# WBUT  Previous Years Question Papers EC

## Digital Signal Processing B Tech Fifth Sem 2010

Time Allotted : 3 Hours

Full Marks: 70

The figures In the margin indicate full marks. Candidates are required to give their answers in their own words

as far as practicable.

GROUP – A (Multiple Choice Type Questions)

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

10 x 1 = 10

1) If x j ( n ) and x2 ( n ) are finite length sequences of

sizes L and M respectively, their linear convolution has the length

a)          L+M-2 b) L+M-l

c)          L +M   d) none of these,

ii) The digital systems in y { n) = x ( n 2 ) is

a)            linear and causal

b)            non-linear and causal

c)            linear and non-causal 1

d)           non-linear and non-causal.

110 Zero padding of a signal

a)            reduces aliasing             , •.

b)            increases frequency

c)             increases time resolution a

d)            has no effect.

iv)           In a system y{-n) =x{ n- 1 )

a)            the system is causal for all

b)            the system is linear and causal for all

c)             the system is stable, linear and causal for all

d)            none of these.

v)             Ifxl n] = { 1, 0 . 0, 1 }, the DFT valueX( 0 ) is a) 2   b) 1 +J

c)                                                                                                0    d) 1 -J.

vi)           The Fourier transform of ah aperiodic discrete time sequence is

a)            discrete and periodic function of frequency

b)            discrete and aperiodic,function of frequency

c)            continuous and periodic function of frequency

d)            continuous and aperiodic function of frequency.

CS/B.Teeh(ECE-N)/SEM-6/EC-601/2010

vii)         The convolution: of u [ n ] with u(n-4]atn = 5ls a) 5           b) 2

c)                1                             v          d)       0.

vlll) A digital filter is said to be”nR                                            .

^ present output depends cm previous output only

• bj if system function H ( z) has one or more non-zoo

denominator co-efficients

c)             if all the poles lie outside the unit circle

d)            if system function has only zeros.

ix)          FIR filter is

a)            recursive and linear

b)        ‘ non-recursive and linear

c)             recursive and non-linear

d)            none of these.

x)            System function of digital filter expressed as H( z) brepresents

a)            HR filter ■ / r b) FIR filter

c)             Butterworth filter d) Chebyshev filter.

xi)          Stability criteria for a discrete time LTI System is

a)            h ( n) >1            b) h ( n) < 1

c)                                                                                                 h ( n) = 1 d) h ( n ) * 0,

CS/B.Tech(ECE-N)/SEM-6/EC-601 /2010

xll) A digital filter has h ( n ) = { – 3, – 2, 0, 2, 3 } then it has

a)            no linear phase

b)      v symmetric linear phase      ‘•

c)             anti-symmetric linear phase

d)            none of these, xffl) (|) n u ( n) is

a)                                                                                               energy signal   b) power signal

c)                                                                                                both (a) and (b) d) none of these.

xiv)      The system y( n) «x( n) + nx( n+1 )1S .

a)            linear time invariant

b)            non-linear time invariant

c)             linear time variant

d)            none of these.

xv)        The mapping from analog to digital domain in Impulse invariant method is              /

a)                                                                                               one to many     b) many to one

c)                                                                                                one to one  d) none of these.

GROUP* B (SkortAaswer Type gnestions)

Answer any three of the following. 3×5= 15

1. Given the following transfer function T( z ) of a DSP system, write the difference equation :

_» 3 + 2z”1 + z~2

r”«k-» ♦ a.-* •

1. If Fourier transform of x ( n) is X { Jxo ), then prove that

a)            jf(-t) <-> X[-j<o),

b> *(at< « tht

1. State the properties of convergence for the Z-transform.
2. Apply bilinear transformation to H ( s )    2 •

( s +1) ( s + 3 ) with T m 0-1 s.

1. Define phase delay and group delay.

The length of an FIR filter is 13. If the filter has a linear phase, show that

‘ i ■

M- 1

. A    •  • • • .. .   •

T, h ( n) sin co ( x – n) = 0. ■ ‘

n*0

Answer any tiyfee of the following. 3 x 15 * 45

1. a) What is ROC ? State its properties.

b)            Find the system function and impulse response of the system described by

y(n) = x(n) + 2x(n-l)-4x(n-2) + x(n-3)

c)             Find the inverse Z-transform of

X ( z) = z|z2-4z + 5 ) / ( z – 3 ) ( z – 2 ) ( z – 1) ; 2 < z < 3

d)           Prove that an LTI system is BIBO stable if the ROC of system function includes the unit circle. 2 + 5 + 5 + 3

1. a) Sketch the magnitude response of Butterworth LPF

filter and derive an expression for order of such a filter.

b)            Design a digital Butterworth filter using the following

specifications using Impulse Invariant method

0-9 < H (Jto ) < 1 for 0 < (0 < 0-2 pi H (jfco ) < 0-2 for 0-4 pi < © < pi

transformation ?                  5 + 5 + 5

‘ ‘ . /. .

1. a) Compute 8-point DFT of the sequence

x ( n ) « { 0-5, 0-5, 0-5, 0-5. 0, 0, 0. 0} using any .     FFT algorithm.

• CS/B.Tech(ECE-N)/SEM-6/EC-601/2010

b)            Find the linear convolution using circular convolution for the two sequences

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

. c) Compute the circular convolution of two sequences x( n) = { 1, 2, 0, 1 }

x( n) = { 2, 2, 1, 1 }            6 + 5 + 4

1. a) Obtain the mapping formula for the approximation of

derivatives method using backward difference :

b)            Determine H { z ) for a Butterworth filter satisfying the following constraints :

VO-5 < | ff ( e*° ) I Sl.OS oo :£ re/2

|n(eJ“) | £ 0-2, 3 re/4 £«o £ re

with T= Is. Apply impulse invariant transformation.

6 + 9

1. Write short notes on any three of the following : 3×5

a)            Gibbs phenomenon

b)            CCS6713 architecture

c)             IIR and FIR filters        i

d)            Periodic and aperiodic signals.

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