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Question 1 A system with impulse response function h[n]=cos[2n] is periodic

Electrical Engineering

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Question 1

A system with impulse response function h[n]=cos[2n] is periodic.

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Question 2

In this problem, we illustrate one of the most important consequences of the properties, of linearity and time variance. Specifically, once we know the the response of a linear time invariant (LTI) system to a single input or the responses to a several inputs. We can directly compute the responses to a many other input Signals. Much of the r remainder of this book deals with a thorough exploitation of this fact in order to develop results and techniques for analyzing and synthesizing LTI system

... Consider an LTI system whose response to the signal X1(t) in figure P1.31 (a) is the signal Y₁(t) illustration in figure P131(b) Determine and sketch carefully the response of the system in the input X2(t) depicted inFigure P1_31(c)

Question 3

A discrete-time system has the following input-output relation:

y[n]=a x[n-1]-3(x[n]+x[n-2])

 where a is an unknown to be found. We are told that H(e^jx)0, where H(e^jx) is the DTFT of the impulse response (frequency response) of the system. Find the value of a.