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Digital Signal Processing Question Paper - Jun 18 - Electronics And Telecomm (Semester 5) - Pune University (PU)
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Digital Signal Processing - Jun 18
Electronics And Telecomm (Semester 5)
Total marks: 80
Total time: 3 Hours
INSTRUCTIONS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Draw neat diagrams wherever necessary.
1.a.
A continuous time signal x(t) with fundamental period T= 1/F is sampled at rate $F_{s} = 1 / T_{s}$ to produce discrete time sinusoid x(n) = x(n $T_{s}$). Show that x(n) is periodic if $\dfrac{T_{s}}{T} = \dfrac{K}{N}$
(5 marks)
00
1.b.
Define Z transform and ROC. Hence clearly mention and draw ROc's for casual , non-casual , finite and infinite duration sequences.
(5 marks)
00
OR
2.a.
The impulsive response of a system is given by h(n) = $2(0.5)^{n}$ u(n). Find the ssytem function H(z) and the difference equation for y(n). Compute y(n) when x(n) = $(1/4)^{n}$ u(n) using Z.T.
(5 marks)
00
2.b.
Derive the relationship between Fourier transform and Z-transform.
(5 marks)
00
3.a.
Define DFT and IDFT. Hence using the frequency shift property show that DFT
(5 marks)
00
3.b.
Find the casual sequence x(n) for
(5 marks)
00
OR
4.a.
An analog signal
(5 marks)
00
$x_{a}(t) = sin(480\small \pi t) + 3 sin(720 \small \pi t)$ is sampled at the rate 600 samples per sec.
i) Determine Nyquist rate.
ii) Determine folding $freq^{n}$
iii)FInd x(n)
iv) What the $freq^{n}$ in rad in x(n)
4.b.
State and prove periodicity and time shift property of DFT.
(5 marks)
00
5.a.
Explain step by step the Impulsive Invariance transformation, its use to design IIR filter and its drawback.
(8 marks)
00
5.b.
Why the transformation are used to convert analog filter into digital filter. Hence convert the analog filter with system function
(10 marks)
00
$H_{a}(s) = \dfrac{2}{(s+1)(s+2)}$
into digital filter by means of
I) Impulsive Invariance Transformation
ii) Bilinear Transformation with T = 1.
OR
6.a
Implement the second order digital filter using Direct form I and DIrect form II for the following difference equation.
(8 marks)
00
$y(n) = 2r cos(w_{0}n) y (n-1) - r^{2} y (n-2) + x(n) - r cos(w_{0}n) x (n-1)$
6.b.
Design a digital IIR filter with following specifications.
(10 marks)
00
with T = 0.1 sec and using BLT.
7.a.
Design a low pass filter with $H_{d}(w)$ as
(10 marks)
00
with Hann window , with N = 5 find H(w) equation.
7.b.
What are the characteristics of FIR filter. Hence prove that FIR filter are inherently stable filter.
(6 marks)
00
OR
8.a.
Draw and explan the characteristics of ideal filters and its requirements, why the ideal filters are not realizable. Explain the Gibbs phenomenon and why it occurs?
(10 marks)
00
8.b.
What is Finite word length effect and how it affects the FIR filter performance.
(6 marks)
00
9.a.
Explain the application of DSP in compact Disc recording system.
(8 marks)
00
9.b.
Explain real time application of DSP in medical field.
(8 marks)
00
OR
10.a.
How the DSP is useful in speech processing. Explain any application of speech processing using DSP.
(8 marks)
00
10.b.
How the mechanical industry is benefited with DSP algorithm, explain with example.
(8 marks)
00
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