USN Fifth Semester B.E. Degree Examination, Dec.2014 I Jan.20l5 Time: 3 hrs. Digital Signal Processing Note: Answer FIVE fuII questions, selecting at least TWO qaestions from esch part. 3 a. Determiney(n):x1(n) @ xz(n), givenxr(n):n* 1,0 <n<5 andxz(n): Using Stockhalm's method. Realize FIR linear phase filter for N to be even. 1OECs2 Max. Marks:100 cosfin,0<n<5. (10 Marks) (08 Marks) (02 Marks) (03 Marks) (07Marks) -4 - j4, -4 * j9.7\. Using (10 Marks) (10 Marks) (04 Marks) (06 Marks) (08 Marks) () ! o. E a d) OJ ! (,X &- -.o co .= oJ <d$ a CJ- -C(l) ?.^ d: O() b0- d! -o >e d- 'ia OE p. 5- oi n.Y O= 6,i €c !o <v >\ q- -.o c olJ o= 9O F> o lr< *ol o z qi o o. a L PART _ A I a. State and prove the relationship between z-transform and DFT. (06 Marks) b. DetermineNpointDFTof x(n)=.or?n5"t, 0<K<N- 1. (06Marks) c. Find the IDFT of X(K) {255, 48.63 + j166.05, -51+j102, -78.63+j46.05, -85, -78.63-j46.05, -51-j102, 48.63 - 166j). (08 Marks) 2 a. State and prove the following properties: i) Symmetry propefty ii) Parseval's theorem (08 Marks) b. Prove: i) Symmetry and ii) Periodicity property of a twiddle factor. (04 Marks) c. Find the output y(n) of a filter whose impulse response is h(n) : {1,2,3,4} and the input signaltothefilterisx(n): {1,2,1,-1?3,0,5,6,2,-2,-5,-6,7,1,2,0,1}.Usingoverlap- add method. [Use 6 point circular convolution]. (08 Marks) b. Develop DIT FFT algorithm and write signal flow graph for N : 8. c. Explain inplace computation of FFT. 4 a. Explain bit reversal property used in FFT algorithm for N: 16. b. Develop DIT-FFT algorithm for N: 9. c. Find IDFT of X(K) : {36, -4+j9.7, -4+j4, -4+j1.7, -4, -4 - j1.7, DIF FFT algorithm. Show clearly all the intermediate results. PART _ B 5 a. Design a Chebyshev filter to meet the following specifications: i) Pass band ripple < 2 db ii) Stop band attenuation > 20 db iii) Pass band edge : 1 radlsec irr) Stop band edge : 1.3 radlsec b. Distinguish between IIR and FIR filters. c. Derive an expression for order of a low pass Butterworth filter. 6a. b. Evaluate the impulse response for input x(n) : 6(n) of three stage lattice structure having coefficients Kr : 0.65, Kz : -0.34 and K: : 0.8. Also draw its direct form - I structure. (12 Marks) I of2 www.bookspar.com | VTU NOTES | QUESTION PAPERS | NEWS | VTU RESULTS | FORUM | VTU BOOKSPAR APP www.bookspar.com | VTU NOTES | QUESTION PAPERS | NEWS | VTU RESULTS | FORUM | VTU BOOKSPAR APP

Examination, I Jan.20l5 Digital Signal Processing Explain how an analog filter is mapped on to a digital filter using impulse invariance method. What are the limitations of the method?

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Page 1: Examination, I Jan.20l5 Digital Signal Processing Explain how an analog filter is mapped on to a digital filter using impulse invariance method. What are the limitations of the method?

USN

Fifth Semester B.E. Degree Examination, Dec.2014 I Jan.20l5

Time: 3 hrs.

Digital Signal Processing

Note: Answer FIVE fuII questions, selectingat least TWO qaestions from esch part.

3 a. Determiney(n):x1(n) @ xz(n), givenxr(n):n* 1,0 <n<5 andxz(n):Using Stockhalm's method.

Realize FIR linear phase filter for N to be even.

1OECs2

Max. Marks:100

cosfin,0<n<5.(10 Marks)(08 Marks)(02 Marks)

(03 Marks)(07Marks)

-4 - j4, -4 * j9.7\. Using(10 Marks)

(10 Marks)(04 Marks)(06 Marks)

(08 Marks)

()

!o.

OJ!

(,X

-.oco

.= oJ<d$a

CJ--C(l)

?.^

O()

b0-d!-o>ed-

'iaOE

p. 5-

oin.YO=

6,i€c!o<v>\ q--.oc olJ

o=9OF>o

lr<*olo

zqi

oo.aL

PART _ AI a. State and prove the relationship between z-transform and DFT. (06 Marks)

b. DetermineNpointDFTof x(n)=.or?n5"t, 0<K<N- 1. (06Marks)

c. Find the IDFT of X(K) {255, 48.63 + j166.05, -51+j102, -78.63+j46.05, -85,-78.63-j46.05, -51-j102, 48.63 - 166j). (08 Marks)

2 a. State and prove the following properties:i) Symmetry propeftyii) Parseval's theorem (08 Marks)

b. Prove: i) Symmetry and ii) Periodicity property of a twiddle factor. (04 Marks)c. Find the output y(n) of a filter whose impulse response is h(n) : {1,2,3,4} and the input

signaltothefilterisx(n): {1,2,1,-1?3,0,5,6,2,-2,-5,-6,7,1,2,0,1}.Usingoverlap-add method. [Use 6 point circular convolution]. (08 Marks)

b. Develop DIT FFT algorithm and write signal flow graph for N : 8.

c. Explain inplace computation of FFT.

4 a. Explain bit reversal property used in FFT algorithm for N: 16.

b. Develop DIT-FFT algorithm for N: 9.

c. Find IDFT of X(K) : {36, -4+j9.7, -4+j4, -4+j1.7, -4, -4 - j1.7,

DIF FFT algorithm. Show clearly all the intermediate results.

PART _ B5 a. Design a Chebyshev filter to meet the following specifications:

i) Pass band ripple < 2 dbii) Stop band attenuation > 20 dbiii) Pass band edge : 1 radlsecirr) Stop band edge : 1.3 radlsec

b. Distinguish between IIR and FIR filters.c. Derive an expression for order of a low pass Butterworth filter.

6a.b. Evaluate the impulse response for input x(n) : 6(n) of three stage lattice structure having

coefficients Kr : 0.65, Kz : -0.34 and K: : 0.8. Also draw its direct form - I structure.(12 Marks)

I of2

Page 2: Examination, I Jan.20l5 Digital Signal Processing Explain how an analog filter is mapped on to a digital filter using impulse invariance method. What are the limitations of the method?

10EC52

Explain how an analog filter is mapped on to a digital filter using impulse invariancemethod. What are the limitations of the method? (10 Marks)Obtain direct form - I and lattice structure for the system described by the difference

)7requation y(n) = x(n) + i *(n - l) +; x(n - 2) +; x(n - 3). (10 Martus)54J

":ffi'the desired

F:-i**'1Jtrt"l'i+ r,,,.,,"'t" a(ro)={ 0, #.lrl.r, ,,,,,,,,,.,',,,

find H(@,fo.r N:7 using Hanning window." rF'M i. li,b. Show ttra'fl{iJF :0, Kaiser window becomes a rectangular window. '

c. Mention feri;i$filantages and disadvantages of windowing technique.l,.,,,ii

(10 Marks)(05 Marks)(05 Marks)

,k{<t<r<*

-d. n

ii t,

ll ,.

2 of2