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
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Page 200
... a deterministic signal x ( t ) are contained in its Fourier transform X ( w ) given by X ( w ) = S . x ( t ) e - jost dt ∞ ( 7.1-1 ) The function X ( w ) , sometimes called simply the spectrum of x ( t ) , has the unit of volts per hertz ...
... a deterministic signal x ( t ) are contained in its Fourier transform X ( w ) given by X ( w ) = S . x ( t ) e - jost dt ∞ ( 7.1-1 ) The function X ( w ) , sometimes called simply the spectrum of x ( t ) , has the unit of volts per hertz ...
Page 309
... signal x ( t ) = u ( t ) [ e ̄W21 - e - aw2t ] if a 1 is a real constant . 9-3 Work Problem 9-1 ( a ) , ( b ) , and ( c ) for the signal if a 1 is a real constant . x ( t ) = u ( − t ) [ eW21 - eaW21 ] * 9-4 By proper inverse Fourier ...
... signal x ( t ) = u ( t ) [ e ̄W21 - e - aw2t ] if a 1 is a real constant . 9-3 Work Problem 9-1 ( a ) , ( b ) , and ( c ) for the signal if a 1 is a real constant . x ( t ) = u ( − t ) [ eW21 - eaW21 ] * 9-4 By proper inverse Fourier ...
Page 310
Peyton Z. Peebles. 9-11 Show that the output signal x ( t ) from a filter matched to a signal x ( t ) in white noise is * [ " . x * ( 5 ) x ( ¿ + t − t ) dě - ∞ x ( t ) = K - That is , x ( t ) is proportional to the correlation integral ...
Peyton Z. Peebles. 9-11 Show that the output signal x ( t ) from a filter matched to a signal x ( t ) in white noise is * [ " . x * ( 5 ) x ( ¿ + t − t ) dě - ∞ x ( t ) = K - That is , x ( t ) is proportional to the correlation integral ...
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