(Part a) Differentiation in frequency of DTFTs. Show that d -jnx[n] ⇒ X(e³¹). dn (Part b) Time-shift property of DTFTs. Show that x[n 1] ⇒e¯ X (ein) ΖΩ (Part c) Using the properties proved in Parts A and B, show that 1 |a| < 1, (1 - ae-in) ² (n+1) au[n+1] →

Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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(Part a) Differentiation in frequency of DTFTs. Show that
d
- jnx[n]
dn
-X(e).
(Part b) Time-shift property of DTFTs. Show that
x[n − 1] ⇒ e¯jª X (e³¹)
(Part c) Using the properties proved in Parts A and B, show that
1
|a| < 1,
(1 - ae-in) ²
(n+1) au[n+1] →
Transcribed Image Text:(Part a) Differentiation in frequency of DTFTs. Show that d - jnx[n] dn -X(e). (Part b) Time-shift property of DTFTs. Show that x[n − 1] ⇒ e¯jª X (e³¹) (Part c) Using the properties proved in Parts A and B, show that 1 |a| < 1, (1 - ae-in) ² (n+1) au[n+1] →
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