KIIT University 2009 B.Tech Electronics and Tele-Communication Engineering Digital signal processing - Question Paper
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SIXTH SEMESTER EXAMINATION-2009
DIGITAL SIGNAL PROCESSING [ EC 603]
Full Marks: 70 Time: 3 Hours
Answer any SIX questions including Question No. I which is compulsory.
The figures in the margin indicate full marks.
CmriMatw are required to give their answers in their own words as far as practicable and nf all parts of a question should be answered at one place only.
1. a) FindtheZ-transformforthefollowingsignalandsketch [2x10 the ROC.
x(n) = a"u(n) + bflu(-n-1)
b) State and prove convolution property of Z-transform.
c) Find frequency response of 1st order fitter
y(n)-ay(n-1) = x(n)
d) Find.whetherthefdlowingislinear/Nonlinear.TIV/TV. Causal/Noncausal.
y(n) = xfn2}
e) EvaluatethestepresponseofLTIsystemrepresented by following impulse response
h(n)= s(n)-8(n-l)
f) Check if the system defined by following i/p. o/p relationship is stable or not y(n) = ax(n)
(0
K/IT*U/200$/5prmg End Semester ExammatH*'2Q09
9) Which accorting to you is a better way to represent HR system, direct form I or direct form Hand why?
1/ 2, 3. *). find OFT by using linear
transfcanaUofl matrix,
i) What b the speed improvement factor in FFT as compared to drect computation of DF T for N=64?
j) How convolution is related to co-relation? Explain,
2. a) Findtfiehputitteoutputofthesystemy(n)is
y(n){1.4, ttl. 16.17.12}, with impulse response h(n)=<U3}
b) Rsateelhetollcwfigsecciftdortetsystemusingclirect form-ll realisation.
y[n)-2y(n-1)3y(n-2)=x{n) -2x(r\-1)
c) FioJtheQUtpily(f))ofafilterwrioseimpulseresponse h(n)*{1,2,3}ardUpBigiial x(n) is x(n) = (12,3,3,2,
1,1,2.3,1} using overlap add method. What are the differences between overlap add and overlap save method?
3. a) Convolve Hietotlcwiiftg;
xi) = u{n)-u(n-4),h(n)* 8M- + 6V'-2> and check the resuH using two different
methods.
b) Explain radix-2 Oil alaorithm wfth its corresponding How graph. considering N*8.
a) Using Z transform find the convolution for following sequences.
x,(n) = {1,2,3,4), x,(n){1,1l1)
b) Find the step response for the following 2nd order difference equation.
y (n) -1 y(n -1) - ly (n - 2) - x(n)
c) What do you mean byx(nMOD,N)? Explain.
d) Find Z-trensforrn for *(n)*na'u(n).
5. a) Find the Z-tranaform for
M)
b) Using impulse invariance transformation with T=lsec,
<JetermineH(2)if H(s)=-jL..
s2W2s+1
c) A causal LTl systerh is described by following difference equation.
y(n)-ay(n-1) = bx(n) + x(n-1), where'a' is real and less than 1 in magnitude. Find a value of b(a * b) such that frequency response of (he system satisfies ll-JI-lhxallw.
3. a) Using a rectangular window, design a low pass filter wfth passband gain of unity, cutoff frequency of 1 KHz <
MtT'U/MOVfynnt End S4mii$r W#
and working at a sampling frequency of 5 KHz. The length of the impulse response should be 7.
b) Find 4-pt DFT of
x(n) = {1,1,0.0} using Direct DFT formula
7. a) Compute eight point DFT for J1 0<ns7 [0 otherwise using DIT algorithm,
b) Determine the output sequence from the spectrum
c) Plot the output that is obtained when u(-n-2) is multiplied with x(n)={1,2,3, A, 5,6,7}.
8. a) Use one sided Z-transform to find y(n) for n i. 0 if
y(n)=~y(n-l)+x(n)
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y(~ 1)1 |
b) Apply bilinear transformation to H(s). Hs) +1)(s+2) withT=1 sec, to find H(z).
xxxxx
KIH-VHOOVSpriKt Stmtsur F-iaMutuim-2009
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Attachment: |
| Earning: Approval pending. |
