Probabilities, Random Variables, and Random Processes: Digital and Analog |
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Page vii
... Random Inputs 338 Summary 358 Problems 360 CHAPTER 8 The Power Spectral Density and Input - Output Relations for a Linear System with Random Inputs 367 8.1 A Summary of Laplace and z Transforms 367 8.2 8.3 8.4 A Summary of Fourier and ...
... Random Inputs 338 Summary 358 Problems 360 CHAPTER 8 The Power Spectral Density and Input - Output Relations for a Linear System with Random Inputs 367 8.1 A Summary of Laplace and z Transforms 367 8.2 8.3 8.4 A Summary of Fourier and ...
Page 367
Digital and Analog Michael O'Flynn. The Power Spectral Density and Input - Output Relations for a Linear System with Random Inputs 8.1 A SUMMARY OF LAPLACE AND TRANSFORMS z The time domain interpretation of random processes and of input ...
Digital and Analog Michael O'Flynn. The Power Spectral Density and Input - Output Relations for a Linear System with Random Inputs 8.1 A SUMMARY OF LAPLACE AND TRANSFORMS z The time domain interpretation of random processes and of input ...
Page 432
... INPUT - OUTPUT SPECTRAL RELATIONS FOR SYSTEMS WITH RANDOM INPUTS This section will develop formulas for relating the output power spectral density of a linear time - invariant causal system to its input power spectral density and the ...
... INPUT - OUTPUT SPECTRAL RELATIONS FOR SYSTEMS WITH RANDOM INPUTS This section will develop formulas for relating the output power spectral density of a linear time - invariant causal system to its input power spectral density and the ...
Contents
1 | 3 |
5 | 54 |
General Formulation and Solution of Problems | 69 |
Copyright | |
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Common terms and phrases
A₁ autocorrelation function average axiom B₁ balls Chapter convolution correlation integrals cross-correlation cross-correlation function cumulative distribution function dadß defined definition delta function denoted derivation deterministic discrete Fourier transform discrete probability theory discrete random process DRILL SET ensemble ergodic evaluate event space Example finite first-order stationary formula fundamental theorem fxy(a fy(B fz(y given impulse response joint density function joint mass function Laplace transform linear system M₁ member waveform notation obtained otherwise output periodic function periodic waveform permutations plotted in Figure points power spectral density probability measure probability theory problem properties pulse px(a random input random phenomenon range Rxx(T sample description space sampled values second-order stationary set theory shown in Figure shown plotted signal sketch SOLUTION solved statistics Sxx(w Ticket Pays two-sided Laplace transform two-sided z transform typical member X₁ z transform zero-mean