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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)
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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
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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
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