This problem deals with scaling properties of DTFTs, which are rather different from those of CTFTs. You are welcome to use tables. Let x[n] ⇒ X(en), as described in the sketch below for N € [-π, +π] (PS: Only one period of the signal is shown). -pi/2 1 (Part a) Let y[n] be defined as follows. v[n] = { ™ X(ein) h[n] = { x[n/2] n even n odd +pi/2 Derive an expression for Y(en) in terms of X(e) and sketch it for € [−π, +π] (Part b) Let z[n] be defined as follows. z[n] = (-1)"x[n]. Derive an expression for Z(en) in terms of X(en) and sketch it for N € [−π, +π]. Hint: (-1) = ein (Part c) Let h[n] be defined as follows. x[n] Ω n even n odd Express h[n] interms of x[n] and z[n]. Using this expression, derive an expression for H(en) in terms of X(en) and sketch it for NE [−π, +π].

This problem deals with scaling properties of DTFTs, which are rather different from those of CTFTs. You are welcome to use tables. Let x[n] ⇒ X(en), as described in the sketch below for N € [-π, +π] (PS: Only one period of the signal is shown). -pi/2 1 (Part a) Let y[n] be defined as follows. v[n] = { ™ X(ein) h[n] = { x[n/2] n even n odd +pi/2 Derive an expression for Y(en) in terms of X(e) and sketch it for € [−π, +π] (Part b) Let z[n] be defined as follows. z[n] = (-1)"x[n]. Derive an expression for Z(en) in terms of X(en) and sketch it for N € [−π, +π]. Hint: (-1) = ein (Part c) Let h[n] be defined as follows. x[n] Ω n even n odd Express h[n] interms of x[n] and z[n]. Using this expression, derive an expression for H(en) in terms of X(en) and sketch it for NE [−π, +π].

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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