STUPIDSID
1 (a)
What is sinc(x) function? Plot graphically sinc(x) function for the range of x: -2.5
5 M
1 (b)
Obtain DTFT and plot the magnitude and phase response of
h(n)={0, 1, 1, 1}
h(n)={0, 1, 1, 1}
5 M
1 (c)
Distinguish between power signals and energy signals. Is x(t)=cos2(w0t) is energy signal or power signal? Find its normalized energy or power.
5 M
1 (d)
State and prove differentiation of Z-transform.
5 M
1 (e)
Check whether the following system is linear, time variant, casual or otherwise: y(n)=x(n)+n*x(n+1).
5 M
2 (a)
Find the response of the system \[ x(t)= \dfrac {d^2 y(t)}{dt^2} + 5 \dfrac {dy(t)}{dt}+ 6y(t) \] Subjected to the initial conditions y'(0)=2, y(0)=1 and input x(t)=e-1 u(t).
10 M
2 (b)
Find and sketch the Even and Odd components of the following:
x(t)=t, 0≤t≤1
x(t)=2-t, 1≤t≤2
x(t)=t, 0≤t≤1
x(t)=2-t, 1≤t≤2
5 M
2 (c)
State and prove frequency shift property of the Fourier transform.
5 M
3 (a)
Compute the convolution y(n)=x(n)*h(n) where X(n)={1, 1, 0, 1, 1} and h(n)={1, -2, -3, 4}.
8 M
3 (b)
Find Inverse Z-transform of the following: \[ X(Z) = \dfrac {2Z^2 + 3Z}{z^2 + Z+1} \] if x(n) is causal.
8 M
3 (c)
Define ESD and PSD. What is the relation of ESD and PSD with autocorrelation?
4 M
4 (a)
Find y(t)=x(t)*h(t) of the signal shown above using graphical convolution.
10 M
4 (b)
Obtain system function H(z) for \[ y(n) + \dfrac {1}{2} y(n-1)=x(n)-x(n-1) \] Determine the poles and zeros and draw a pole zero plot.
5 M
4 (c)
Obtain DTFT and plot the magnitude and phase response of h(n)={2, 1, 2}.
5 M
5 (a)
Determine the Z transform and sketch ROC. \[ 1) \ x_1[n] = \left [ \dfrac {1}{3} \right ]^n; \ n\ge 0 \\ 2) \ x_2 [n] = x_1 [ n+4] \]
10 M
5 (b)
Obtain Laplace transform by using properties of Laplace transform only.
5 M
5 (c)
Determine Fourier transform of signum signal.
5 M
6 (a)
Obtain initial Laplace transform of \[ X(s) = \dfrac {2s^2 + 5s+ 5}{(s+2)(s+1)^2} \] for all possible ROC conditions.
10 M
6 (b)
Obtain Fourier transform by using properties of Fourier transform only.
10 M
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