Signal Processing - Study Mode

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[#346] Two independent random signals X and Y are known to be Gaussian with mean values x 0 and y 0 and variance $$sigma _{ ext{x}}^2$$xa0and $$sigma _{ ext{y}}^2.$$ xa0A signal Z = X - Y is obtained from them. The mean z 0 , variance $$sigma _{ ext{z}}^2$$xa0and p.d.f. p(z) of the signal Z are given by:

(A) $${{ ext{x}}_0} - {{ ext{y}}_0},,sigma _{ ext{x}}^2 - sigma _{ ext{y}}^2,,{ ext{Gaussian}}$$

(B) $${{ ext{x}}_0} + {{ ext{y}}_0},,sigma _{ ext{x}}^2 + sigma _{ ext{y}}^2,,{ ext{Rayleigh}}$$

(C) $${{ ext{y}}_0} - {{ ext{x}}_0},,sigma _{ ext{y}}^2 - sigma _{ ext{x}}^2,,{ ext{Uniform}}$$

(D) $${{ ext{x}}_0} - {{ ext{y}}_0},,sigma _{ ext{x}}^2 + sigma _{ ext{y}}^2,,{ ext{Gaussian}}$$

Correct Answer

(D) $${{ ext{x}}_0} - {{ ext{y}}_0},,sigma _{ ext{x}}^2 + sigma _{ ext{y}}^2,,{ ext{Gaussian}}$$

[#347] Three analog signals, having bandwidth of 1200 Hz, 600 Hz and 600 Hz are sampled at their respective Nyquist rates, encoded with 12 bit words and time division multiplexed. The bit rate for the multiplexed signal is

(A) 115.2 kbps

(B) 28.8 kbps

(C) 57.6 kbps

(D) 38.4 kbps

Correct Answer

(C) 57.6 kbps

[#348] A stable Linear Time Invariant (LTI) system has a transfer function $${ ext{H}}left( { ext{s}}
ight) = frac{1}{{{{ ext{s}}^2} + { ext{s}} - 6}}.$$ xa0 xa0To make this system causal it needs to be cascaded with another LTI system having a transfer function H 1 (s). A correct choice for H 1 (s) among the following option is

(A) s + 3

(B) s - 2

(C) s - 6

(D) s + 1

Correct Answer

(B) s - 2

[#349] A square wave is defined by [xleft( t
ight) = left{ x08egin{gathered}
A,,0 < t < frac{{{T_0}}}{2} hfill \
- A,,frac{{{T_0}}}{2} < t < {T_0} hfill \
end{gathered}
ight.] It is periodically extended outside this interval. What is the general coefficient a n in the Fourier expansion of this wave?

(A) 0

(B) $$frac{{2Aleft( {1 - cos npi } ight)}}{{npi }}$$

(C) $$frac{{2Aleft( {1 + cos npi } ight)}}{{npi }}$$

(D) $$frac{{2Aleft( {1 - cos npi } ight)}}{{left[ {left( {n + 1} ight)pi } ight]}}$$

Correct Answer

(A) 0

[#350] A periodic signal x(t) has a trigonometric Fourier series expansion $$xleft( t
ight) = {a_0} + sumlimits_{n = 1}^infty {left( {{a_n}cos n{omega _0}t + {b_n}sin n{omega _0}t}
ight)} $$ If $$xleft( t
ight) = - xleft( { - t}
ight) = - xleft( {t - frac{pi }{{{omega _0}}}}
ight),$$ xa0 xa0 xa0we can conclude that

(A) a n are zero for all n and b n are zero for n even

(B) a n are zero for all n and b n are zero for n odd

(C) a n are zero for n even and b n are zero for n odd

(D) a n are zero for n odd and b n are zero for n even

Correct Answer

(A) a n are zero for all n and b n are zero for n even