Find f(t) if100f(t)= F(@)eitw dw, where2π04+jw.F(w) =F (ω)8+jwπδω).Express your answer in complex form.

Consider the given expression, ft=12π∫0∞Fωejtωdω Substitute the given parameters in the above…

Answered: • Find f(t) if f(t)= S F(@)eitw dw,…

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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Find f(t) if
1
00
f(t)= F(@)eitw dw, where
2π0
4+jw.
F(w) =
F (ω)
8+jw
πδω).
Express your answer in complex form.

Expert Solution

Step 1

Consider the given expression,

$f (t) = \frac{1}{2 π} \int_{0}^{\infty} F (ω) e^{j t ω} d ω$

Substitute the given parameters in the above expression,

$\begin{array}{rcl} f (t) & = & \frac{1}{2 π} \int_{0}^{\infty} \frac{4 + j ω}{8 + j ω} π δ (ω) e^{j t ω} d ω \\ = & \frac{1}{2 π} \int_{0}^{\infty} (\frac{4 + j ω}{8 + j ω} π e^{j t ω}) δ (ω) d ω \end{array}$

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