# WBUT  Previous Years Question Papers EC

## Digital Signal Processing  B Tech Fifth Sem Sixth June 2009

Time : 3 Hours ]

[ Pull Marks : 70

GROUP-A (Multiple Choice Type Questions)

1. Choose the correct alternatives for any ten of the following:  10 x 1 * 10

i)               If X1 (n) and X2 (n) are finite length sequences of sizes L and M repectively, their linear convolution has length

a)             L + M-2 b) L + M

c)    ‘ L + M-1                 d) Max{L, M}.   1    1

 ii)             A system having impulse response h(t) will be BIBO stable if . • . – ‘ • ‘ • • • 00 • ‘ . . _ 00 • . . a) J|h(t)|dt<»                   b) J*/i(t)dt<<»

 oo – ‘ :              ”                                ■ ‘                              oo

 c) J|h(t)|dt>«>                                            dj J|h(t)|dt-0. ‘                    ■           -oo                    ”                             :                       ‘ ■ . -oo

iii)           Why 16 point DFT is preferable than 4 point DFT ?

Resolution of spectriun is poor for 4 point DFT than 16 point DFT

b)    Resolution of spectrum is high but not reliable in 4 point DFT

c)               Calculation of 4 point DFT is more complex

d)              None of these are true.

iv)            Given a system with h(n)-an u(rt), a is constant, then the system is

a)              HR system                 b) FIR system

c)    both IIR and FIR system d) none of these.

I8fr04 (05/O5T

4

v)              Overlap save method Is used to find

a)              Circular convolution

c)              DFT

 Is the highest frequency available in fa.-0-5FMX

vli) The energy of constant amplitude complex valued exponential function X (n) – A exp (Jw) where A and o> are constant, is given by

 a) c)
 b) d)
 2(o

0)

viii)       Determine If the systems described by the following input-output equations are causal or non-causal.

1. y(n)-x(n2)

N-l ,

2– y(n)-y£x(n)

a)               1 Is linear, 2 is non>linear b) 2 is linear, 1 is non-linear

d)              I and 2 both are non-linear.

ix)           If the Fourier transform of a sequence x ( n ) is X(eJa>), then the Fourier transform of x ( n – k ) is

b)  (e-Jmk)x(eJ,°)

d)   cannot be determined.

a)              zero appending in X (K)sequence

b)             value of X {K) is zero

c)              Dummy sample added with zero value in X ( K)

d)              none of these.

xi)            Ifx(n)-—*X( z), then the valid one is

a)     ‘x(-n-) *-*X (z )          b) x (- n ) *-

c)     x(-n)*—^ d) x (- n ) *-

xii)

The value of the twiddle factor w£ is given by

a)                                                                                                                                               1   b) -j

°] jz’js                                                        d)

xiii)

 a) energy signal c) both of these
 b) power signal d) none of these.

GROUP-B ( Short Answer Type Questions)

Answer any three of the following questions.

1. Differentiate between analog and digital signals. Why is digital signal processing widely used than analog signal processing ?  5
2. Determine the convolution of the two following finite sequences using overlap add method:                                                                                                           5

x ( n ) = { 3, 2, 1,2} h(n ) = { 1, 2, 1, 1 }

1. The Impulse response of linear time Invariant system ish(n)-{ 1, 2, 1, -1}. Determine the response of the system to the input signalx (n)-{ 1, 2, 3, 1 }.                                                                    5
2. Show that if a discrete-time LPF is described by the difference equation

N                        t M

y[n]–2)a,c y[n-fc)+^bfc x[n-fc]: then the discrete-time filter described by

fc-l k-0 •

y [ n ] — 2 (- l)fc ak y [ n – k ] + ^ (-1)* bk x [ n – k ] is a high-pass filter.                                       5

k-l fc-0

1. Design a digital Butterworth filter using following specifications using Impulse Invariant method :      5

0*9 < H [J Q ) < 1 for 0 < G < 0-2 plH (j Q ) < 0-2 for 0-4 pi < Q < pi.

Answer any three of the following questions.    3 x 15 = 45

1. a) A low-pass filter should have the frequency response given below. Find the filter

coefficients hd (n). Also determine t so that hd (n)-hd (-n).

e’-,t,-coj.s{osa}c

0,coc <|a>|<3i

b)              A filter is to be designed with the following desired frequency response Hd V)-

Determine the filter coefficients hd(n) if the window function is defined as

l,0ssns4

0,elsewhere

7

1. a) Realize the system with difference equation :

3                                     1                              1

y(n)m—y(n —1)-—y(n-2)+x(n)+–x(n-l) In cascade form.                                      8

4                                   8                              3

b)     Define LTI system with an example.                                                                                  5

c)      What Is window technique ?                                                                                               2

1. a) What is ROC ? State Its properties.                                                                                           2
2. b) Find the system function and impulse response of the system described by
3. y { n ) = x { n j + 2x ( n- 1 ) – 4x ( n- 2 ) + x ( n- 3 )                                                           5

c)               Find the inverse Z-transform of

X[z) = ziz2 – 4z + 5)/ (z – 3)(z – 2)(z – 1) 2 < * < 3.                                              5

d)              Prove that an LTI system is BIBO stable if the ROC system function includes the unit’circle.    3

1. a) Distinguish between FIR and IIR filters.

b)              What is warping effect ? How can you remove this effect ?

c)               Convert the analog filter with the system function G (s ) = —————- –                     Into

(s + 01) + 16

a digital filter usmg bilinear transformation. The digital filter should have a