STUPIDSID
1(a)
Explain about power and energy signal with example. Determine whether signal given in Fig. Q1(a) is power of energy signal, find correseponding value.
6 M
1(b)
Findout the even and odd component of the following signals i) x(t) = cost+sint+sint cost
ii) x(t) = 1+t+3t2+6t3+9t4
iii) x(t) = 1+t cost + t2 sint+ t3 sint cost.
ii) x(t) = 1+t+3t2+6t3+9t4
iii) x(t) = 1+t cost + t2 sint+ t3 sint cost.
6 M
1(c)
For the given signal x(t) shown in FigQ1(c) sketch and label i) x(0.5t)
ii) x(t+3)
iii) x(3t+2)
iv) x(-3(t-1))
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ii) x(t+3)
iii) x(3t+2)
iv) x(-3(t-1))
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8 M
2(a)
Impulse response of a system is given by \( x\left [ n \right ] =\left\{\begin{matrix}
1& &n=0 \\
\frac{1}{2}& &n=1 \\
0& & \text{otherwise}
\end{matrix}\right. \)/
Input for the given system is \( x\left [ n \right ] = \left\{\begin{matrix} 2& &n=0 \\ 4& &n=1 \\ {-2}& &n=2 \\ 0& &\text{otherwise} \end{matrix}\right. \)/ Findout the y[n] of the system.
Input for the given system is \( x\left [ n \right ] = \left\{\begin{matrix} 2& &n=0 \\ 4& &n=1 \\ {-2}& &n=2 \\ 0& &\text{otherwise} \end{matrix}\right. \)/ Findout the y[n] of the system.
6 M
2(b)
Given inpulse response of the system\( h[n]=\left [ \frac{1}{2} \right ]^n u\left [ n-2 \right ]. \)/ Find out step response of the system.
8 M
2(c)
Draw direct from - I and direct from - II implementation for the following difference equation. \(y\left [ n \right ]+\frac{1}{4}y\left [ n-1 \right ]-\frac{1}{8}y\left [ n-2 \right ]=2x\left [ n \right ]+3x\left [ n-1 \right ] \)/
6 M
3(a)
Obtain the convolution integral for a system with input x(t) and inpulse response h(t), as shown in Fig Q3(a).
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8 M
3(b)
For the given impulse response determine whether system is memory less, stable and cause justify your answer. h[n] = [2]nu[-n].
4 M
3(c)
Find out the complete solution for the system described by the following differential equations.\( \frac{d^2y(t)}{dt^2}+5\frac{d}{dt}y(t)+6y(t)=x(t) \)/, Where x(t) = e4u(t) With initial conditions \( y(0)= -\frac{1}{2},\frac{d}{dt}y(t)\bigg|_{t=0}=\frac{1}{2} \)/
8 M
4(a)
Determine the Fourier series representation of the square wave shown in FigQ4(a)
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8 M
4(b)
Determine the discrete Fourier series representation for the following signal.\( x\left [ n \right ]=\cos \frac{\pi }{3}n+\sin \frac{\pi }{4}n \)/
8 M
4(c)
State and prove the time shift and frequency shift property of Fourier series.
6 M
5(a)
Using the properties of Fourier Transform find out Fourier transform of the following signals.
i) x(t) = sin(πt)e-2tu(t)
ii) x(t) = e-3(t-2)
i) x(t) = sin(πt)e-2tu(t)
ii) x(t) = e-3(t-2)
12 M
5(b)
Obtain the Fourier Transform of the following signals. i) x(t) =u(t)
ii) x(t)=e-utu(t)
iii) \( \begin{matrix} x(t)=1 & -0.5\leq t\leq 0.5\\ \ \ =0 & \text{elsewhere}. \end{matrix} \)/
ii) x(t)=e-utu(t)
iii) \( \begin{matrix} x(t)=1 & -0.5\leq t\leq 0.5\\ \ \ =0 & \text{elsewhere}. \end{matrix} \)/
8 M
6(a)
Find DTFT of the following signal \[i)x\left [ n \right ]=\left [ \frac{1}{2} \right ]^{n+2} u\left [ n \right ] \ \ ii) x\left [ n \right ] =n\left [ \frac{1}{2} \right ]^{2n} u\left [ n \right ]\ \ iii) x\left [ n \right ]= -\left [ \frac{1}{2} \right ]^n u\left (- n-1 \right )\]
12 M
6(b)
An LTI causal system is having a frequency response as \( H\left ( e^{j\Omega } \right )=\frac{e^{j\Omega }}{1+\cos \Omega } \)/. Obtain linear constant difference equation of the system.
8 M
7(a)
Obtain z transform and the ROC and location of poles and zero's of x(z) for the following x[n]. \[i)x[n]=\left [ \frac{1}{2} \right ]^n u[n]+\left ( -\frac{1}{3} \right )^n u[n] \ \ ii)x[n]=-\left ( \frac{3}{4} \right )^n u(-n-1)+\left ( -\frac{1}{3} \right )^n u[n]\]
10 M
7(b)
Obtain inverse 'z' transform of the given(z) using partial fraction expansion \(x(z)=\frac{1-z^{-1}+z^{-2}}{\left ( 1-\frac{1}{2^{z-1}} \right )\left ( 1-2z^{-1} \right )\left ( 1-z^{-1} \right )} \)/ i) with ROC 1<|z|<2
ii) with ROC |z|<&fraction;1and2
ii) with ROC |z|<&fraction;1and2
10 M
8(a)
Use convolution property of 'z' transform to obtain x(z) for the given x(n) \[x(n)= u(n-2)*\left ( \frac{2}{3} \right )^n u(n)\]
6 M
8(b)
Obtain inverse 'z' transform of \( x(z)=\frac{2+z^{-1}}{1-\frac{1}{2}^{z-1}} \)/ with ROC |z|>\[\frac{1}{2}\]
6 M
8(c)
Solve the following linear constant coefficient difference equation using z transform method \( y[n]-\frac{1}{2}y[n-1]=x[n] \)/ with given input \( x[n]=\left ( \frac{1}{3} \right )^n\)/ and initial condition y[-1]=1
8 M
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