! 7.x,(1) has a band-limited spectrum X,UN), as sketched in Figure 7.2(a), and is beingsampled at the Nyquist rate. The discrete-time processor is an ideal lowpass filter with afrequency response H(e"), as shown in Figure 7.2(b), and has a cutoff frequency0, =2_T/2, where T is the sampling period. Sketch as accurately as possible thespectrum Y,(2) of the output continuous-time signal y,(1).Consider the system of Figure 7.1, where the input continuous-time signalDiscrete-IdealIdealtimeInter-samplerprocessorpolatorFigure 7.1H(e®)2(a)Figure 7.2

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Answered: 7. x,(1) has a band-limited spectrum…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 17EQ

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a. The general continuous-time random walk is defined by g_(ij)={[mu_(i)",",j=i-1","],[-(lambda_(i)+mu_(i))",",j=i","],[lambda_(i)",",j=i+1","],[0","," otherwise "]:} Write out the forward and backward equations. b. The continuous-time queue with infinite buffer can be obtained by modifying the general random walk in the preceding problem to include a barrier at the origin. Put g_(0j)={[-lambda_(0)",",j=0","],[lambda_(0)",",j=1","],[0","," otherwise ".]:} Find the stationary distribution assuming sum_(j=1)^(oo)((lambda_(0)cdotslambda_(j-1))/(mu_(1)cdotsmu_(j))) < oo. If lambda_(i)=lambda and mu_(i)=mu for all i, simplify the above condition to one involving only the relative values of lambda and mu. c. Repeat a and b assuming there is a boundary at j=N. Comments.need explicit calculation process, step by step

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