Download GTU B.Tech 2020 Winter 7th Sem 2171003 Digital Signal Processing Question Paper

Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Winter 7th Sem 2171003 Digital Signal Processing Previous Question Paper

Seat No.: ________
Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER?VII (NEW) EXAMINATION ? WINTER 2020
Subject Code:2171003 Date:30/01/2021
Subject Name:Digital Signal Processing
Time:10:30 AM TO 12:30 PM Total Marks: 56
Instructions:
1. Attempt any FOUR questions out of EIGHT questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.



MARKS
Q.1 (a) Compare the direct form-I and II structures of an IIR
03
systems, with M-zeros and N-poles.

(b) Calculate the percentage saving in calculations in a 512-
04
point radix-2 FFT, When compared in direct DFT.

(c) Draw and explain architectural block diagram of
07
TMSC6000 DSP processor.


Q.2 (a) Give any three properties of Butterworth lowpass filters.
03

(b) Give the equation specifying Kaiser window. List the
04
advantages of Kaiser window.

(c) Design a single-pole lowpass digital filter with a 3-db
07
bandwidth of 0.2, using the bilinear transformation applied
to the analog filter
() =
+
Where is the 3-dB bandwidth of the analog filter.




Q.3 (a) List the application of an adaptive filter. Briefly explain any
03
one of it.

(b) Realize the following FIR system with minimum number of
04
multipliers. h(n)={-0.5, 0.8, -0.5}

(c) Determine all the FIR filters which are specified by the
07
lattice parameters
1
1
1 = ,
2
2 = 0.6, 3 = -0.7 4 = 3.




Q.4 (a) Determine a direct-form realization for the following linear
03
phase filter.
() = {1, 2,3,4,3,2,1}

(b) Find the inverse DFT of Y(k)= {1,0,1,0}.
04

(c) Derive the signal flow graph for the N= 16-point, radix-4
07
decimation-in-time FFT algorithm in which the input
sequence is in normal order and the computations are done
in place.
1

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Q.5 (a) Determine the inverse Fourier transform of
03
() = 2( - 0), |0| .

(b) Determine the inverse of the system with impulse response
04
1
() = ( ) ().
2

(c) Determine |()|2 for the system
07
() = -0.1( - 1) + 0.2( - 2) + () + ( - 1).



Q.6 (a) Determine the energy density spectrum of the signal
03
() = () , - 1 < < 1

(b) Prove the Parseval's relation
04
1
1()
2() =
1()2()
=-
2 -

(c) Determine the particular solution of the difference equation
07
5
1
() = ( - 1) - ( - 2) + ()
6
6
When the forcing function () = 2, 0 and zero
elsewhere.
Q.7 (a) Find the z-transform of ().
03

(b) Test the stability of the following systems.

i.
y(n) = cos[x(n)]
04
ii.
y(n) = x(- n -2 )

(c) Find the response of the time invariant system with impulse
07
response h(n) = {1,2,1,-1} to an input signal
x(n) = {1,2,3,1}.



Q.8 (a) Determine the regions of convergence of right-sided, left-
03
sided, and finite-duration two-sided sequences.
(b) An analog ECG signal contains useful frequencies up to
04
100Hz.
i.
What is the Nyquist rate for this signal?
ii.
Suppose that we sample this signal at a rate of
250 samples/s. What is the highest frequency that
can be represented uniquely at this sampling rate?
Justify your answer.
(c) Determine the inverse z-transform of
07
1
X(z)
1
2
11.5z 0.5z
when ROC is || < 0.5 and || > 1 .

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