Kurukshetra University 2008 B.Tech Electrical Engineering Digital Signal Processing( EE-306E) - Question Paper

8. Design Bulterworth or Chebyshev digital filter for the following specifications :

(i)    Pass band gain required :

(ii)    Frequency upto which pass-band gain must remain more or less steady : 300 Hz

(iii)    Amount of attenuation required : 0-2

(iv)    Frequency from which attenuation must start : 600 Hz.

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Roll No..................k..................Total No. of Pages : 4

BT-6/J08    9070

Digital Signal Processing Paper : EE-306 E

Time : Three Hours]    [Maximum Marks : 100

Note :Attempt FIVE questions selecting at least ONE question from each section.

SECTIONI

1. (a) Determine the z-transforms of the following functions :

(i)    x(n) = [0, 0, 1, 2, 5, 7, 0, 1]

(ii)    x(n) = (1/2)" u(n)

(iii)    x(n) = anu(n) + bn u(-n - 1) x(n) = an(cos con) uOnoTy*    2x4=8

<w

(b)    Determine the causal signal x(n) having the z-transform

x(z) = 1/[(1 + z-1) (1 - z-1)1].    5

(c)    Determine the unit step response of the system described by the difference equation

y(n) = 0-9y (n - 1) - 0-8ly (n - 2) + x(n).    7

(b)    By means of the DFT and IDFT, determine the response of the FIR filter with impulse response h(n) = {l, 2,3) to the

input sequence x(n) = {1,2,2,1) . Show the effect of aliasing. If the aliasing occurs show that how it can be overcome.

(c)    State the properties of DFT. Prove the symmetry properties of DFT.

SECTIONII

3. (a) Obtain direct form-I, direct form-II, cascade and parallel realization structures for the system

2z² +2-2z + 0-48 z²+01z-0-3

(b) Determine all the FIR filters which are specified by the lattice parameters K, = 0-5, K₂ = 0-6, K₃ = -0-7 and K. = 0-33.    5

4

4.    Determine the cascade and parallel realizations for the system described by the system function

10(1 - 0-5Z'¹) (1 - 0-66Z'¹) (1 + 2z^_I)

H(Z)=-:-:-:-r- 20

(1 -0-75Z'¹)(1 -0-22z')(1 -z'¹ + 0-5z-²)

SECTIONIII

5.    (a) What type of windows are used for the design of FIR filters ?

Give their mathematical representation and characteristics.

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(b)    What are the characteristics that must be kept in mind while designing practical frequency selective filters ?

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(c)    Where the linear phase filters find the wide application ? Determine the frequency response of FIR filter both for symmetric and antisymmetric case.    - 6

6. Determine the coefficients of linear phase FIR filter of the M = 32, a = 0, linear phase FIR filter which has frequency samples

1, k = 0,l,2 H(2nk/32)-¹/₂ k = 3

0 k = 4,5,6.....15.    20

SECTIONIV

7. (a) What are the properties of the s-plane to z-plane mapping

1 + z^-1

defined by s =--r and what might this mapping be used

1 - z

for ?    10

(b) A second order continuous time filter has a system function

H(s) =-I- where a < 0 and b < 0 are real, s-a s-b

Determine the locations of poles and zeros of H(z) if the filter is designed using the bilinear transformation with sampling time 2 sec.    10

9070(C>L)    (Contd.)

1

(a) For the system function H(z) = ⁺ + 3z +2z

Attachment: kurukshetra-university-2008-b-tech-electrical-engineering-47880-1.tif

Earning:   Approval pending.