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. |
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Page 320
Peyton Z. Peebles. APPENDIX D REVIEW OF FOURIER TRANSFORMS The Fourier transform † or spectrum X ( w ) of a signal x ( t ) is given by ∞ X ( ∞ ) = x ( t ) e - jor dt ( D - 1 ) The inverse Fourier transform allows the recovery of x ( t ) ...
Peyton Z. Peebles. APPENDIX D REVIEW OF FOURIER TRANSFORMS The Fourier transform † or spectrum X ( w ) of a signal x ( t ) is given by ∞ X ( ∞ ) = x ( t ) e - jor dt ( D - 1 ) The inverse Fourier transform allows the recovery of x ( t ) ...
Page 323
... FOURIER TRANSFORMS The Fourier transform X ( w1 , w2 ) of a function x ( t1 , t2 ) of two " time " variables t1 and t2 is defined as the iterated double transform . Upon Fourier transforming x ( t1 , t2 ) first with respect to t , we ...
... FOURIER TRANSFORMS The Fourier transform X ( w1 , w2 ) of a function x ( t1 , t2 ) of two " time " variables t1 and t2 is defined as the iterated double transform . Upon Fourier transforming x ( t1 , t2 ) first with respect to t , we ...
Page 326
... Fourier transform h ( t ) of H ( w ) which is the impulse response of the network , in terms of sampling functions ( see Problem D - 12 ) . D - 14 Let x ( t ) have the Fourier transform X ( w ) . Find the transforms of the fol- lowing ...
... Fourier transform h ( t ) of H ( w ) which is the impulse response of the network , in terms of sampling functions ( see Problem D - 12 ) . D - 14 Let x ( t ) have the Fourier transform X ( w ) . Find the transforms of the fol- lowing ...
Contents
0 | 1 |
The Random Variable | 34 |
Star indicates more advanced material | 43 |
Copyright | |
14 other sections not shown
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Probability, Random Variables, and Random Signal Principles Peyton Z. Peebles,Bertram Emil Shi No preview available - 2015 |
Common terms and phrases
A₁ Advanced Book Program applied assumed autocorrelation function available power gain average power B₁ bandpass characteristic function correlation covariance cross-correlation cross-correlation function denoted discrete random variable distribution function Example expected value Find and sketch Fourier transform frequency Fx(x fy(y gaussian random variable given impulse response integral joint density function jointly wide-sense stationary lowpass matched filter mean value noise figure noise power noise temperature output noise power Peebles power density spectrum power spectrum probability density Problem properties publishers Addison-Wesley R₂ random process X(t random signal random vari real constants real number resistor Rxx(t Rxy(t Ryy(t S₁ S₂ sample function sample space shown in Figure signal x(t SNN(W stationary process statistically independent Sxx(w Sxy(w t₁ t₂ transfer function uncorrelated variance voltage W₁ waveform white noise wide-sense stationary X₁ Y₁ Y₂ zero-mean