a) I am a continuous-time signal x(t). When you convolute me with any other continuous-timesignal v(t) then the result will be v(t) itself. Who am I?b) Let A € R4. Define the set Sa to be the set of all continuous-time signals x(t) whose FourierTransform X (w) is zero for lw| > AT. I am a signal from SA . When you convolute me withany other signal v(t) E Sa then the result will be v(t) itself. Who am I?c) Let SĄ be defined as in part b). Consider a signal æ(t) of finite duration in the time domain.Then there exists no A e R, such that x(t) E SA. Show that this statement is true.

According to guidelines we need to solve only the first question. According to the question we have…

Answered: a) I am a continuous-time signal æ(t).…

a) I am a continuous-time signal æ(t). When you convolute me with any other continuous-time signal v(t) then the result will be v(t) itself. Who am I?

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Question

a) I am a continuous-time signal x(t). When you convolute me with any other continuous-time
signal v(t) then the result will be v(t) itself. Who am I?
b) Let A € R4. Define the set Sa to be the set of all continuous-time signals x(t) whose Fourier
Transform X (w) is zero for lw| > AT. I am a signal from SA . When you convolute me with
any other signal v(t) E Sa then the result will be v(t) itself. Who am I?
c) Let SĄ be defined as in part b). Consider a signal æ(t) of finite duration in the time domain.
Then there exists no A e R, such that x(t) E SA. Show that this statement is true.

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