IUSN 06EC52

Fifth Semester B.E. Degree Examination, Dec.2013 lJan.20l4Digital Signal Processing

Time: 3 hrs. Max. Marks:100

Note: Answer FIVEfull questions, selectingat lesst TWO questions from each part.

oPART _ A /.+

q/Marks)

I. (06 Marks)

d. What is a relation between Fourier series coefficients of a periodic sequence and DFT?(03 Marks)

la.b.

c.

doo0.

ooL

oX

!-

=-3bol-6

.=N

xo0Y(/oE-O

u2,=c

U(J

(!d

a6

'iaoi=

:E

oj

o=a<)otEC'-

!O

o.i>'tu0"cooo=*otr>=o3:ciU<

i a.l

o

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2 a. State and prove time shifting property of DFT.b. Find the output y(n) of a filter whose impulse response is h(n): {1, 1, 1}

signal x(n) : {3.-1.0. 1.3.2.0. 1.2. l} using overlap save method.c. Obtain the 8-point circular convolution of the following sequences:

xr(n) : 12.3.6" 8.2. 1.7,5|x2(n) : {0. 0. 0. 0. 0. l, 0. 0}.

What is zero padding? What are its uses?Find the DFT of a sequence x(n) : {1, 1, 0, 0} and the IDFT of y(k)Find the DFT of a sequence

x(n):l for n<n<L: 0 otherwise

fbr N:4 plot lx(k)l and EG)(08 Marks)

(05 Marks)and the input

(08 Marks)

(07 Marks)

3 a. FindtheDFTofasequencex(n): {1,2,3,4,4,3,2, 1}usingDIT-FFTalgorithm.' (I0 Marks)

b. Compute the IDFT of the sequencex(k): {7,A:707 - j0.707,-j,0.707 -j0.707,1,0.707 +i0.707, j,-A.7A7 + j0.707}using DIF-FFT algorithm. (10 Marks)

4 a. Discuss Chirp-z transform algorithm.b. Explain the following properlies of twiddle factor WN:

i) Symmetric ptopertyii) Periodicity property.

c. Find x(k) forthe input sequence x(n) : n * 1 and N : 8 using DIF - FFT algorithm.(10 Marks)

PART - B

S a. Design an analog Chebyshev filter for which the squared magnitude response lff , (jgi)l'

satisfies the condition 201og,o lH.0O)ln=or, ) -l ; 20 log,o lu"(jei)ln=nr, s -15(08 Marks)(04 Marks)

(06 Marks)

(04 Marks)

b. Distinguish between Butterworlh and Chebyshev filters.

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06ECs2

c. Let H(s) = , + represent the transfer function of a lowpass filter with a passband ofs'+J2s +lI radlsec. Use frequency transformation to find the transfer functions the following analogfilters:i) A lowpass filter with passband of l0 radlsec.

.,r! ii) A highpass filter with cut off frequency of 10 radlsec.

iiis

(os l\{$iiib}|

6.',,i, s. What is a rectangular window function? Obtain its frequency domain characteristie5;'.';:r:' r ,-,'(05 Marks)

. b:'.,',p-esign FI^R low pass filter using Hamming window (M : 7) and also obt[#[;q;;;y. fe,sp nse for * .

Ho (aj*) = g-rw ; 3nl 4 <w <3nl 4

1' 7*tl-1"'l'- (l2Marks)' =o ; 3nt4.l*l=,

c. Explain Gibb's phenomenon. "r. . (03 Marks)

7 a. What is Uitin8tlr-" ansformation? Obtain the traqsfoimation formula for bilineartransformatio^n-- , ,.,,: t' (loMarks)

s+aH(s) =;. into a dieilal filter with ffinite impulse response by the use of impulse(s+a)'+b' : '--------'

{i,,..,..1,,,,,,,,,,,,,. ""''

I a. i) Obtain the cascade realization,dfuhd system functionH(z): (l + 2z-t - z-1 0 +. q., _ r-r). ... Liit Determine the direct forrn realization of the system function

b. Find the impulse response of an FIR lattice filter with coefficientS kr : 0.65. kz : 0.34,k3 :0.8.

(09 Marks)*r (09 Marks)Obtain the direct forpl and direct form-Il structure for the filters given by system function1+0sz,+' '",-,.*.

l-A-52-t +0.062-2'. .' ,:.: (05 Marks)

qt'",:::"

iri

'' "::' " '" rir" ::

,,,.,,,:::,,1r. {<**** 1,,,,,,"'.l;',', .!,

" i.::::!i,rii :::: ::: _j tiN

:::: 11!l

'. ':: " ' ,.--.j, .l

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