STUPIDSID
1(a)
Find whether the following signals are energy or power and find the corresponding value:
\[x(t)=\left ( 1/2 \right )^n.u[n]\]
\[x(t)=\left ( 1/2 \right )^n.u[n]\]
4 M
1(b)
Find the convolution between:
\[\begin{align*} x[n]=\left \{ 1, 1, 1, 1 \right \}\text{and}\\ h[n]=\left \{ 1, 1, 1,1 \right \}\end{align*}\]
\[\begin{align*} x[n]=\left \{ 1, 1, 1, 1 \right \}\text{and}\\ h[n]=\left \{ 1, 1, 1,1 \right \}\end{align*}\]
4 M
1(c)
Find odd and even components of the signal:
\[x[n]=u[n]-u[n-4].\]
\[x[n]=u[n]-u[n-4].\]
4 M
2(a)
An analog signal is given by the equation:
\[x(t)=2\sin 400\pi t +10\cos 1000\pi t.\] It is sampled at sampling frequency 1000 Hz.
i) What is the Nyquist rate for the above signal?
ii) What is the Nyquist interval of the signal?
\[x(t)=2\sin 400\pi t +10\cos 1000\pi t.\] It is sampled at sampling frequency 1000 Hz.
i) What is the Nyquist rate for the above signal?
ii) What is the Nyquist interval of the signal?
2 M
2(b)
Find the convolution between:
x(t) = u(t) and h(t) = u(t-2)
x(t) = u(t) and h(t) = u(t-2)
6 M
2(c)
Check whether the following signal is periodic or non-periodic. If periodic, find period of the signal:
\[x(t)=\cos \left ( n/8 \right ).\cos \left ( n\pi /8 \right ).\]
\[x(t)=\cos \left ( n/8 \right ).\cos \left ( n\pi /8 \right ).\]
4 M
Solve any one question fromQ3(a,b) and Q.4(a,b)
3(a)
State and explain the properties of Continuous Time Fourier Series.
6 M
3(b)
Determine the transfer function and impulse response for the system described by the differential equation shown below for zero initial condtitions: \[d/dt[y(t)]+3 y (t)=x(t).\]
6 M
4(a)
Draw the magnitude and phase spectrum of the signal:
\[x(t)= 5\cos \left ( 2\pi 10t +30\right )-10\cos \left ( 2\pi 20t+60 \right ).\]
\[x(t)= 5\cos \left ( 2\pi 10t +30\right )-10\cos \left ( 2\pi 20t+60 \right ).\]
6 M
4(b)
Find the Fourier transform of the signal:
\[x(t)= \sin \omega _c t.u(t).\]
\[x(t)= \sin \omega _c t.u(t).\]
6 M
Solve any one question fromQ5(a,b) and Q.6(a,b)
5(a)
State and prove convolution property of Laplace transform.
6 M
5(b)
Find the initial and final value of:
\[X(s)= 5s+50/s\left ( s+5 \right ).\]
\[X(s)= 5s+50/s\left ( s+5 \right ).\]
7 M
6(a)
Find the Laplace transform of the given signal and draw its ROC:
\[X(t)=-e^{at}u\left ( -t \right ).\]
\[X(t)=-e^{at}u\left ( -t \right ).\]
6 M
6(b)
Find the inverse Laplace transform of:
\[X(s)= 3s+7/\left ( s^2-2s-3 \right ).\]
\[X(s)= 3s+7/\left ( s^2-2s-3 \right ).\]
7 M
Solve any one question fromQ.7(a,b) and Q.8(a,b)
7(a)
List the properties of auto correlation and cross correlation for energy signals.
6 M
7(b)
A perfect die is thrown. Find the probability that:
i) You get even number.
ii) You get a perfect square.
i) You get even number.
ii) You get a perfect square.
7 M
8(a)
List the properties of probability. Explain conditional probability with an example and formula.
6 M
8(b)
A three digit message is transmitted over a noisy channel having a probability of error as P(E) = 2/5 per digit. Find and draw the CDF.
7 M
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