1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Given that, ∫2TTx(t).dt=2 x(t),y(t)=ddxx(t) signals are periodic signals of time period T = 8, with Fourier series coefficient ak and bk respectively. Which one of the following expressions are correct ?

A
a0=0.25,a4=jb4π,a8=jb82π
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
a0=0.25,a4=jπb4,a8=j2πb8
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
a0=4,a4=jb4π,a8=jb82π
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
a0=4,a4=jπb4,a8=j2πb8
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A a0=0.25,a4=−jb4π,a8=−jb82πGiven that, x(t)F.S⟷ak g(t)=(dx(t)dtx(t))F.S⟷bk=(jk2πTak) ak=bkj(2πT)k,k≠0 When k = 0, ak=1T∫T0x(t).dt=2T ak=⎧⎪ ⎪ ⎪⎨⎪ ⎪ ⎪⎩2T,k=0bkj(2πT)k,k≠0 ∴a0=28=0.25 a4=b4j(2π8)×4=−jb4π a8=b8j(2π8)×8=−jb82π

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Simple Harmonic Oscillation
PHYSICS
Watch in App
Join BYJU'S Learning Program