250+ TOP MCQs on Useful Signals and Answers

Signals & Systems Multiple Choice Questions on “Useful Signals”.

1. What is the value of d[0], such that d[n] is the unit impulse function?
A. 0
B. 0.5
C. 1.5
D. 1

Answer: D
Clarification: The unit impulse function has value 1 at n = 0 and zero everywhere else.

2. What is the value of u[1], where u[n] is the unit step function?
A. 1
B. 0.5
C. 0
D. -1

Answer: A
Clarification: The unit step function u[n] = 1 for all n>=0, hence u[1] = 1.

3. Evaluate the following function in terms of t: {sum from -1 to infinity:d[n]}/{Integral from 0 to t: u(t)}
A. t
B. ¹⁄_t
C. t²
D. ¹⁄_t²

Answer: B
Clarification: The numerator evaluates to 1, and the denominator is t, hence the answer is 1/t.

4. Evaluate the following function in terms of t: {integral from 0 to t}{Integral from -inf to inf}d(t)
A. ¹⁄_t
B. ¹⁄_t²
C. t
D. t²

Answer: C
Clarification: The first integral is 1, and the overall integral evaluates to t.

5. The fundamental period of exp(jwt) is
A. pi/w
B. 2pi/w
C. 3pi/w
D. 4pi/w

Answer: B
Clarification: The function assumes the same value after t+2pi/w, hence the period would be 2pi/w.

6. Find the magnitude of exp(jwt). Find the boundness of sin(t) and cos(t).
A. 1, [-1,2], [-1,2]
B. 0.5, [-1,1], [-1,1]
C. 1, [-1,1], [-1,2]
D. 1, [-1,1], [-1,1]

Answer: D
Clarification: The sin(t)and cos(t) can be found using Euler’s rule.

7. Find the value of {sum from -inf to inf} exp(jwn)*d[n].
A. 0
B. 1
C. 2
D. 3

Answer: B
Clarification: The sum will exist only for n = 0, for which the product will be 1.

8. Compute d[n]d[n-1] + d[n-1]d[n-2] for n = 0, 1, 2.
A. 0, 1, 2
B. 0, 0, 1
C. 1, 0, 0
D. 0, 0, 0

Answer: D
Clarification: Only one of the values can be one at a time, others will be forced to zero, due to the delta function.

9. Defining u(t), r(t) and s(t) in their standard ways, are their derivatives defined at t = 0?
A. Yes, Yes, No
B. No, Yes, No
C. No, No, Yes
D. No, No, No

Answer: D
Clarification: None of the derivatives are defined at t=0.

10. Which is the correct Euler expression?
A. exp(2jt) = cos(2t) + jsin(t)
B. exp(2jt) = cos(2t) + jsin(2t)
C. exp(2jt) = cos(2t) + sin(t)
D. exp(2jt) = jcos(2t) + jsin(t)

Answer: B
Clarification: Euler rule: exp(jt) = cos(t) + jsin(t).

11. The range for unit step function for u(t – A., is ________
A. t < a
B. t ≤ a
C. t = a
D. t ≥ a

Answer: D
Clarification: A unit step signal u(t) = 1 when t ≥ 0 and 0 when t < 0
∴ u(t – A. = 1 when t – a ≥ 0 ⇒ t ≥ a

12. Which one of the following is not a ramp function?
A. r(t) = t when t ≥ 0
B. r(t) = 0 when t < 0
C. r(t) = ∫u(t)dt when t < 0
D. r(t) = ^du(t)⁄_dt

Answer: D
Clarification: Ramp function r(t) = t when t ≥ 0 and r(t) = 0 when t < 0
Also, r(t)= ∫u(t)dt = ∫dt = t (∵u(t) = 1 for t≥0)
⇒ ^du(t)⁄_dt = ^d(1)⁄_dt = 0 which is not a ramp function.

14. Unit Impulse function is obtained by using the limiting process on which among the following functions?
A. Triangular Function
B. Rectangular Function
C. Signum Function
D. Sinc Function

Answer: B
Clarification: Unit impulse function can be obtained by using a limiting process on the rectangular pulse function. Area under the rectangular pulse is equal to unity.

15. Evaluate:
A. {2,1.5,0,6}
B. {2,1.5,6,0}
C. {2,0,1.5,6}
D. {2,1.5,0,3}

16. When is a complex exponential signal pure DC?
A. σ = 0 and Ω < 0
B. σ < 0 and Ω = 0
C. σ = 0 and Ω = 0
D. σ < 0 and Ω < 0

Answer: C
Clarification: A complex exponential signal is represented as x(t)= e^st
Where, s = σ + jΩ
⇒ x(t) = e^σt [cosΩt + jsinΩt]
When, σ = 0 and Ω = 0 ⇒ x(t) = e⁰ [cos0 + jsin0] = 1 × 1 = 1 which is pure DC.