Practice Questions on Communications

Q1.

A message signal $ m(t)=\cos 200\pi t+4\cos \pi t $  modulates the carrier $ c(t)=\cos 2\pi f_{c} t $ where $ f_{c}= $ 1 MHz to produce an $ AM $ signal. 

For demodulating the generated $ AM $ signal using an envelope detector, the time constant $ RC $ of the detector circuit should satisfy,

A.

$ 0.5\text{ms}<\text{RC}<1 \text{ms} $

B.

$ 1\mu s<< \text{RC} <<0.5 \text{ms} $

C.

$ \text{RC}<<\mu s $

D.

$ \text{RC}>>0.5\text{ms} $

 View Ans

Q2.

$ x(t) $ is a stationary random process with auto-correlation function.\[R_{x}(\tau)=e^{\pi r^2}\] This process is passed through the system shown below. 


The power spectral density of the output process $ y(t) $ is:

A.

$ (4\pi^2f^2+1)e^{-\pi f^2} $

B.

$ (4\pi^2f^2-1)e^{-\pi f^2} $

C.

$ (4\pi^2f^2+1)e^{-\pi f} $

D.

$ (4\pi^2f^2-1)e^{-\pi f} $

 View Ans

Q3.

A source generates 4 symbols with probabilities \(\dfrac{1}{2},\;\dfrac{1}{4},\;\dfrac{1}{8},\;\dfrac{1}{8}\). The source uses a practical coding scheme has an average code word length of 2 bits/symbol. the efficiency of the code is:

A.

\(1\)

B.

\(7/8\)

C.

\(1/2\)

D.

\(1/4\)

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Q4.

Consider the low pass filter given in the diagram. 

A white noise process, $ x(t) $ of zero-mean and PSD $ \text N_{0}/2 $ is applied to the input of the filter. What is the autocorrelation function of the random process $ y(t) $ at the output of the filter.

A.

$ \dfrac{\text N_{0}R}{L}e^{-(R/L)|\tau|} $

B.

$ \dfrac{\text N_{0}}{3}\dfrac{R}{L}e^{-(R/L)|\tau|} $

C.

$\dfrac{\text N_{0}}{2}\dfrac{R}{L}e^{-(R/L)|\tau|}  $

D.

$ \dfrac{\text N_{0}}{4}\dfrac{R}{L}e^{-(R/L)|\tau|} $

 View Ans

Q5.

A noise signal $ n_{i}(t)$ with power spectral density $ S(\omega)=\text K $ is applied at input of an ideal differentiator. The power spectral density of the output $ n_{0}(t) $ is:

A.

$ \text K^2 $

B.

$ \omega \text K^2 $

C.

$ \omega \text K $

D.

$\omega^2\text K$

 View Ans


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