a.) Sketch each of the following signals, and starting with the defining relation, finds its Fourier transform X (w) - a) x(t) = rect(t − 3) b) x(t)=3t rect(t) c) x(t) = 2te 3u1(t) d) x(t) = e−2|t| b.) Sketch the magnitude and phase spectrum for the four signals in Problem (a). c) Calculate energy using time-domain and frequency domain formulas for signals in Problem (a) and (b). Confirm Parseval's theorem using these calculations.

Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter6: Power Flows
Section: Chapter Questions
Problem 6.16P
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a.) Sketch each of the following signals, and starting with the defining relation, finds its Fourier transform
X (w)
-
a) x(t) = rect(t − 3)
b) x(t)=3t rect(t)
c) x(t) = 2te 3u1(t)
d) x(t) = e−2|t|
b.) Sketch the magnitude and phase spectrum for the four signals in Problem (a).
c) Calculate energy using time-domain and frequency domain formulas for signals in Problem (a) and
(b). Confirm Parseval's theorem using these calculations.
Transcribed Image Text:a.) Sketch each of the following signals, and starting with the defining relation, finds its Fourier transform X (w) - a) x(t) = rect(t − 3) b) x(t)=3t rect(t) c) x(t) = 2te 3u1(t) d) x(t) = e−2|t| b.) Sketch the magnitude and phase spectrum for the four signals in Problem (a). c) Calculate energy using time-domain and frequency domain formulas for signals in Problem (a) and (b). Confirm Parseval's theorem using these calculations.
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