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Discrete Time Signal & System : Question Paper Dec 2013 - Electronics Engineering (Semester 6) | Mumbai University (MU)
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Discrete Time Signal & System - Dec 2013

Electronics Engineering (Semester 6)

TOTAL MARKS: 100
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks.


Solve any four:-

1 (a) If Fs is sampling frequency then the relation between analog frequency F and digital frequency f is :-
(i) f = F/(2Fs)
(ii) f = Fs/f
(iii) f = F/Fs
(iv) f = 2F/Fs
Justify the answer with an example.
(5 marks)
1 (b) The evaluation of correlation involves:-
(i) Shifting, rotation and summation.
(ii) Shifting, multiplication and summation.
(iii) Change of index, folding and summation.
(iv) Change of index, folding and shifting.
(5 marks)
1 (c) Compare IIR and FIR.(5 marks) 1 (d) State and explain Parseval's Theorem in DFT.(5 marks) 1 (e) State the relationship between Z-transform and DTFT.(5 marks) 2 (a) Determine the energy of the sequence:-
x[n] = (0.5)n n≥0
=3n n<0
and plot the same.
(10 marks)
2 (b) If x[n]={1,-2,1} and
h[n] = 1 for 0≤n≤5
=0 elsewhere
Determine linear convolution.
(10 marks)
3 (a) Determine the response of the system:-
y[n] = (5/6)y[n-1] - (1/6)y[n-2] + x[n]
For inputx[n] = δ[n] - (1/3)δ[n-1]
(10 marks)
3 (b) Using Z transform properties prove that:-
$$n x[n]\overset{z}\leftrightarrow {-z} \dfrac{dx(z)}{dz}\\ if \ x[n]\overset{z}\rightarrow x(z) $$
(10 marks)
4 (a) The system function of the LTI system is given as:-
Specify ROC of H(z) and determine unit sample response h(n) for the following conditions:
(i) Stable system.
(ii) Causal system.
(10 marks)
4 (b) Explain Overlap add and Overlap save method.(10 marks) 5 (a) Find DFT of the following sequence using FFT:-
x(n) = {1,1,1,0,0,0,1,1}
(10 marks)
5 (b) Using the result derived in Q.5 (A) Find the DFT of the signal and not otherwise:-
x1[n] = {1,0,0,0,1,1,1,1}
x1[n] = {1,1,1,1,1,0,0,0}
(10 marks)
6 (a) Determine the frequency, magnitude and phase response of the system given by the differential equation:-
y[n] = x[n] - x[n-1] + x[n-2]
(10 marks)
6 (b) Find the 4pt. DFT of the sequence:-
x[n] = cos(0.25nπ)
(10 marks)


Write short notes on any four:-

7 (a) Geortzel Algorithm.(5 marks) 7 (b) Give difference between DSP and Microprocessor.(5 marks) 7 (c) Applications of DSP [any two].(5 marks) 7 (d) Mapping of s-plane to z-plane.(5 marks) 7 (e) Properties of DTFT.(5 marks)

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