250+ TOP MCQs on Elementary Signals – 1 and Answers

Signals & Systems Multiple Choice Questions 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
Answer: A
Clarification: 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
Answer: B
Clarification: 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?
signals-systems-questions-answers-elementary-signals-1-q3″>
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
Answer: A
Clarification: 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
Answer: A
Clarification: 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?
signals-systems-questions-answers-elementary-signals-1-q5″>
Answer: A
Clarification: 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
Answer: D
Clarification: 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
Answer: C
Clarification: 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
Answer: A
Clarification: 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