STUPIDSID
1(a)
Test, whether the system y[n]=x[n]cos(ω0n) is linear or nonlinear.
2 M
1(b)
Determine the range of values of and b for which the L.T.I. system with impulse response<br>h[n]=\[\left\{\begin{matrix}
a^{n},n\geq 0 & \\
b^{n},n< 0&
\end{matrix}\right.\] is stable
a^{n},n\geq 0 & \\
b^{n},n< 0&
\end{matrix}\right.\] is stable
2 M
1(c)
The discrete time system y[n]=ny[n-1]+x[n],n≥0 is at rest[i.e. y(-1)=0\. Test whether the system is L.T.I.
3 M
Solve any one question from Q.1(d) & Q.1(e)
1(d)
Determine the zero input response of the system described by the 2nd order difference equation.
x[n]=3y[n-1]-4y[n-2]=0
x[n]=3y[n-1]-4y[n-2]=0
7 M
1(e)
Determine the particular solution of the difference equation.
\[y[n]=\dfrac{5}{6}y[n-1]-\dfrac{1}{6}y[n-2]+x[n]\] When the forcing function is x[n]=2n u[n]
\[y[n]=\dfrac{5}{6}y[n-1]-\dfrac{1}{6}y[n-2]+x[n]\] When the forcing function is x[n]=2n u[n]
7 M
2(a)
Determine the Z-transform of the signal,
x[n]={3,0,0,0,0,6,1,-4}
x[n]={3,0,0,0,0,6,1,-4}
2 M
2(b)
Obtain inverse Z-transform using residue method of the signal.
\[X[Z]=\dfrac{1}{\left ( Z-1 \right )\left ( Z-3 \right )}\]
2 M
2(c)
Determine the response of the system characterized by impulse response h[n]=(0.5)n u[n] to the input signal x[n]=2n u[n]
3 M
Solve any one question from Q.2(d) & Q.2(e)
2(d)
Determine the unit step response of the system characterized by the difference equation
y[n]=06y[n-1]-0.08y[n-2]+x[n]
y[n]=06y[n-1]-0.08y[n-2]+x[n]
7 M
2(e)
Find the linear convolution of x1[n]and x2[n] using z-transform
x1[n]={1,2,3,4}↑ and x2[n]={1,2,0,2,1}↑
x1[n]={1,2,3,4}↑ and x2[n]={1,2,0,2,1}↑
7 M
3(a)
Compute the DFT of the following finite length sequence of length N, (N is even)
x[n]\[\ \left\{\begin{matrix} 1, & 0\leq n\leq \dfrac{N}{2}-1\\ 0, & \dfrac{N}{2}\leq n\leq N-1 \end{matrix}\right.\]
x[n]\[\ \left\{\begin{matrix} 1, & 0\leq n\leq \dfrac{N}{2}-1\\ 0, & \dfrac{N}{2}\leq n\leq N-1 \end{matrix}\right.\]
2 M
3(b)
State and prove the linearity property of DFT.
2 M
3(c)
Let x[n] be a real and odd periodic signal with period N=7 and Fourier coefficients ak. Given that a15=j,a16=2j,a17=3j.
Determine the values of a0 ,a-1,a2 and a-3.
Determine the values of a0 ,a-1,a2 and a-3.
3 M
Solve any one question from Q.3(d) & Q.3(e)
3(d)
Prove that multiplication of two DFT's is equivalent to the circular convolution of their sequences in time domain.
7 M
3(e)
Using graphical method, obtain a 5-point circular convolution of two discrete time signals defined as:
x[n]=(1.5)n u[n] , 0≤n≤2
y[n]=(2n-3)u[n] , 0≤n≤3
x[n]=(1.5)n u[n] , 0≤n≤2
y[n]=(2n-3)u[n] , 0≤n≤3
7 M
4(a)
State the computational requirements of FFT.
2 M
4(b)
What is decimation in-time FFT algorithm?
2 M
4(c)
Explain the Goertzel algorithm.
3 M
Solve any one question from Q.4(d) & Q.4(e)
4(d)
Develop a radix-3 DIT FFT algorithm for evaluating the DFT for N=9
7 M
4(e)
Obtain DFT of a sequence \[x[n]\left \{ \dfrac{1}{2},\dfrac{1}{2},\dfrac{1}{2},\dfrac{1}{2}0,0,0,0 \right \}\] using decimation in-frequency FFT algorithm.
7 M
5(a)
An analog filter has the following system function. Convert this filter into a digital filter using backward difference for the derivative.
\[\ H(s)=\dfrac{1}{\left ( s+0.1 \right )^{2}+9}\]
\[\ H(s)=\dfrac{1}{\left ( s+0.1 \right )^{2}+9}\]
2 M
5(b)
Convert the analog filter into a digital filter whose system function is\[\ H(s)=\dfrac{s+0.2}{\left ( s+0.2 \right )^{2}+9}\]
Use the impulse invariant technique. Assume T=1s.
Use the impulse invariant technique. Assume T=1s.
2 M
5(c)
Convert the analog filter with system function is\[\ H(s)=\dfrac{s+0.2}{\left ( s+0.2 \right )^{2}+9}\]
into a digital IIR filter using bilinear transformation. The digital filter should have a resonant frequency of \(\omega_r=\dfrac{\pi }{4}\)
3 M
Solve any one question from Q.5(d) & Q.5(e)
5(d)
Describe the Butter worth filters.
7 M
5(e)
Describe Chebyshev filters.
7 M
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