STUPIDSID
1 (a)
Check whether the following signal is energy or power signal, find its energy and power x(t)=3u(t).
5 M
1 (b)
Find the single side and double side spectrum of the signal-sketch the magnitude and phase spectrum.
x(t)=1+3sin (6πt+π/3)+6cos (8πt+π/6)+4 sin (12 πt).
x(t)=1+3sin (6πt+π/3)+6cos (8πt+π/6)+4 sin (12 πt).
5 M
1 (c)
Find the Laplace transform of the signal x(t)=e-2|t|.
5 M
1 (d)
Find h[n] if \( H(z) = \dfrac {5z^{-3}}{(z-0.1)(z-0.2)} \) and if the system is stable.
5 M
2 (a)
Check whether the following signal is period or not if periodic find the period.
i) x(t)=7cos(2t+π/6) ii) x[n]=ei7π.
i) x(t)=7cos(2t+π/6) ii) x[n]=ei7π.
4 M
2 (b)
Find the even and odd part of the signal,
i) x(t)=cos(t)+sin(t)+sin(t) cos(t)
\[ x[n]= [1, 2, 8, \underset{\uparrow}{7}, -2,2,5,6] \]
i) x(t)=cos(t)+sin(t)+sin(t) cos(t)
\[ x[n]= [1, 2, 8, \underset{\uparrow}{7}, -2,2,5,6] \]
6 M
2 (c)
Check whether the following system is linear, causal and stable or not.
i) y(t)=cos [x(t)],
x(t) is the input & y(t) is the output
ii) y[n]=nx[n]
where x[n] is the input and y[n] is the output.
i) y(t)=cos [x(t)],
x(t) is the input & y(t) is the output
ii) y[n]=nx[n]
where x[n] is the input and y[n] is the output.
10 M
3 (a)
Find the output y(t)=e-2tu(t)*u(t). sketch the output.
8 M
3 (b)
Find the convoluted out put of the signals. \[ x[n]= \big [7, 6, \underset{\uparrow}{2}, 3, -1, 4 \big ] \ and \\
h[n]=\big [ 1,\underset{\uparrow}{-1}, 0, 2\big] \]
6 M
3 (c)
Check whether the following system given by the impulse response h(t)=u(t+1)-u(t-2) is stable or not, memory less or not, justify.
6 M
4 (a)
Find the Fourier series co-efficients (exponential) of the half wave rectified sine wave of Amplitude A and period 4 seconds. Sketch the amplitude and phase spectrum.
10 M
4 (b)
Explain Gibb's phenomenon.
5 M
4 (c)
Find Fourier transform of x(t)=u(t).
5 M
5 (a)
Find the inverse Fourier transform of \[ \begin {align*}
X(j\omega) &=2 \cos (\omega) &|\omega| \le \pi \\
&=0 &|\omega |>\pi
\end{align*} \]
6 M
5 (b)
Find x[n] if \( X(z) = \dfrac {z}{z^3+3z+2} \) for all possible ROC.
8 M
5 (c)
Find Fourier transform of the signals x(t)=te-3t u(t) using frequency differentiation property. Prove the property also.
6 M
6 (a)
Find the z-transform of the signal \[ x[n]=u[n-2]*\left (\dfrac {2}{3} \right )^n u[n] \]
6 M
6 (b)
Determine Forced response, natural response and total response of the system described by \( \dfrac {dy(t)}{dt} + 3y(t) = 4 x(t) \text { where } x(t)=\cos(2t) \ u(t) \) and initial condition y(o*)=-2.
8 M
6 (c)
Find the Laplace transform of \( \dfrac {d\big [e^{-3(t-2)}u(t-2)\big]}{dt} \) state the properties used.
6 M
7 (a)
Explain Gain margin and phase margin.
6 M
7 (b)
Sketch the root locus for unity feed back system. \[ G(s) = \dfrac {k}{s(s^2 + 2s+2)} \]
10 M
7 (c)
Examine the stability using Routh Criteria.
s6+2s5+18s3+20s2+16s+16=0.
s6+2s5+18s3+20s2+16s+16=0.
4 M
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