# Signals & Systems Questions and Answers – Useful Signals

This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses 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

Explanation: 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

Explanation: 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) 1t
c) t2
d) 1t2

Explanation: 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) 1t
b) 1t2
c) t
d) t2

Explanation: 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

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

Explanation: 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

Explanation: 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

Explanation: 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

Explanation: 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)

Explanation: 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

Explanation: 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

Explanation: 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.

13. Which one of the following is not a unit step function?
a) u(t)=1 for t ≥ 0
b) u(t)=0 for t < 0
c) u(t)=$$\frac{dr(t)}{dt}$$ for t ≥ 0
d) u(t)=$$\frac{dp(t)}{dt}$$ for t ≥ 0

Explanation: Unit step function, u(t) = 1 for t ≥ 0 and u(t) = 0 for t < 0. Also,

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

Explanation: 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}

Explanation: From the impulse function property,

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

Explanation: A complex exponential signal is represented as x(t)= est
Where, s = σ + jΩ
⇒ x(t) = eσt [cosΩt + jsinΩt] When, σ = 0 and Ω = 0 ⇒ x(t) = e0 [cos0 + jsin0] = 1 × 1 = 1 which is pure DC.

Sanfoundry Global Education & Learning Series – Signals & Systems.

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