wiz-icon
MyQuestionIcon
MyQuestionIcon
22
You visited us 22 times! Enjoying our articles? Unlock Full Access!
Question

The Fourier transform of the complex sinusoidal pulse shown below is z(t)={ej10t;|t|<π0;|t|>π

A
1ω10sin((ω10)π)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
2ω10sin((ω10)π)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
2ωsin((ω10)π)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
12ωsin((ω10)π)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 2ω10sin((ω10)π)
Given, sinusoidal pulsez(t)={ej10t;|t|<π0;|t|>πWe may express z(t) as the product of a complex sinusoid ej10t and a rectangluar pulse x(t)Letx(t)={1;|t|<π0;|t|>πFourier transform of x(t) is X(jω)X(jω)=x(t)ejωtdt=ππ1.ejωtdt=[ejωtjω]ππ=1jω[ejπωe+jωπ]=ejωπejωπjω=2ω[ejωπejωπ2j]X(jω)=2ωsin(ωπ)By using frequency shifting property of Fourier transform, we get,z(t)=ej10t.x(t)FTX(j(ω10))z(t)FT2ω10sin((ω10)π)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Relative Motion in 2D
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon