1. The general form of real exponential signal is________
a) X (t) = beat
b) X (t) = (b+1)eat
c) X (t) = b (at)
d) X (t) = be (a+1)t
Explanation: X (t) = beat is the most general way of representing the exponential signals where both b and a are real parameters.
2. In the equation x (t) = beat if a < 0, then it is called ______
a) Growing exponential
b) Decaying exponential
c) Complex exponential
d) Both Growing and Decaying exponential
Explanation: If a > 0 in x (t) = beat it is called growing exponential and if <0 it is called decaying exponential. Hence Decaying exponential is correct.
3. 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
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.
4. 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 = \(\frac{1}{\sqrt{πLC}}\)
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.
5. 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
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.
6. 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
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.
7. 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
Explanation: By substituting N=8 and m=1 in the equation w=2πm⁄N we get the smallest angular frequency as π⁄4.
8. Euler’s identity ejθ 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
Explanation: The complex exponential ejθ 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.
9. Exponentially damped sinusoidal signal is ______
a) Periodic
b) Non periodic
c) Insufficient information
d) Maybe periodic
Explanation: Exponentially damped sinusoidal signal of any kind is not periodic as it does not satisfy the periodicity condition.
10. Is the system y(t) = Rx(t), where R is a arbitrary constant, a memoryless system?
a) Yes
b) No
Explanation: The output of the system depends on the input of the system at the same time instant. Hence, the system has to be memoryless.