# Exponential Fourier Series and Fourier Transforms MCQ’s

This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Exponential Fourier Series and Fourier Transforms”.

1. Given, X (e^{jω}) = (b−a)ejωe−j2ω−(a+b)ejω+ab, |b|<1<|a|

The value of x[n] is __________

a) b^{n} u [n] + a^{n} u [n-1]

b) b^{n} u [n] – a^{n} u [-n-1]

c) b^{n} u [n] + a^{n} u [-n-1]

d) b^{n} u [n] – a^{n} u [n+1]

2. The input and output of an LTI system are x (t) = e^{-3t} u (t) and y (t) = e^{-t} u (t). The differential equation which characterizes the system is ___________

a) dy(t)dt+y(t)=dx(t)dt+3x(t)

b) dy(t)dt+2y(t)=dx(t)dt+3x(t)

c) dy(t)dt–y(t)=dx(t)dt+3x(t)

d) dy(t)dt–2y(t)=dx(t)dt+3x(t)

3. The Fourier transform of u (t) is B (jω) and the Laplace transform of u (t) is A(s). Which of the following is correct?

a) B(jω) = A(s)

b) A(s) = 1s but B(jω) ≠ 1jω

c) A(s) ≠ 1s but B(jω) ≠ 1jω

d) A(s) ≠ 1s but B(jω) = 1jω

4. The Fourier transform of signal e^{-2t} u(t-3) is ___________

a) e−3(2−jω)2−jω

b) e−3(2+jω)2+jω

c) e3(2−jω)2−jω

d) e3(2+jω)2+jω

5. The Inverse Fourier transform of the signal e^{-2|ω|} is ____________

a) 2π(4+t2)

b) 12π(4+t2)

c) 1π(4+t2)

d) 1(4+t2)

6. The Laplace transform of the function e^{-2t}cos(3t) + 5e^{-2t}sin(3t) is ____________

a) (s+2)−15(s+2)2−9

b) (s+2)+15(s+2)2−9

c) (s+2)+15(s+2)2+9

d) (s+2)−15(s+2)2+9

7. The Fourier transform of the signal e^{-4|t|} is ____________

a) 816+ω2

b) −816+ω2

c) 416+ω2

d) −416+ω2

8. The inverse Laplace transform of F(s) = 2s+ce−bs is _____________

a) 2e^{-k (t+b)} u (t+b)

b) 2e^{-k (t-b)} u (t-b)

c) 2e^{k (t-b)} u (t-b)

d) 2e^{k (t-b)} u (t+b)

9. A band pass signal extends from 1 KHz to 2 KHz. The minimum sampling frequency that is needed to retain all information of the sampled signal is ___________

a) 1 KHz

b) 2 KHz

c) 3 KHz

d) 4 KHz

10. The inverse Laplace transform of F(s) = e−3ss(s2+3s+2) is ______________

a) {0.5 + 0.5e^{-2(t+3)}-e^{-(t+3)}} u (t+3)

b) {0.5 + 0.5e^{-2(t-3)}-e^{-(t-3)}} u (t-3)

c) {0.5 – 0.5e^{-2(t-3)}-e^{-(t-3)}} u (t-3)

d) 0.5 + 0.5e^{-2t}-e^{-t})

11. The Fourier transform of the signal te^{-3|t-1|} is _____________

a) 6e−jω9+ω2–12jωe−jω9+ω2

b) 6e−jω9+ω2

c) –12jωe−jω9+ω2

d) 6e−jω9+ω2+12jωe−jω9+ω2

12. The Laplace transform of the function 6e^{5t}cos(2t) – e^{7t} is ______________

a) 6(s−5)(s−5)2+4–1s−7

b) 6(s−5)(s−5)2+4+1s−7

c) 6(s+5)(s+5)2+4–1s−7

d) 6(s+5)(s+5)2+4+1s−7

13. The Fourier transform of the signal e^{-t+2} u (t-2) is ___________

a) e−2jω1−2ω

b) e2jω1+2ω

c) e−2jω1+2ω

d) e2jω1−2ω

14. The Fourier transform of the signal te^{-t} u(t) is _____________

a) 11+ω2

b) −11+ω2

c) 1(1+jω)2

d) 1(1−jω)2

15. The Fourier transform of the signal ∑∞m=0amδ(t−m) is _____________

a) 11+ae−jω

b) 11+aejω

c) 11−aejω

d) 11−ae−jω

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