STUPIDSID
1 (a)
Determine whether the following signals are energy signals or power signals > calculate their energy or power
(i) x(t)=Acos(2?f0t+?)
(ii) x(n)=(1/4)n u(n)
(i) x(t)=Acos(2?f0t+?)
(ii) x(n)=(1/4)n u(n)
5 M
1 (b)
Let x(n)=u(n+1)-u(n-5). Find and sketch even and odd parts of x(n).
5 M
1 (c)
Mention and explain the conditions for the system to be called as IIR.
5 M
1 (d)
State and explain Gibb's phenomenon.
5 M
2 (a)
(i) Plot the signals with respect to time.
x(t)=u(t)-r(t-1)+2r(t-2)-r(t-3)+u(t-4)-2u(t-5)
(ii) Find the even odd parts of the signal.
x(t)=u(t)-r(t-1)+2r(t-2)-r(t-3)+u(t-4)-2u(t-5)
(ii) Find the even odd parts of the signal.
10 M
2 (b)
State and prove the following properties of the Fourier transform
(i) Frequency Different and time integration.
(i) Frequency Different and time integration.
10 M
3 (a)
An analog signal x(t) is given by x(t)=2cos(2000?t)+3 sin(6000?t)+8 cos(1200?t)
(i) calulate nyquist sampling rate.
(ii) If x(t) is sampled at the rate F(s)=5 KHz. What is the discrete time signal obtained after sampling.
(iii) What is the analog signal y(t) we can reconstruct from the samples if the ideal interpolation is used
(i) calulate nyquist sampling rate.
(ii) If x(t) is sampled at the rate F(s)=5 KHz. What is the discrete time signal obtained after sampling.
(iii) What is the analog signal y(t) we can reconstruct from the samples if the ideal interpolation is used
10 M
3 (b)
Find the Laplace Transform of the signal show below
10 M
4 (a)
Obtain the transfer function of the system defined by the following state space equations
\[\left[\begin{array}{ccc}x1\left(t\right) \\x2\left(t\right) \\x3\left(t\right)\end{array}\right]=\left[\begin{array}{ccc}-1 & 1 & -1 \\0 & -2 & 1 \\0 & 0 & -3\end{array}\right]\left[\begin{array}{ccc}x1\left(t\right) \\x2\left(t\right) \\x3\left(t\right)\end{array}\right]+\left[\begin{array}{ccc}1 & 0 \\0 & 1 \\1 & 0\end{array}\right]\left[\begin{array}{cc}u1\left(t\right) \\u2\left(t\right)\end{array}\right]\]
\[\left[\begin{array}{cc}y1\left(t\right) \\y2\left(t\right)\end{array}\right]=\left[\begin{array}{cc}1 & 1 & 1 \\0 & 1 & 1\end{array}\right]\left[\begin{array}{ccc}x1\left(t\right) \\x2\left(t\right) \\x3\left(t\right)\end{array}\right]\]
\[\left[\begin{array}{ccc}x1\left(t\right) \\x2\left(t\right) \\x3\left(t\right)\end{array}\right]=\left[\begin{array}{ccc}-1 & 1 & -1 \\0 & -2 & 1 \\0 & 0 & -3\end{array}\right]\left[\begin{array}{ccc}x1\left(t\right) \\x2\left(t\right) \\x3\left(t\right)\end{array}\right]+\left[\begin{array}{ccc}1 & 0 \\0 & 1 \\1 & 0\end{array}\right]\left[\begin{array}{cc}u1\left(t\right) \\u2\left(t\right)\end{array}\right]\]
\[\left[\begin{array}{cc}y1\left(t\right) \\y2\left(t\right)\end{array}\right]=\left[\begin{array}{cc}1 & 1 & 1 \\0 & 1 & 1\end{array}\right]\left[\begin{array}{ccc}x1\left(t\right) \\x2\left(t\right) \\x3\left(t\right)\end{array}\right]\]
10 M
4 (b)
Find the state equations and output equtions for the system given by
\[G\left(s\right)=\frac{1}{s^3+4s^2+3s+3}\]
\[G\left(s\right)=\frac{1}{s^3+4s^2+3s+3}\]
10 M
5 (a)
Find the Fourier series for the function x(t) defined by
\[f\left(x\right)=\left\{\begin{array}{cc}0 & \frac{-T}{2}<1<0 \\A\sin{{\bar{\omega{}}}_0t} & 0<1<\frac{T}{2}\end{array}\right\}\]
\[And\ x\left(t+T\right)=x\left(t\right),\ {\bar{\omega{}}}_0=\frac{2\pi{}}{T}\]
\[f\left(x\right)=\left\{\begin{array}{cc}0 & \frac{-T}{2}<1<0 \\A\sin{{\bar{\omega{}}}_0t} & 0<1<\frac{T}{2}\end{array}\right\}\]
\[And\ x\left(t+T\right)=x\left(t\right),\ {\bar{\omega{}}}_0=\frac{2\pi{}}{T}\]
10 M
5 (b)
Obtain the Fourier transform of rectangle pulse of duration 2 seconds and having a mangnitude of 10 volts.
10 M
6 (a)
Develop cascade and parallel realization structures for
\[H\left(z\right)=\frac{\frac{z}{6}+\frac{5}{24}z^{-1}+\frac{1}{24}z^{-2}}{1-\frac{1}{2}z^{-1}+\frac{1}{4}z^{-2}}\]
\[H\left(z\right)=\frac{\frac{z}{6}+\frac{5}{24}z^{-1}+\frac{1}{24}z^{-2}}{1-\frac{1}{2}z^{-1}+\frac{1}{4}z^{-2}}\]
10 M
6 (b)
Determine the system function, unit sample response and pole zero plot of the system decribe by the different equations y(n)- 1/2 y(n-1)=2x(n) and also comment on types of the system.
10 M
7 (a)
Explain the relationship between tha laplace transform and Fourier transform.
7 M
7 (b)
State properties of state transition matrix.
6 M
7 (c)
State and discuss the properites of the region of convergence for Z-transform.
7 M
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