input noise temperature integral joint density function jointly wide-sense stationary k₁ lowpass mean value noise figure noise power noise temperature output noise power Peebles Poisson power density spectrum power spectrum Problem properties R₁ R₂ random process X(t random variables X1 real constants real number resistor response h(t Rxy(t Ryy(t sample function sample space Show shown in Figure signal x(t spot noise figure stationary process statistically independent Sxx(w Sxy(w t₁ t₂ transfer function uncorrelated variance voltage W₁ W₂ waveform white noise wide-sense stationary wide-sense stationary process X₁ Y₁ Y₂ zero-mean