How many poles does the Laplace Transform of a square wave have? a) 0 b) 1 c) 2 d) Infinitely Manhy

Dottie Parra 2021-02-26 Answered
How many poles does the Laplace Transform of a square wave have?
a) 0
b) 1
c) 2
d) Infinitely Manhy
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Expert Answer

Cullen
Answered 2021-02-27 Author has 89 answers
Solution:
The Fourier series for square wave is f(x)=4πi=1,3,5,1nsin(nπxL)
The Laplace transform is L{sin(ax)}=ax2+a2
The function is f(x)=4π[sin(πxL)+13sin(3πxL)+15sin(5πxL)+]
Apply Laplace transform:
Conclusion:
Lf(x)=4π[L{sin(πxL)}+13L{sin(3πxL)}+15L{sin(5πxL)}+]
=4π[πLx2+(πL)2+13(3πLx2+(3πL)2)+5πLx2+(5πL)2+]
=4π[πLx2+(πL)2+πLx2+(3πL)2+πLx2+(5πL)2]
=4L[1x2+(πL)2+1x2+(3πL)2+1x2+(5πL)2+]
Hence, as there are no real singularities, therefore the number of poles are 0.
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