STUPIDSID
1 (a)
Determine if the systems described by the following input-output relations are causal or non-causal.
Also give an example of LTI system.
(i) y(n)= x(n)-x(n-1)
(ii) y(n)= ax(n)
(iii) y(n)= x(n)+ 3x(n+4)
(iv) y(n)= x(-n).
Also give an example of LTI system.
(i) y(n)= x(n)-x(n-1)
(ii) y(n)= ax(n)
(iii) y(n)= x(n)+ 3x(n+4)
(iv) y(n)= x(-n).
7 M
1 (b)
Determine if the systems described by following input-output relations are
linear or non-linear.
Also give an example of stable system.
i) y(n)=nx(n)
ii) y(n)=x(n2)
iii) y(n)=Ax(n)+B
iv) y(n)=x2(n).
Also give an example of stable system.
i) y(n)=nx(n)
ii) y(n)=x(n2)
iii) y(n)=Ax(n)+B
iv) y(n)=x2(n).
7 M
2 (a)
Determine the z-transform of the signals cos ωon u(n) and sin ωon u(n).
7 M
Solve any one question from Q2(b) & Q2(c)
2 (b)
Determine the inverse-z transform of the function X(z)=log(1+az-1).
7 M
2 (c)
Determine the inverse-z transform of the function \[ X(z)= \dfrac {1}{(1-1.5z^{-1}+0.5z^{-2})}, \ |z|>1 \]
7 M
Solve any two question from Q3(a), Q3(b) & Q3(c), Q3(d)
3 (a)
Convert the analog filter with system function \( H(s)= \dfrac {s+0.1}{(s+0.1)^2+9} \) into a digital IIR filter by means of the impulse invariance technique.
7 M
3 (b)
Describe bilinear transformation method of IIR filter design.
7 M
3 (c)
Compare FIR and IIR filters.
7 M
3 (d)
List the steps involved in design of an FIR filter using Kaiser window.
7 M
Solve any two question from Q4(a), Q4(b) & Q4(c), Q4(d)
4 (a)
By means of DFT and IDFT, determine the circular convolution of two sequences x 1 (n) ={1,2,3,4} and x 2 (n)={2,1,2,1}.
7 M
4 (b)
State and prove time reversal property of the DFT.
7 M
4 (c)
Give parallel 'form realization for system function \[ H(z)= \dfrac {-14.75-12.90 \ z^{-1}}{1-(7/8)z^{-1}+ (3/32)z^{-2}} + \dfrac {24.50+26.82z^{-1}}{1-z^{-1} + 0.5 z^{-2}} \]
7 M
4 (d)
Draw Direct form-I and Direct form-II realizations for any IIR system.
7 M
Solve any two question from Q5(a), Q5(b) & Q5(c), Q5(d)
5 (a)
What is FFT ? How do we save number of computations in Decimation-in-time algorithm?
7 M
5 (b)
Draw first stage of decimation-in-frequency FFT algorithm.
7 M
5 (c)
Give salient features of DSP architecture.
7 M
5 (d)
Compare undersampling and oversampling from frequency domain analysis point of view.
7 M
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