hip between input X (t) and output Y (t) of a diode is expressed Y(t) = X2(t) Let X(t) be a wide sense stationary Gaussian random process with m autocorrelation Rxx(t,, t2) = e-altz-tl a > 0 a) Find the mean of the diode output. b) Find the autocorrelation of the diode output. c) Is the diode output wide sense stationary? Give reasoning. Hint: For any two Gaussian RVs X, and X2; E[X?X3] = E[X{]E[X3]+ 2(E[X,X_])² %3D

Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter6: Power Flows
Section: Chapter Questions
Problem 6.22P
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The relationship between input X(t) and output Y (t) of a diode is expressed as
Y(t) = X²(t)
Let X(t) be a wide sense stationary Gaussian random process with mea
autocorrelation
Rxx(t, t2) = e-alt;-l,
a >0
a) Find the mean of the diode output.
b) Find the autocorrelation of the diode output.
c) Is the diode output wide sense stationary? Give reasoning.
Hint: For any two Gaussian RVs X, and X2;
E[X?X3] = E[Xf]E[X?]+ 2(E[X;X2])²
%3D
Transcribed Image Text:The relationship between input X(t) and output Y (t) of a diode is expressed as Y(t) = X²(t) Let X(t) be a wide sense stationary Gaussian random process with mea autocorrelation Rxx(t, t2) = e-alt;-l, a >0 a) Find the mean of the diode output. b) Find the autocorrelation of the diode output. c) Is the diode output wide sense stationary? Give reasoning. Hint: For any two Gaussian RVs X, and X2; E[X?X3] = E[Xf]E[X?]+ 2(E[X;X2])² %3D
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