Answer any one question from Q1 and Q2

1 (a)
A discrete time signal is given below. Check for following system properties:

i) Static/Dynamic

ii) Linearity

iii) Causality

iv) Stability

y(n)=8 cos x(n)

i) Static/Dynamic

ii) Linearity

iii) Causality

iv) Stability

y(n)=8 cos x(n)

6 M

1 (b)
Sate and prove the convolution Integral property. With suitable block diagram & mathematical equation.

3 M

1 (c)
Find Y(n) discrete time signal convolution Integral.

x(n)= (u(n) -u (n-4)) and h(n)= {1,1,1,1}

x(n)= (u(n) -u (n-4)) and h(n)= {1,1,1,1}

3 M

2 (a)
Find given signal is whether energy signal or power signal. Find its value x(t)=rect (t); for t=-1 to t+1

3 M

2 (b)
Find the convolution of flowing signal plot Y(t).

6 M

2 (c)
Find Even and Odd Component for given signal.

x(t)=1+3t+4 sin (t) + 6 cos (3t)

x(t)=1+3t+4 sin (t) + 6 cos (3t)

3 M

Answer any one question from Q3 and Q4

3 (a)
State and Prove the following property of Laplace Transform.

i) Periodic Signal Property

ii) Time Scaling Property

i) Periodic Signal Property

ii) Time Scaling Property

6 M

3 (b)
Find the Quadrature Fourier series for the full wave rectifier output signal. With amplitude 'A' and periodic 0 to π.

6 M

4 (a)
Find the Initial Value and Final Value of the signal x(t) its Laplace Transform \[ X(S) = \dfrac {2S+3} {S^2 +5S -7} \]

6 M

4 (b)
Show that Rectangular function in time domain to become Sinc function in Frequency Domain.

6 M

Answer any one question from Q5 and Q6

5 (a)
Determine the Auto Correlation Function Energy Spectral density of x(t)=cos πt [u(t+2)] -u [t-2] and sketch the auto-correlation.

10 M

5 (b)
State the properties of Energy Spectral Density, Power Spectral Density, Autocorrelation and Cross Correlation.

8 M

5 (c)
Explain the properties of Probability, CDF and PDF.

8 M

6 (a)
The probability density function of a random Variable 'x' is defined as \[ \] Find

i) Constant ii) P(1

i) Constant ii) P(1

10 M

6 (b)
Draw and explain the following probability distribution model.

i) Gaussian distribution Model.

ii) Uniform Distribution Function.

i) Gaussian distribution Model.

ii) Uniform Distribution Function.

8 M

6 (c)
Find Cross-Correlation of following discrete time signal.

x(n)={1,2,3,4} and y(n)={3,2,1,0}

x(n)={1,2,3,4} and y(n)={3,2,1,0}

8 M

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