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Let x(t) be the complex exponential signal, x(t) = ejot with radian frequency and fundamental period T = 27/a. Consider the discrete-time sequence x(n) obtained by the uniform sampling of x(t) with sampling interval T,, i.e., x(n) = x(nT₂) = enoot, Show that x(n) is periodic if the ratio of the sampling interval T, to the fundamental period T of x(t), i.e., T/T is a rational number.

Let x(t) be the complex exponential signal, x(t) = ejot with radian frequency and fundamental period T = 27/a. Consider the discrete-time sequence x(n) obtained by the uniform sampling of x(t) with sampling interval T,, i.e., x(n) = x(nT₂) = enoot, Show that x(n) is periodic if the ratio of the sampling interval T, to the fundamental period T of x(t), i.e., T/T is a rational number.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Let x(t) be the complex exponential signal, x(t) = ejot with radian frequency and fundamental period T = 27/a. Consider the discrete-time sequence x(n) obtained by the uniform sampling of x(t) with sampling interval T,, i.e., x(n) = x(nT₂) = ejnoots Show that x(n) is periodic if the ratio of the sampling interval T, to the fundamental period T of x(t), i.e., T/T is a rational number.
Transcribed Image Text:Let x(t) be the complex exponential signal, x(t) = ejot with radian frequency and fundamental period T = 27/a. Consider the discrete-time sequence x(n) obtained by the uniform sampling of x(t) with sampling interval T,, i.e., x(n) = x(nT₂) = ejnoots Show that x(n) is periodic if the ratio of the sampling interval T, to the fundamental period T of x(t), i.e., T/T is a rational number.
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