This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Elementary Signals – 1”.

1. The general form of real exponential signal is________

a) X (t) = be^{at}

b) X (t) = (b+1)e^{at}

c) X (t) = b (at)

d) X (t) = be ^{(a+1)t}

View Answer

Explanation: X (t) = be

^{at}is the most general way of representing the exponential signals where both b and a are real parameters.

2. In the equation x (t) = be^{at} if a < 0, then it is called ______

a) Growing exponential

b) Decaying exponential

c) Complex exponential

d) Both Growing and Decaying exponential

View Answer

Explanation: If a > 0 in x (t) = be

^{at}it is called growing exponential and if <0 it is called decaying exponential. Hence Decaying exponential is correct.

3. In the below figure if R value is increased then which of the following is true?

a) Slower the rate of decay of v (t)

b) Greater the rate of decay of v (t)

c) Decay rate is independent of R

d) Decay rate depends only on the capacitor value

View Answer

Explanation: In the circuit shown voltage across capacitor decays exponentially with time at a rate determined by time constant RC. Hence the larger the resistor, the slower will be the rate of decay of v (t) with time.

4. The time period of continuous-time sinusoidal signal is given by _____

a) T = 2π / w

b) T = 2π / 3w

c) T = π / w

d) T = π / 2w

View Answer

Explanation: X (t) = A cos (wt+φ) is the continuous-time sinusoidal signal and its period is given by

T = 2π / w where w is the frequency in radians per second.

5. The natural angular frequency of the parallel LC circuit is?

a) wo = \(\frac{1}{\sqrt{LC}}\)

b) wo = \(\frac{2π}{\sqrt{LC}}\)

c) wo = \(\frac{π}{\sqrt{LC}}\)

d) wo = \(\frac{1}{\sqrt{πLC}}\)

View Answer

Explanation: Wo is the natural angular frequency and for parallel LC circuit it is given by wo=

^{1}⁄

_{√LC}where, L is value of inductor and C is value of capacitor.

6. X [n] = 2 cos (2n) is periodic or not?

a) Periodic with period 2n

b) Periodic with period 2π

c) Periodic with period 2

d) Non periodic

View Answer

Explanation: The given signal x [n] is non periodic as it doesn’t satisfy the equation w=

^{2πm}⁄

_{N}where, N is fundamental period and m is an integer.

7. Check whether x [n] = 7 sin (6πn) is periodic and if it is period calculate its fundamental period?

a) Periodic with fundamental period 6π

b) Periodic with fundamental period 3

c) Periodic with fundamental period 1

d) Non periodic

View Answer

Explanation: X [n] = 7 sin (6πn) is a periodic discrete time signal with period 1. By substituting w = 6π and m=3 in w=

^{2πm}⁄

_{N}we get N =1.

8. Find the smallest angular frequency for which the discrete time signal with fundamental period N=8 would be periodic?

a) ^{π}⁄_{4}

b) ^{π}⁄_{2}

c) ^{3π}⁄_{4}

d) ^{π}⁄_{16}

View Answer

Explanation: By substituting N=8 and m=1 in the equation w=

^{2πm}⁄

_{N}we get the smallest angular frequency as

^{π}⁄

_{4}.

9. Euler’s identity e^{jθ} is expanded as _____

a) cos θ + j sin θ

b) cos θ – j sin θ

c) cos θ + j sin 2θ

d) cos 2θ+j sinθ

View Answer

Explanation: The complex exponential e

^{jθ}is expanded as cos θ + j sin θ and is called Euler’s identity with cos θ as real part sin θ as imaginary part.

10. Exponentially damped sinusoidal signal is ______

a) Periodic

b) Non periodic

c) Insufficient information

d) Maybe periodic

View Answer

Explanation: Exponentially damped sinusoidal signal of any kind is not periodic as it does not satisfy the periodicity condition.

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

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