M3 | MCQ | FOURIER TRANSFORM

   Fourier Transform

1. In Fourier transform f(p)=∫∞−∞e(ipx)F(x)dx,e(ipx) is said to be Kernel function.
a) True
b) False
View Answer

Answer: a

2. Fourier Transform of e−|x|is 21+p2. Then what is the fourier transform of e−2|x|?
a) 4 / (4+p2)
b) 2 / (4+p2)
c) 2 / (2+p2)
d) 4 / (2+p2)
View Answer

Answer: a

3. What is the fourier sine transform of e^-ax?
a) 4 / (4+p2)
b) 4a / (4a2+p2)
c) p / (a2+p2)
d) 2p / (a2+p2)
View Answer

Answer: c

4. Find the fourier sine transform of x(a2+x2).
a) 2πe−ap
b) π/2e−ap
c) 2π/e−ap
d) πe−ap
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Answer: b

5. Find the fourier transform of F(x) = 1, |x|<a0, otherwise.
a) 2sin(ap)/p
b) 2asin(ap)/p
c) 4sin(ap)/p
d) 4asin(ap)/p
View Answer

Answer: a

 

6. In Finite Fourier Cosine Transform, if the upper limit l = π, then its inverse is given by ________
a) F(x)=2π∑∞p=1fc(p)cos(px)+1/πfc(0)
b) F(x)=2π∑∞p=1fc(p)cos(px)
c) F(x)=2π∑∞p=1fc(p)cos(pxπ)
d) F(x)=2π∑∞p=0fc(p)cos(px)+1/πfc(0)
View Answer

Answer: a

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7. Find the Fourier Cosine Transform of F(x) = 2x for 0<x<4.
a) fc(p)=32 / (p2π2)(cos(pπ)−1)p not equal to 0 and if equal to 0 fc(p)=16
b) fc(p)=32 / (p2π2)(cos(pπ)−1)p not equal to 0 and if equal to 0 fc(p)=32
c) fc(p)=64 / (pπ2)(cos(pπ)−1)p not equal to 0 and if equal to 0 fc(p)=16
d) fc(p)=32 /(pπ2)(cos(pπ)−1)p not equal to 0 and if equal to 0 fc(p)=64
View Answer

Answer: a

8. If Fourier transform of e−|x|=21+p2, then find the fourier transform of t2e−|x|.
a) 4 /1+p2
b) −2 / 1+p2
c) 2 / 1+p2
d) −4 / 1+p2
View Answer

Answer: b

9. If Fc{e−ax}=pa2+p2, find the Fs{−ae−ax}.
a) 4p / a2+p2
b) −p^2 /ca2+p2
c) 4p2 / a2+p2
d) p / a2+p2
View Answer

Answer: b

10. Find the fourier transform of ∂2u∂x2 . (u’(p,t) denotes the fourier transform of u(x,t)).
a) (ip)² u’(p,t)
b) (-ip)² u’(p,t)
c) (-ip)² u(p,t)
d) (ip)² u(p,t)
View Answer

Answer: a

11. What is the fourier transform of e^-a|x| * e^-b|x|?
a) 4ab / (a2+p2)(b2+p2)
b) 2ab / (a2+p2)(b2+p2)
c) 4 / (a2+p2)(b2+p2)
d) a2b2 / (a2+p2)(b2+p2)
View Answer

Answer: a

12. What is the Fourier transform of e^ax? (a>0)
a) pa2+p2
b) 2aa2+p2
c) −2aa2+p2
d) cant’t be found

View Answer

Answer: d

13. F(x)=x(−12)is self reciprocal under Fourier cosine transform.
a) True
b) False
View Answer

Answer: a
  

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14. Find the fourier cosine transform of e^-ax * e^-ax.
a) p2 / a2+p2
b) p2 / (a2+p2)2
c) 4p2 / (a2+p2)2
d) −p2 / (a2+p2)2
View Answer

Answer: b

15. Find the fourier sine transform of F(x) = -x when x<c and (π – x) when x>c and 0≤c≤π.
a) π/ccos(pc)
b) π/pcos(pc)
c) π/ccos(pπ)
d) pπ/ccos(pc)
View Answer

Answer: b

1. Find the Z-Transform of nCp.
a) (1-z^-1)ⁿ
b) (1+z^-1)ⁿ
c) (1-z^-1)^-n
d) (1+z^-1)^-n
View Answer

Answer: b

 

2. Find the function whose Z – Transform is 1z.
a) δ(n)
b) δ(n+1)
c) U(n)
d) U(n+1)
View Answer

Answer: b

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3. Find the function whose Z transform is e1z.
a) log(n)
b) 1/n
c) 1/n!
d) 1/(n+1)!
View Answer

Answer: c

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4. Find the inverse Z- Transform of (zz−a)3.
a) 1/2.(n+1)(n−2)an−2U(n)
b) 1/2.(n−1)(n−2)an−3U(n)
c) 1/2.(n−1)(n+2)an−1U(n)
d) 1/2.(n+1)(n+2)anU(n)
View Answer

Answer: d

5. Find the inverse Z – Transform of logzz+1.
a) (−1)^n / n
b) (−1)^n /n+1n
c) 1n
d) (−1)^n /n+1
View Answer

Answer: a

6. Find the Z – Transform of sinh ⁡nθ.
a) sinhθ / z^2−2zcoshθ+1
b) 1/2sinhθ / z^2−2zcoshθ+1
c) zsinhθ) / z^2−2zcoshθ+1
d) z(z−sinhθ) / z^2−2zcoshθ+1
View Answer

Answer: a

7. Find the value of u₃ if U(z)=3z2+2z+10(z−1)4.
a) 12
b) 13
c) 14
d) 15
View Answer

Answer: c

8. Find the Z – Transform of n^p.
a) −zd /dz(Z(np−1))
b) zd /dz(Z(np))
c) −zd /dz(Z(np+1))
d) zd /dz(Z(np+1))
View Answer

Answer: a

9. The Z – Transform of a function is given by U(z)=z3+6z2+9z+3(z−1)4. Find the Z-Transform of u_n+2.
a) 10z^3+3z^2+7z1−1/(z−1)4
b) 10z^4+3z^3+7z^2−z /(z−1)4
c) 10z^4+4z^3+7z^2−2z /(z−1)4
d) 10z^4+3z^3−4z /(z−1)4
View Answer

Answer: b

10. Find u₂ if U(z)=z3+6z2+9z+3(z−1)4.
a) 8
b) 9
c) 10
d) 11
View Answer

Answer: c

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11. Find the order of the difference equation Δ³y_n – Δ²y_n – Δy_n = 3.
a) 3
b) 4
c) 2
d) 5
View Answer

Answer: a

12. Find the order of the difference equation y_n+3 -3 y_n+1 – y_n-2 = 4.
a) 3
b) 4
c) 5
d) 6
View Answer

Answer: c

 

 

13. Find the difference equation of y_n = A 3ⁿ + B 5ⁿ.
a) y_n+2 -16 y_n+1 + 15 y_n-1 = 0
b) y_n+3 -14 y_n+1 + 30 y_n = 0
c) 2 y_n+2 -14 y_n+1 + 15 y_n = 0
d) 2 y_n+2 -16 y_n+1 + 30 y_n = 0
View Answer

Answer: d

14. Find the difference equation of y = ax + b.
a) Δ²y = 0
b) Δ²y = 1
c) Δ²y + 3Δy = 2
d) Δ²y + 4Δy = 5
View Answer

Answer: a

15. Solve u_n+2 + 10 u_n+1 + 9 u_n = 2ⁿ.
a) un=2^n+1 / 33+(−9)^n+1 / 88+(−1)^n+1 / 24
b) un=2n^ / 33+(−9)^n / 88+(−1)^n−1 / 24
c) un=2^n+1 / 11+(−9)^n+1 / 88+(−1)^n / 24
d) un=2^n / 11+(−9)^n / 88+(−1)n−1^ / 24
View Answer

Answer: b

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