Explore topic-wise MCQs in Fourier Analysis.

This section includes 15 Mcqs, each offering curated multiple-choice questions to sharpen your Fourier Analysis knowledge and support exam preparation. Choose a topic below to get started.

1.

Find the fourier sine transform of F(x) = -x when x<c and ( x) when x>c and 0 c .

A. ( frac{ }{c} cos(pc) )
B. ( frac{ }{p} cos(pc) )
C. ( frac{ }{c} cos(p ) )
D. (p frac{ }{c} cos(pc) )
Answer» C. ( frac{ }{c} cos(p ) )
Discussion
2.

Find the fourier cosine transform of e-ax * e-ax.

A. ( frac{p^2}{a^2+p^2} )
B. ( frac{p^2}{(a^2+p^2)^2} )
C. (4 frac{p^2}{(a^2+p^2)^2} )
D. ( frac{-p^2}{(a^2+p^2 )^2} )
Answer» C. (4 frac{p^2}{(a^2+p^2)^2} )
Discussion
3.

(F(x) = x^{( frac{-1}{2})} )is self reciprocal under Fourier cosine transform.

A. True
B. False
Answer» B. False
Discussion
4.

What is the Fourier transform of eax? (a>0)

A. ( frac{p}{a^2+p^2} )
B. (2 frac{a}{a^2+p^2} )
C. (-2 frac{a}{a^2+p^2} )
D. cant t be found
Answer» E.
Discussion
5.

What is the fourier transform of e-a|x| * e-b|x|?

A. ( frac{4ab}{(a^2+p^2)(b^2+p^2)} )
B. ( frac{2ab}{(a^2+p^2)(b^2+p^2)} )
C. ( frac{4}{(a^2+p^2)(b^2+p^2)} )
D. ( frac{a^2 b^2}{(a^2+p^2)(b^2+p^2)} )
Answer» B. ( frac{2ab}{(a^2+p^2)(b^2+p^2)} )
Discussion
6.

Find the fourier transform of ( frac{ ^2 u}{ x^2} ) . (u (p,t) denotes the fourier transform of u(x,t)).

A. (ip)<sup>2</sup> u (p,t)
B. (-ip)<sup>2</sup> u (p,t)
C. (-ip)<sup>2</sup> u(p,t)
D. (ip)<sup>2</sup> u(p,t)
Answer» B. (-ip)<sup>2</sup> u (p,t)
Discussion
7.

If (Fc {e^{-ax} } = frac{p}{a^2+p^2} ), find the (Fs {-a , e^{-ax} }. )

A. (4 frac{p}{a^2+p^2} )
B. ( frac{-p^2}{a^2+p^2} )
C. (4 frac{p^2}{a^2+p^2} )
D. ( frac{p}{a^2+p^2} )
Answer» C. (4 frac{p^2}{a^2+p^2} )
Discussion
8.

If Fourier transform of ( e^{-|x|} = frac{2}{1+p^2} ), then find the fourier transform of (t^2 e^{-|x|}. )

A. ( frac{4}{1+p^2} )
B. ( frac{-2}{1+p^2} )
C. ( frac{2}{1+p^2} )
D. ( frac{-4}{1+p^2} )
Answer» C. ( frac{2}{1+p^2} )
Discussion
9.

Find the Fourier Cosine Transform of F(x) = 2x for 0&lt;x&lt;4.

A. (fc(p) = frac{32}{(p^2 ^2)} (cos(p )-1)p ) not equal to 0 and if equal to 0 ( fc(p) = 16 )
B. (fc(p) = frac{32}{(p^2 ^2)} (cos(p )-1)p ) not equal to 0 and if equal to 0 ( fc(p) = 32 )
C. (fc(p) = frac{64}{(p ^2)} (cos(p )-1)p ) not equal to 0 and if equal to 0 ( fc(p) = 16 )
D. (fc(p) = frac{32}{(p ^2)} (cos(p )-1)p ) not equal to 0 and if equal to 0 ( fc(p) = 64 )
Answer» B. (fc(p) = frac{32}{(p^2 ^2)} (cos(p )-1)p ) not equal to 0 and if equal to 0 ( fc(p) = 32 )
Discussion
10.

In Finite Fourier Cosine Transform, if the upper limit l = , then its inverse is given by ________

A. (F(x) = frac{2}{ } _{p=1}^ fc (p)cos(px)+ frac{1}{ } fc(0) )
B. (F(x) = frac{2}{ } _{p=1}^ fc (p)cos(px) )
C. (F(x) = frac{2}{ } _{p=1}^ fc (p)cos( frac{px}{ }) )
D. (F(x) = frac{2}{ } _{p=0}^ fc (p)cos(px)+ frac{1}{ } fc(0) )
Answer» B. (F(x) = frac{2}{ } _{p=1}^ fc (p)cos(px) )
Discussion
11.

Find the fourier transform of F(x) = 1, |x|&lt;a0, otherwise.

A. (2sin frac{(ap)}{p} )
B. (2asin frac{(ap)}{p} )
C. (4sin frac{(ap)}{p} )
D. (4asin frac{(ap)}{p} )
Answer» B. (2asin frac{(ap)}{p} )
Discussion
12.

Find the fourier sine transform of ( frac{x}{(a^2+x^2)}. )

A. (2 e^{-ap} )
B. ( frac{ }{2} e^{-ap} )
C. ( frac{2}{ } e^{-ap} )
D. ( e^{-ap} )
Answer» C. ( frac{2}{ } e^{-ap} )
Discussion
13.

What is the fourier sine transform of e-ax?

A. ( frac{4}{(4+p^2)} )
B. (4 frac{a}{(4a^2+p^2 )} )
C. ( frac{p}{(a^2+p^2)} )
D. (2 frac{p}{(a^2+p^2)} )
Answer» D. (2 frac{p}{(a^2+p^2)} )
Discussion
14.

Fourier Transform of (e^{-|x|} , is ) ( frac{2}{1+p^2} ). Then what is the fourier transform of ( e^{-2|x|} )?

A. ( frac{4}{(4+p^2)} )
B. ( frac{2}{(4+p^2)} )
C. ( frac{2}{(2+p^2)} )
D. ( frac{4}{(2+p^2)} )
Answer» B. ( frac{2}{(4+p^2)} )
Discussion
15.

In Fourier transform (f(p) = int_{- }^ e^{(ipx)} F(x)dx, e^{(ipx)} ) is said to be Kernel function.

A. True
B. False
Answer» B. False
Discussion