CS2403 Digital Signal Processing

7/23/2019 CS2403 Digital Signal Processing

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SELVAM COLLEGE OF TECHNOLOGY,

NAMAKKAL-637003,TAMIL NADU IT6502-DIGITAL SIGNAL PROCESSING

Collected By: Mr.R.Logarasu AP /ECE www.selvamtech.edu.in Page 1 of 54


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Reg.No:

B.E./B.Tech. DEGREE EXAMINATION, MAY/JUNE 2013

Seventh Semester

Computer Science and Engineering

CS 2403/CS 73 - DIGITAL SIGNAL PROCESSING

(Common to Fifth Semester- Information Technology)

(Regulation 2008)

Time: Three hours Maximum: 100Marks

Answer ALL questions

PART A- (10 x 2=20 marks)

1. Define energy signals and network signals.

2. What is the correlation? What are its types?

3. What is meant by radix-2 FFT?

4. Give transform pair equation of DFT.

5. What are the characteristics of Chebyshev filter?

6. Write the transformation equation to convert low pass filter into band stop filter.

7. Write the equation for Blackman window.

8. What is zero input limit cycle oscillation?

9. What is decimation?

10. List various special audio effects that can be implemented digitally.

Question Pa er Code:21321





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)80165( =BPART

11. (a) (i).Consider the analog signal

ttttxa

12000cos106000sin52000cos3)( ++=

(1).What is the Nyquist rate for this signal?

(2).Assume now that we sample this signal using sampling rate SecsamplesFa /5000= .What

is the discrete time signal obtained after sampling?

(3).What is the analog signal )(ty a that we can reconstruct from the samples if we use ideal

interpolated. (8)

(ii).Derive the equation for convolution sum and summarize the steps involved in computing

convolution. (8)

Or

(b) (i).Determine the Z-transform and ROC of the signal )1()( = nunx n . (6)

(ii).Check whether the discrete time system [ ])(cos)( nxny = is

(1).Static or dynamic

(2).Linear or nonlinear

(3).Time invariant or time varying

(4).Casual or non-casual

(5).Stable or unstable. (10)

12. (a) (i).Find eight point DFT of the following sequence using direct method: (10)

(1) }{ 0,0,1,1,1,1,1,1

(ii).State any six properties of DFT. (6)

Or

(b) (i).Compute eight point DFT of the following sequences using radix-2 decimation in time FFT

algorithm }{ 1,1,1,1,1,1,1,1)( =nx (10)

(ii).Discuss the use of FFT in linear filtering. (6)





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13. (a) (i).Obtain the direct form I, direct form II, cascade and parallel form realization for the system

)2(6.0)1(6.3)(3)2(2.0)1(1.0)( ++++= nxnxnxnynyny (8)

(ii).For the analog transfer function)2)(1(

2)(

++=

sssH .Determine )(zH using impulse

invariance method. Assume sec1=T (8)

Or

(b) A low pass filter meeting the following specification is required:

Passband - 0-500Hz

Stopband - 2-4KHz

Passband ripple - 3dB

Stopband attenuation - 20dB

Determine following:

(i).Pass and stopband edge frequencies for a suitable analog prototype low pass filter.

(ii).Order N of the prototype low pass filter.

(iii).Coefficients and hence the transfer function of the discrete time filter using the bilinear z-

transform.

Assume Butterworth characteristics of the filter. (16)

14. (a) (i).Given a three stage lattice filter with coefficients ,3

1,

4

1,

4

1321 === KKK determine the

FIR filter coefficients for the direct form structure. (8)

(ii).Determine the coefficients of a linear phase FIR filter of length 15=M has a symmetric

unit sample response and a frequency response that satisfies the conditions

=

==

7,6,5,40

3,2,1,01

15

2

k

kkH

(8)

Or





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(b) Design an ideal high pass filter with a frequency response

( )

=

40

41

for

for

eH j

d

Find the values of )(nh for 11=N using hamming window. Find )(zH and compute magnitude

response. (16)

15 (a) (i) Explain the method for converting the sampling rate by a factor I/D with block diagram and

equations. (8)

(ii) Discuss sub band coding process in detail. (8)

Or

(b) (i) .With block diagram explain adaptive filtering based adaptive channel equalization. (8)

(ii) .What is image enhancement? Explain various image enhancement techniques. (8)





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Reg.No:

B.E./B.Tech. DEGREE EXAMINATION, MAY/JUNE 2012

Seventh Semester


CS 2403/CS 73 - DIGITAL SIGNAL PROCESSING

(Common to Fifth Semester Information Technology)

(Regulation 2008)

Time: Three hours Maximum: 100Marks



1. Determine even and odd components of the signal,

+=

24exp)(

jnjnx, where

1=

j.

2. Compute autocorrelation of the signal, ( ) )(5.0)( nunx n= .

3. Write the formula for Discrete Cosine Transform(DCT) pair.

4. What is FFT?

5. What are the limitations of impulse invariant technique of designing filter?

6. Give the low pass transfer function 1

1)( == ssH

a .Find the high pass transfer function having a cut-

off frequency SecRad/10 .

7. Compare the digital signal processing systems with fixed point and floating point representation.

8. List the few applications, where in linear phase is preferred.

9. Draw the basic building Blocks of Adaptive filters.

{ }

= )4()(

3

)(5.7,5.1,2.0,5.0,1,5.1)(.10 nxbn

xaComputenxLet

Question Paper Code:20239





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)80165( =BPART

11. (a) (i).State sampling theorem and explain aliasing graphically. (8)

(ii).Find the circular convolution of )()( nhnx .Given that

}{

( )

=

=

9950,0499,5.0)(

990,1)(

n

nnh

nnx

n

(4)

(iii).Find the Z-transform of the given sequence )()2()5(8)( nunuennx n ++= . (4)

Or

(b) (i).Find the Linear Convolution of )()( nhnx through circular convolution. Assume the

suitable length .M

( )

=

=

Otherwise

nnh

Otherwise

nnx

n

n

,0

190,8.0)(

,0

90,)5.0()(

(8)

(ii).List all the properties of Analog and Digital frequencies. (4)

(iii).Find the Z-transform of Auto correlation of signal. (4)

12. (a) (i).Let }{ )()( nxDFTKX = with n: )1(,.......,1,0 = NK .Determine the relationship between

)(KX and the following DFTs.

(1) }{ )(Re nxDFT

(2) }{ )1( nxDFT (9)

(ii).State and prove any two properties of DFT. (7)

Or

(b) (i).Compute the DFT of the following sequences.

(1) ]0,1,0,1[)( =nx

(2) 7,...2,1,1),25.0()( == nnCosnx (8)

(ii).Write short notes on filtering methods using DFT. (8)





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13. (a) (i).An impulse response, )()5.0exp()( tutth = of certain LTI system. Find the T.F. )(ZH

using impulse invariant technique. Assume SecT 2= . (8)

(ii).Compare Analog filters with Digital filters. (4)

(iii).Differentiate between Bilinear transformation with frequency translations of filter transfer

function. (4)

Or

(b) (i).Draw the Ideal Gain Vs frequency characteristics of HPF and BPF and also how the

above filters(practically) specified. (8)

(ii).Write short notes on frequency translation in both Analog and Digital domain. (8)

14. (a) The Hamming window is given by 10,1

2cos04654.0)(

= mnm

nn

.Compute the

first 10 coefficients using above window functions having the magnitude response. (16)

(b) (i) Draw three different structure of ).(zH

(8)

(ii) Draw three different structure of ).(zH with coefficients represented by (1) 4-bit word length (2) 6-

bit word length at frequency3

=

752352.0

1).(

=

zzH

(8)

311 )75.01)(5.01()( ++= zzzH





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15 (a) (i) Explain the salient features of image enhancement techniques. (10)

(ii) Write a brief note on speech compression techniques. (6)

Or

(b) (i) Determine the output y(n) for each of the given input signal x(n) (8)

)4(8)()1( = nnx

)()2.0exp()()2( nunjnx =

(ii) Explain the sampling by rational factor by taking an example of your own. Also state its

uses in DSP systems. (8)





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Reg. No. :

B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2011.

Seventh Semester


CS 2403 DIGITAL SIGNAL PROCESSING

(Common to Fifth Semester Information Technology)

(Regulation 2008)

Time : Three hours Maximum : 100 marks

Answer ALL questions.

PART A (10 2 = 20 marks)

1. Define and express the transfer function of Nthorder LTI system.

2.

Compare linear convolution and circular convolution.

3. What is the relation between DFT and Z-Transform?

4.

What is phase factor or twiddle factor?

5.

Sketch the various tolerance limits to approximate an ideal lowpass and

highpass filter.

6.

What is the importance of poles in filter design?

7. What is frequency warping?

8.

What is Butterworth approximation?

9.

List various voice compression and coding techniques.

10. What are the various enhancement techniques in image processing?

Question Paper Code :





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553102

PART B (5 16 = 80 marks)

11. (a) (i) Find the inverse Z-Transform of

( )( )( )

3:,31

2

>

+= ZROC

ZZ

ZZzX ,

using

(1) Residue method and

(2) Convolution method. (8)

(ii) State and prove circular convolution. (8)

Or

(b) LTI system is described by the difference equation( ) ( ) ( )nxbnyany += 1 . Find the impulse response, magnitude

function and phase function. Solve b, if ( ) 1=wH . Sketch themagnitude and phase response for a= 0.6. (1

12.

(a) (i) Evaluate the 8-point for the following sequences using DIT-FFTalgorithm (8)

( )

=otherwise0

33for1 nnx

(ii) Calculate the percentage of saving in calculations in a 1024-point radix -2 FFT, when compared to direct DFT. (8)

Or

(b) Determine the response of LTI system when the input sequence( ) { }1,1,2,1,1 =nx by radix 2 DIT FFT. The impulse response of the

system is ( ) { }1,1,1,1 =

nh . (16)

13. (a) The specification of the desired lowpass filter is

( )

( )

wwH

wwH

4.0;08.0

2.00;0.12

1

Design a Butterworth digital filter using bilinear transformation. (16)

Or

(b) The specification of the desired low pass filter is

( )

( )

wwH

wwH

5.0;24.0

25.00;0.19.0

Design a Chebyshev digital filter using impulse invarianttransformation. (16)





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553103

14. (a) (i) Design a single tier notch filter to reject frequencies in the range1 to 2 rad/sec using rectangular window with 7=N . (8)

(ii) Compare Hamming window and Kaiser window. (8)

Or

(b) (i) Explain the characteristics of a limit cycle oscillation withrespect to the system described by the equation

( ) ( ) ( )nxnyny += 195.0 . Determine the dead band of the filter. (8)

(ii) Explain Gibbs phenomenon (or Gibbs oscillation). (8)

15. (a) Explain the methods of speech analysis and synthesis in detail. (16)

Or

(b) Explain how image enhancement restoration and coding can be doneusing signal processing. (16)





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Reg. No. :

B.E./ B.Tech. DEGREE EXAMINATION, APRIL/ MAY 2011

Fifth Semester

Information Technology


(Regulation 2008)

Time : Three hours Maximum : 100 marks


PART A (10 2 = 20 marks)

1. State sampling theorem.

2. Distinguish between power and energy signal with an example.

3. State and prove Parseval's theorem.

4. Compute the DFT of the four point sequence [ ]3,2,1,0)( =nx .

5. What is meant by warping?

6. What are the limitations of impulse invariance method?

7. List out the conditions for the FIR fi lter to be linear phase.

8. What is meant by limit cycle oscillations?

9. Let [ ]6,5,4,3,2,1)( =nx . Sketch ( )2nx and ( )nx3 .

10. Give any two image enhancement methods.

Question Paper Code :11273





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112732

PART B (5 16 = 80 marks)

11. (a) (i) Suppose a LTI system with input )(nx and output )(ny is

characterized by its unit sample response )()8.0()( nunh n= . Find

the response )(ny of such a system to the input signal

)()( nunx = .(8)

(ii) A causal system is represented by the following differenceequation

)1(2

1)()1(

4

1)( +=+ nxnxnyny

Compute the system function )(zH and find the unit sample

response of the system in analytical form. (8)

Or

(b) (i) Compute the normalized autocorrelation of the signal10),()(


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(b) Design an IIR fi lter using impulse invariance technique for the given

1217

1)(

2 ++=

sssHa . Assume T = 1 sec. Realize this filter using direct

form I and direct form II. (16)

14. (a) Design and obtain the coefficients of a 15 tap linear phase FIR low

pass filter using Hamming window to meet the given frequencyresponse (16)

=

||6

for0

6||for1

)(

w

wwHd .

Or

(b) (i) Determine the coefficients of a linear phase FIR filter of lengthM = 15 which has a symmetric unit sample response and afrequency response that satisfies the conditions

=

=

=

=

7,6,50

44.0

3,2,1,01

15

2

k

k

kk

Hr

. (8)

(ii) The output of A/ D converter is applied to digital filter with the

system function5.0

5.0)(

=

zzH . Find the output noise power

from the digital filter when the input signal is quantized to have8 bits. (8)

15. (a) Derive and explain the frequency domain characteristics of theDecimator by the factor M and interpolator by the factor L. (16)

Or

(b) With neat diagram explain any two applications of adaptive filterusing LMS algorithm. (16)





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Reg. No. :

B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2010

Fifth Semester

Information Technology


(Regulation 2008)

Time : Three hours Maximum : 100 Marks


PART A (10 2 = 20 Marks)

1.

Calculate the minimum sampling frequency required for ( ) 0.5 sin 50t t=

+ 0.25 t25sin , so as to avoid aliasing.

2. State any two properties of Auto correlation function.

3. Write down DFT pair of equations.

4.

Calculate % saving in computing through radix 2, DFT algorithm of DFTcoefficients. Assume N= 512.

5. What are the limitations of Impulse invariant method of designing digital

filters?

6. Draw the ideal gain Vs frequency characteristics of :

(a) HPF and

(b) BPF.

7.

Compare FIR filters and FIR filters with regard to :

(a) Stability and

(b) Complexity




Question Paper Code : 53110


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531102

8. Represent decimal number 0.69 in fixed point representation of length

N= 6.

9. Prove that up sampling by a factor M is time varying system.

10. State a few applications of adaptive filter.

PART B (5 16 = 80 Marks)

11. (a) (i) Find the convolution )(*)( nhnx , where

)()( nuanx n=

)()( nunh n=

(ii) Find the Z-transform of the following sequences :

)1()()5.0()( += nununx n

)5()( = nnx .

Or

(b) (i) State and explain sampling theorems.

(ii) Find the Z-transform auto correlation function.

12. (a) (i) Explain, how linear convolution of two finite sequences are obtained

via DFT.

(ii) Compute the DFT of the following sequences :

(1) ]0,1,0,1[ =x

(2) ]1,,0,[ jjx = when 1=j .

Or

(b) Draw the flow chart for N= 8 using tadix-2, DIF algorithm for finding

DFT coefficients.

13. (a) Design digital low pass filter using Bilinear transformation, Given that

)1732.1)(1(1)(

+++

=

ssssHa .

Assume sampling frequency of 100 rad/sec.

Or





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531103

(b) Design FIR filter using impulse invariance technique. Given that

)65(

1)(

++

=

sssHa

and implement the resulting digital filter by adder, multipliers and

delays Assume sampling period T = 1 sec.

14.

(a) Design the first 15 coefficients of FIR filters of magnitude specification is

given below :

,1)( =jweH 2///


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Reg.No:

B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2010

Fourth Semester


IT1252 - DIGITAL SIGNAL PROCESSING

(Common to Seventh Semester- Computer Science and Engineering)

(Regulation 2004)

Time: Three hours Maximum: 100 Marks



1. Consider the analog signal ttttxa

12000cos106000sin52000cos3)( ++= .What is the Nyquist

rate for this signal?

2. Determine the system described by the following input and output equation is linear or nonlinear

BnAxny += )()(

3. What is impulse computation?

4. How many complex multiplication and addition are required in DFT and FFT?

5. Indicate the location in the z plane to which the ve points on the j axis in the s plane go to due to

the bilinear transformation.

6. Convert the analog filter with system function )(sH into digital IIR filter by

)6.0)(2.0(

1)(

++=

sssH

7. Write down the equation of Kaiser Window for 10 Mn .

8. What are the possible phase angles if the impulse response is anti-symmetric and legth of the filter

is odd?

9. What is limit cycle oscillation?

10. Define over flow error.





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)80165( =BPART

11. (a) (i). Compute and plot the convolution )()( nhnx for the following signal: (6)

[ ] [ ]

== 1,2,3,4,5,6)(1,1,1,1)( nhnx

(ii). Determine the response )(ny , 0n of the system described by the second order

differential equation )1()()2(4)1(4)( =+ nxnxnynyny when the input is

)()1()( nunx n= and initial conditions are 0)2()1( == yy (10)

Or

(b) (i). Determine the Z-transform and ROC of the signal:

)()3(4)2(3)( nunx nn

= . (6)

(ii). A linear time invariant system is characterized by the system function

11

1

5.15.31

43)(

+

=

zz

zzH specify the ROC of )(zH and determine for the following

conditions:

(1).The system is sable

(2).The system is causal.

(3).The system is anti-causal. (10)

12. (a) (i). Obtain the FFT of the sequence using decimation in frequency (12)

}{ 1,2,3,4,5,6,7,8)( =nx

(ii). How can you compute IDFT using FFT(4)

Or

(b) Multiplication of the DFTs of two sequences is equivalent to the circular convolution of

the two sequences in the time domain. Prove this property by the following sequences:

[ ]1,2,1,2)(1 =nx [ ]14,3,2,1)(2 =nx

13. (a) Design a digital low pass Butterworth filter using Bilinear transformation method to

meet the following specifications:

Pass band ripple dB25.1 ,pass band edgez

H200= ,stop band attenuation dB15 ,Stop

band edgez

H300= ,sampling frequencyz

kH2= .





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Or

(b). (i). Find the transfer function of low pass analog Chebyshev filter to meet the following

requirements:

Pass band ripple dB1.0 ,pass band edge SecRad/1 ,stop band attenuation is almost

dB40 for SecRad/2 (12)

(ii). Compare FIR and IIR filter.(4)

14. (a) (i). Design a low pass FIR with 11 coefficients for the following specifications:

Pass band frequency edge iszkH25.0 and sampling frequency is zkH1 .(Use

Rectangular window)(12)

(ii). Realize the above designed filter by direct form structures.(4)

Or

(b) Determine the coefficients of a linear-phase FIR filter length 15=M which has a

symmetric unit sample response and a frequency response that satisfy the condition:

=

=

=

=

7,6,50

4,4.0

3,2,1,1

15

2

k

k

kk

Hr

15 (a) For the all polo second order IIR digital filter described by difference equation

)()2()1()( 21 nxnanyany += . Determine the dead band region governing the

limit cycle

Or

(b). Derive the expressions for the variance at the output of a digital filter characterized by

)(nh Where the input is quantization noise.





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