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) = (b−a)ejωe−j2ω−(a+b)ejω+ab, |b|<1<|a|
The value of x[n] is __________
a) bn u [n] + an u [n-1]
b) bn u [n] – an u [-n-1]
c) bn u [n] + an u [-n-1]
d) bn u [n] – an 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-2tcos(3t) + 5e-2tsin(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) 2ek (t-b) u (t-b)
d) 2ek (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 6e5tcos(2t) – e7t 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