## Signals & Systems Questions and Answers Part-11

1. What is exp(ja) equal to, where j is the square root of unity?
a) cos ja + jsin a
b) sin a + jcos a
c) cos j + a sin j
d) cos a + jsin a

Explanation: This is the corollary of DeMoivre/Euler’s Theorem.

2. What is the magnitude of exp(2+3j)?
a) exp(2.3)
b) exp(3)
c) exp(2)
d) exp(3/2)

Explanation: exp(a+b) =exp(a) * exp(b), and |exp(3i)| = 1.

3. What is the fundamental frequency of exp(2pi*w*j)?
a) 1pi*w
b) 2pi*w
c) w
d) 2w

Explanation: Fundamental period = 2pi/w, hence fundamental frequency will be w.

4. Total energy possessed by a signal exp(jwt) is?
a) 2pi/w
b) pi/w
c) pi/2w
d) 2pi/3w

Explanation: Energy possessed by a periodic signal is the integral of the square of the magnitude of the signal over a time period.

5. Sinusoidal signals multiplied by decaying exponentials are referred to as
a) Amplified sinusoids
b) Neutralized sinusoids
c) Buffered sinusoids
d) Damped sinusoids

Explanation: The decaying exponentials dampen the amplitudes of sinusoids. Hence, the term damped sinusoids.

6. What is the power possessed by a signal exp(jwt)?
a) 1
b) 0.5
c) 1w
d) w

Explanation: The power = Energy/Time period for a periodic signal. Hence, Power = 1.

7. What is the period of exp(2+pi*j/4)t?
a) 4
b) 8
c) 16
d) 20

Explanation:The fundamental period = 2pi/(pi/4) = 8.

8. exp(jwt) is periodic
a) for any w
b) for any t
c) for no w
d) for no t

Explanation: Any two instants, t and t + 2pi will be equal, hence the signal will be periodic with period 2pi.

9. Define the fundamental period of the following signal x[n] = exp(2pi*j*n/3) + exp(3*pi*j*n/4)?
a) 8
b) 12
c) 18
d) 24