STUPIDSID
1(a)
Determine if the following system is memoruless, causal, linear, time inavariant y(t) = t x(t)
5 M
1(b)
Explain in brief ROC ( Region Convergnce) conditions of Laplace transform.
5 M
1(c)
Explain Gibbs phenomenon. What is a Gibbs oscillation?
5 M
1(d)
Explain relation between Fourier Transform and Laplace transform.
5 M
1(e)
Determine if the given sequence is periodic or not. If periodic, find out fundamental period.\[x[n]=\sin \left ( \frac{6\pi }{7}n+1 \right )\]
5 M
2(a)
Find the reponse of the time invariant system with impulse response h [n] = {1, 2, 1, -1} to an input signal x [n] = {1, 2, 3, 1} using convolution as well as using Z transform. Verify your answers.
10 M
2(b)
Determine inverse Laplace Transform of \[x(s)=\frac{3s^2+8s+23}{\left ( s+3 \right )\left ( s^2+2S+10 \right )}\]
10 M
3(a)
Determine the Fourier Transform of the trapezoidal function shown in the figure below.
!mage
!mage
10 M
3(b)
Find the inverse Z transform of the following function \(X(z)=\frac{1}{1-0.8z^{-1}+0.12z^{-2} \)/ for the following ROCs
a) |z| >0.6
b) |z|<0.2
c) 0.2<|z|<0.6
a) |z| >0.6
b) |z|<0.2
c) 0.2<|z|<0.6
10 M
4(a)
Find out DTFT of the following
i)x[n]={1, -1, 2, 2}
ii) x[n] = -a^n u [-n-1], where |a| <1
i)x[n]={1, -1, 2, 2}
ii) x[n] = -a^n u [-n-1], where |a| <1
10 M
4(b)
An LTI system is described by the following equations. Determine the transfer function and impulse response of the system, Sketch the poles & zeros of the z-plane.
\[y[n]-4[n-1]+4y[n-2]=x[n-1]\]
\[y[n]-4[n-1]+4y[n-2]=x[n-1]\]
10 M
5(a)
Find Compact trigonometric Fourier Series for the signal x(t) shown in the following figure Sketch the amplitude and phase spectra for x(t).
!mage
!mage
10 M
5(b)
The impulse response of a CT system is given below. Determine the unit step response of the system using convolution theorem of Laplace Transform. h(t) = u (t+2) +u ( t-2)
10 M
6(a)
A CT signal has been shown below. Sketch the following signals.
!mage
i) x(t-4) ii) x(4-t) iii) x(-2t+2) iv) x(0.5t)
!mage
i) x(t-4) ii) x(4-t) iii) x(-2t+2) iv) x(0.5t)
10 M
6(b)
State and prove with appropriate mathematical derivation. 'convolution in time domain' property and 'time reversal' property of Z transform. Also comment on importance of these properties in the field of communication and signal processing.
10 M
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