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
View Answer

Answer: d
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

Answer: a
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
View Answer

Answer: b
Explanation: The numerator evaluates to 1, and the denominator is t, hence the answer is 1/t.
advertisement
advertisement

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
View Answer

Answer: c
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

Answer: b
Explanation: The function assumes the same value after t+2pi/w, hence the period would be 2pi/w.
Note: Join free Sanfoundry classes at Telegram or Youtube

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

Answer: d
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

Answer: b
Explanation: The sum will exist only for n = 0, for which the product will be 1.
advertisement

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

Answer: d
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

Answer: d
Explanation: None of the derivatives are defined at t=0.
advertisement

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

Answer: b
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

Answer: d
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

Answer: d
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
View Answer

Answer: d
Explanation: Unit step function, u(t) = 1 for t ≥ 0 and u(t) = 0 for t < 0. Also,
Unit step function, u(t) = 1 for t greater than equal to 0 & u(t) = 0 for t less than 0

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

Answer: b
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: Evaluate from the impulse function property
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

Answer: a
Explanation: From the impulse function property,
The impulse function property in given figure

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

Answer: c
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.

To practice all areas of Signals & Systems, here is complete set of 1000+ Multiple Choice Questions and Answers.

If you find a mistake in question / option / answer, kindly take a screenshot and email to [email protected]

advertisement
advertisement
Subscribe to our Newsletters (Subject-wise). Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!

Youtube | Telegram | LinkedIn | Instagram | Facebook | Twitter | Pinterest
Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

Subscribe to his free Masterclasses at Youtube & discussions at Telegram SanfoundryClasses.