a) A function, f(t), is defined as(1,f (t) =0st< 4otherwiseDetermine the Fourier transform of f(t)b) Determine the inverse Fourier transform of3G(ω)2+j (ω- 1)c) Use the t-w duality principle to find the Fouriertransform off (t) = e-jtd) Determine the inverse z-transform of the functionF(z)z² – 2z – 3e) A difference equation is defined asx[k + 2] + 7x[k + 1] + 10x[k] = 0where x[0] = 0 and x[1] = 1. Use Z transforms to solvethe difference equation.

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a) A function, f(t), is defined as f(t) = {". 0

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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Question

a) A function, f(t), is defined as
(1,
f (t) =
0st< 4
otherwise
Determine the Fourier transform of f(t)
b) Determine the inverse Fourier transform of
3
G(ω)
2+j (ω- 1)
c) Use the t-w duality principle to find the Fourier
transform of
f (t) = e-jt
d) Determine the inverse z-transform of the function
F(z)
z² – 2z – 3
e) A difference equation is defined as
x[k + 2] + 7x[k + 1] + 10x[k] = 0
where x[0] = 0 and x[1] = 1. Use Z transforms to solve
the difference equation.

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