Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary


1 (a) Define joint probability density function. Prove that total volume under the surface representable by the joint PDF is always 1.
7 M
1 (b) State and prove central limit theorem.
7 M
1 (c) Find the CDF for an experiment of tossing a coin. The random variable maps head (H) with value 1 and tail (T) with value-1.
6 M

2 (a) Explain the generation of DSB-SC using ring moduilator.
7 M
2 (b) Explain with block diagrams, quadrature carrier multiplexing and demultiplexing system.
7 M
2 (c) A 500W carrier is modulated on a depth of 70%, calculate the total power in the modulated wave in the following forms of A.M.
i) Double sideband with full carrier.
ii) Double sideband suppressed carrier.
iii) Single sideband suppressed carrier.
6 M

3 (a) Define Hilbert transform. Using Hilbert transform, derive the equation for SSB signals only with USB and rejecting the LSB. Explain with block diagram.
7 M
3 (b) With block diagram explain third method for generation of SSB modulated waves.
7 M
3 (c) X(t) =Ac cos 2 π fc t, obtain its pre-envelope and complex conjugate of pre-envelope.
6 M

4 (a) Explain the method of envelope detection of a USB wave plus carrier.
6 M
4 (b) With the help of block diagram explain the working of FDM system.
7 M
4 (c) Explain with a block diagram working of a superheterodyne receiver. Mention its advantages over TRF receiver.
7 M

5 (a) Derive the equation for FM waves. Define modulation index, maximum deviation and bandwidth of a FM signal.
7 M
5 (b) With the help of block diagram, explain the generation of narrowband FM using DSB-SC modulator.
7 M
5 (c) A carrier wave of amplitude 5V and frequency 90MHZ is frequency modulated by a sinusoidal voltage of amplitude 5V and frequency 15 kHz. The frequency deviation constant is kHz/V. Sketch the spectrum of the modulated FM wave. Given J0=0.96, J1=0.18 and J2=0.02.
6 M

6 (a) Explain the working of a balanced slope detector.
7 M
6 (b) With a block diagram, explain the working of a FM stereo multiplexing.
7 M
6 (c) Explain the liner model of phase locked loop.
6 M

7 (a) Derive Friiss's formula for cascade connection of two post network.
7 M
7 (b) Define noise factor of a network. Show that by proving suitable equations that with the increase in noise factor the noise power at the output will also increases.
7 M
7 (c) If each stage has a gain of 10dB and noise figure of 10dB. Determine the overall noise figure of a two stage cascaded amplifier.
6 M

8 (a) Derive the equation for the figure of merits of an AM receiver operating on single tone AM.
7 M
8 (b) Derive the equation for the signal to noise ratio at the output of the DSB-SC receiver.
7 M
8 (c) Explain about pre-emphasis and de-emphasis in FM.
6 M



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