Communications - Online Test
Q1. Let X(t) be a wide sense stationary random process with the power spectral density SX(f) as shown in Figure (a), where f is in Hertz (Hz). The random process X(t) is input to an ideal low pass filter with frequency response
As shown in Figure (b). The output of the lowpass filter is Y(t ).
Let E be the expectation operator and consider the following statements.
I. E( X(t)) = E(Y(t))
II. E( X2(t)) = E(Y2(t))
III. E(Y2(t)) = 2
Select the correct option:
Answer : Option A
Explaination / Solution:
Q2. A half wavelength dipole is kept in the x-y plane and oriented along 450 from the x-axis. Determine the direction of null in the radiation pattern for 0 ≤ ϕ ≤ π. Here the angle θ (0 ≤ θ ≤ π) is measured from the z-axis, and the angle ϕ (0 ≤ ϕ ≤ 2π) is measured from the x-axis in the x-y plane.
Answer : Option A
Explaination / Solution:
The null occurs along axis of the antenna which is θ = 900and ϕ= 450
Q3. Consider the signal 
where 
denotes the Hilbert transform of m(t) and the bandwidth of m(t) is very small compared to fc. The signal s(t) is a
where denotes the Hilbert transform of m(t) and the bandwidth of m(t) is very small compared to fc. The signal s(t) is a
Answer : Option C
Explaination / Solution:
We have the signal,
Here, s(t) represents SSB - Lower side band, and thus a band pass signal.
Q4. A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and step-size Δ of the delta modulator are 20,000 samples per second and 0.1 V, respectively. To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is
Answer : Option A
Explaination / Solution:
For preventing slope overload, we should have
(slope of m(t) ≤ (slope of sampling)
For sinusoidal signal, if
Q5. The time domain behavior of an RL circuit is represented by 
For an initial current of
For an initial current ofFor an initial current of 
the steady state value of the current is given by
the steady state value of the current is given by
Answer : Option A
Explaination / Solution:
Steady state all transient effect die out and inductor act as short circuits and forced response acts only. It doesn’t depend on initial current state. From the given time domain behavior we get that circuit has only R and L in series with v0 Thus at steady state 
Q6.
The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric conductor is given by the following expression 
The cross-sectional dimensions of the waveguide are given as a = 0.08 m and b = 0.033 m. The mode of propagation inside the waveguide is
The cross-sectional dimensions of the waveguide are given as a = 0.08 m and b = 0.033 m. The mode of propagation inside the waveguide is
Answer : Option C
Explaination / Solution:
We have the expression,
and the cross sectional dimension is
a = 0.08 m, b = 0.033m
Now, we compare the equation for TEm,n mode whose Hz is given as
Hence, given mode is TE21 mode
Q7. Consider a system whose input x and output y are related by the equation 
where h(t) is shown in the graph.
Which of the following four properties are possessed by the system ?
BIBO : Bounded input gives a bounded output.
Causal : The system is causal,
LP : The system is low pass.
LTI : The system is linear and time-invariant.
where h(t) is shown in the graph.Which of the following four properties are possessed by the system ?
BIBO : Bounded input gives a bounded output.
Causal : The system is causal,
LP : The system is low pass.
LTI : The system is linear and time-invariant.
Answer : Option B
Explaination / Solution:
Here h(t) ! 0 for t < 0. Thus system is non causal. Again any bounded input x(t) gives bounded output y(t). Thus it is BIBO stable.
Q8. For a parallel plate transmission line, let v be the speed of propagation and Z be the characteristic impedance. Neglecting fringe effects, a reduction of the spacing between the plates by a factor of two results in
Answer : Option B
Explaination / Solution:
No Explaination.
Q9.
A communication channel with AWGN operating at a signal to noise ration SNR >> 1 and bandwidth B has capacity C1. If the SNR is doubled keeping constant, the resulting capacity C2 is given by
Answer : Option B
Explaination / Solution:
Q10. 
A transmission line terminates in two branches, each of length 
as shown. The branches are terminated by 50W loads. The lines are lossless and have the characteristic impedances shown. Determine the impedance Zi as seen by the source.
as shown. The branches are terminated by 50W loads. The lines are lossless and have the characteristic impedances shown. Determine the impedance Zi as seen by the source.
Answer : Option D
Explaination / Solution:
The transmission line are as shown below. Length of all line is 
