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

View Answer

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

View Answer

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) ^{1}⁄_{t}

c) t^{2}

d) ^{1}⁄_{t2}

View Answer

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) ^{1}⁄_{t}

b) ^{1}⁄_{t2}

c) t

d) t^{2}

View Answer

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

View Answer

Explanation: 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]

View Answer

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

View Answer

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

View Answer

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

View Answer

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)

View Answer

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

View Answer

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}

View Answer

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?

View Answer

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

View Answer

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}

View Answer

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

View Answer

Explanation: 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) = e

^{0}[cos0 + jsin0] = 1 × 1 = 1 which is pure DC.

**Sanfoundry Global Education & Learning Series – Signals & Systems.**

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