UNIT-I. 2. A real valued sequence x(n) is anti symmetric if a) X(n)=x(-n) b) X(n)=-x(-n) c) A) and b) d) None Ans: b)

Size: px
Start display at page:

Download "UNIT-I. 2. A real valued sequence x(n) is anti symmetric if a) X(n)=x(-n) b) X(n)=-x(-n) c) A) and b) d) None Ans: b)"

Transcription

1 DIGITAL SIGNAL PROCESSING UNIT-I 1. The uit ramp sequece is Eergy sigal b) Power sigal c) Either Eergy or Power sigal d) Neither a Power sigal or a eergy sigal As: d) 2. A real valued sequece x() is ati symmetric if X()=x(-) b) X()=-x(-) c) A) ad b) d) Noe As: b) 3. The discrete time system described by y 2 ( ) x( ) Causal, liear ad time varyig b) Causal, o liear ad time varyig c) No Causal, liear ad time varyig d) No Causal, No liear ad time varyig As: c) 4. Fid the rage of a for which the LTI system with impulse respose h( ) a u( ) is stable a 1 b) a 1 c) a 0 d) Noe As: 5. The process of computig the covolutio ivolves Foldig b) Shiftig c) Multiplicatio ad Summatio d) All the above As: d) 6. The Fourier trasform of ( ) is 1/ j b) 1 is

2 c) j d) j / As: b) 7. The umber of elemets i the covolved sequece of x() havig N elemets ad h() havig M elemets is M+N b) N+M+1 c) N+M-1 d) N-M As: c) 8. Determie the covolutio of x( ) a u( ) ad h( ) b u( ) 1 1 b a / b a 1 1 b) b a / b a c) a / b a d) Noe As: b) 9. Compute the uit step respose of a LTI System whose impulse respose is h( ) c u( ) 1 1 c / 1 c 1 b) 1 c / 1 c 1 c) 1 c / 1 c 1 d) 1 c / 1 c As: 10. Fid the covolutio of x()={1,1,1,1,} with h()={2,2,2,2} {2,4,6,8,6,4,2} b) {2,4,6,8,6,4,4} c) {2,4,6,6,8,4,2} d) {2,4,6,8,6,2,2} As: 11. The discrete time system described by y( ) cos[ x( )] is Ustable b) Stable c) Dyamic

3 d) Nocausal As: 12. Express the impulse sequece i terms of uit step sequece ( ) u( ) u( 1) b) ( ) u( ) u( 1) c) ( ) u( ) u( 2) d) ( ) u( ) u( 1) As: d) j 13. The sufficiet coditio for covergece of Xe ( ) x ( ) b) x ( ) c) x ( ) is absolutely summable d) Noe As: c) 14. The Fourier Trasform of u() j 1 1 e j b) 1 1 e j c) 1 1 e j d) 1 1 e As: is 15. Fid the fourier trasform of ( 100) b) c) d) e e j10 j100 j10 e j100 e As: b) jw0 16. F[ e x( )] = b) X e j w w 0 X e j w w 0

4 jw c) Xe 0 d) Noe As: b) 17. F[ x( )* y( )] = X ( w) / Y( w ) b) X ( w) Y( w ) c) X ( w) Y( w) d) X ( w) Y( w) As: b) 18. F. x( ) jw d X ( e ) / b) jw jd X ( e ) / c) jw d X ( e ) / d) jd X e jw dw dw dw ( ) / dw As: b) 19. The Uit step sequece is Eergy sigal b) Power sigal c) Either Eergy or Power sigal d) Neither a power sigal or eergy sigal As: b) 20. Fid the power of the sigal A b) A / 2 c) A 2 jw Ae d) 2A As: c) UNIT-II 21. Express the N-poit DFT i Matrix form X W X N N N b) X W X * N N N

5 c) ad b) d) Noe As: 22. Express the N-poit IDFT i Matrix form X W X N N N b) * c) X X 1/ N W X N N N W X * N N N d) Noe As: b) 23. Fid the 4-pt DFT of {1,1,1,1} b) {1,1,0,0} c) {0,0,1,1} d) {1,0,0,0} As: 24. Fid the 4-pt DFT of 2 {1,1,1,1} b) {1,-1,1,-1} c) {1,-1,1,1} d) {-1,1,-1,1} As: b) 25. Fid the 4-pt DFT of 1 u() {0,0,0,4} b) {0,4,0,0} c) {1,1,1,1} d) {0,0,4,0} As: d) 26. Differetiate betwee DFT ad DFS of sequece Both periodic b) Both o periodic c) No periodic ad periodic d) All the above As: c) 27. Periodicity property of N-pt DFT is x( N) x() b) X(K N) X(K) c) ad b) d) oe As: c)

6 28. X(K) = X(N K) b) X(N K) c) X( K) d) b) ad c) As: d) 29. Fid the liear covolutio of x1 ={ } ad 2 x = { } {1,3,6,10,9,7,4} b) {1,3,6,10,9,7,1} c) {3,3,6,10,9,7,1} d) {1,3,6,10,9,7,7} As: 30. Fid the IDFT of X(K)=1 for N=4 {1,1,1,1} b) {1,0,0,0} c) {0,0,0,1} d) {1,1,0,0} As: b) 31. X K R XR N K b) X N K R c) ad b) d) oe As: b) 32. XI K = XI N K b) XI N K c) X N K I d) b) ad c) As: c) 33. Fid circular covolutio of {1,1,1,1,} ad {2,2,2,2} {8,8,8,8} b) {8,0,0,0} c) {0,0,0,8} d) {0,0,8,0} As:

7 34. 2K W N = b) c) d) 4K W N K W N2 2K W N2 K W 2N As: b) 35. The umber of complex multiplicatios required i DIFFFT algorithm is Nlog2 N b) N / 2log 2 N c) 2Nlog 2 N d) Nlog 2 2N As: b) 36. The umber of complex multiplicatios required i N-Pt DFT algorithm is 2 N b) 2N c) N/2 d) N-1 As: 37. The umber of complex additios required i N-Pt DFT algorithm is N(N+1) b) N(N-1) c) (N-1)(N-2) d) (N+1)(N-1) As: b) 38. Arg[X(K)]= Arg[X(N+K)] b) Arg[X(N-K)] c) -Arg[X(N-K)] d) b) ad c) As: c) 39. The umber of complex additios ad multiplicatios required i 16-Pt DFT 250, 250 b) 256, 250 c) 256, 240 d) 253, 243 As: c)

8 40. The Bit Reversal Order for a 8-poit FFT is 0,1,2,3,4,5,6,7 b) 0,4,2,6,1,5,3,7 c) 4,5,6,7,0,1,2,3 d) 3,2,1,0,7,6,5,4 As: b) 41. Z () = UNIT-III 1/z b) z c) 1 d) -1/z As: c) Z 1 u(n) z/(z+1) b) z/(z-1) c) 1/(z+1) d) 1/(z-1) As: Zx(2) = a. X(2z) b. X z c. X(z / 2) d. X(z) As: b) 44. if the x x / k,for / k is a itger k k = 0, otherwise X z = k Xz

9 b) Xkz c) Xz / k d) Xk / z As: 45. fid the G(z) i terms of F(z) if g()= b) 1 G(z) F(z) / (1 z ) 1 G(z) F(z) / (1 z ) c) G(z) F(z) / (1 z) k0 f (k) u() d) G(z) F(z) / (1 z) As: 46. The miimum umber of delay elemets required i realizig a digital filter with the 1 2 1az bz trasfer fuctio H(z) cz dz dz 2 b) 3 c) 4 d) 5 As: b) 47. Fid the iverse z-trasform of 2 a u() b) c) d) 1 a u() a u() a 1 u() z / z a As: b) 48. Fid the ROC of a u 1 z a b) z a c) z a d) z a As: b) 49. The z-trasform of A x() is X(Az) b) X(A/z) c) X(z/A) d) Noe As: c)

10 50. Fid the ROC of a sequece 100 All values of z except z=0 b) All values of z except z= c) ad b) d) Noe As: 51. Fid the ROC of z a b) z a c) z a a cos(w)u() d) z a As: 52. Fid the ROC of {1,2,3,4,5} all values of z except z=0 b) all values of z except z= c) ad b) d) Noe As: c) 53. The system fuctio of a LTI system described by the differece equatio y() 5y( 1) 6y( 2) 2x( 1) 1 2z H(z) 1 5z 6z z b) H(z) z 6z c) ad b) d) Noe As: a 54. The stability coditioof a LTI system i z-plae is ROC of sysem fuctio excludes the uit circle b) ROC of sysem fuctio icludes the uit circle c) Etire z plae except z=0 ad z= d) Uit circle As: b)

11 The system fuctio H(z) 1/ 1 1 2z 1 1 4z is Ustable b) Stable c) Udefied d) Noe As: b) 56. Digital filter realizatio techiques are Direct b) Caoic c) Cascade d) All of the above As: d) jw 57. The iverse Fourier trasform of 1 2 u() b) 1/ 2 u() c) d) 1 2 u() 1 2 u( 1) X(w) 1 1/ 2e As: b) UNIT-IV 58. The filter desiged by cosiderig all the ifiite samples of impulse respose is called Ifiite impulse filter b) Fiite impulse filter c) Impulse Ivariat trasformatio d) Biliear trasformatio As: 59. The two techiques used to trasform aalog filter to digital filter are Chebyshev, butterworth b)biliear, impulse ivariat c) IIR, FIR d) Noe As: b) 60. The tolerace i the pass bad ad stop bad are called Stable pulses b) causal delays c) ivariat delays d) ripples As: d) 61. I impulse ivariat mappig the poles of s-plae are mapped ito of uit circle i z-plae

12 Left half, iterior b) Right half, exterior c) Left half, exterior d) Right half, iterior As: 62. The pheomea of high frequecy compoets acquirig the idetity of low frequec compoets is called Samplig b) aliasig c) Wrapig d) Noe As: b) 63. The Impulse Ivariat mappig is mappig may-to-oe c) oe-to-may b) oe-to-oe d) may-to-may As: 64. The distorto i frequecy axis due to oliear relatioship betwee aalog ad digital frequecy is called Aliasig c) frequecy wrappig b) Prewrappig d) Noe As: c) 65. At the cut-off frequecy, the magitude of the butterworth filter is times the maximum value 2 b) 1/ 2 c) 3 d) 1/ 3 As: b) 66. I type-i chebyshev approximatio the magitude respose is i the Pass bad ad is i the stop bad equiripple, mootoic c) mootoic, equiripple b) mootoic, mootoic d) Noe 67. The type-2 magitude respose is called respose Iverse butterworth c) iverse chebyshev b) Butterworth d) Noe As: c) 68. The poles of Chebyshev trasfer fuctio symmetrically lies o i s-plae Circle b) parabola c) Ellipse d) Noe As: b) 69. The relatio betwee aalog ad digital frequecies i impulse ivariat trasformatio is 2 2 /T b) T c) T d) Noe As: c) 70. The Biliear mappig is accomplished whe 1 z s 2 / T 1 z z s T / 2 1 z b) 1 1 c) 1 z s 2T 1 z 1 1 d) Noe As:

13 71. I Biliear Trasformatio the digital frequecy is give by ta T / 2 b) 2cot T / 2 c) ta T / 2 1 d) ta T As: UNIT-V 72. DTMF stads for Dual Toe Multi Frequecy b) Discrete Trasform Mai Frequecy c) Double Time Multiple Format d) Noe As: 73. The Frequecy, f k i Hz correspodig to the DFT idex, k is give by where F T is samplig frequecy fk kf T / N b) fk knft c) NF T / k d) Noe As: 74. STFT stads for Short Time Fourier Trasform b) Sequetial Timig i Frequecy Toes c) Short Trouble Fial Toe d) Noe As: 75. Idetify the Ideal Hilbert Trasformer jw j, 0 to jw 1, 0 to H(e ) b) H(e ) j, to 0 1, to 0 c) jw 1, 0 to jw j, 0 to H(e ) d) H(e ) 0, to 0 0, to 0 As: 76. I Voice Privacy system, TFSP stads for Toe Frequecies Sequetial Primitives b) To ad Fro Soud Privacy c) Time ad Frequecy Segmet Permutatio d) Noe As: c)

14 77. A applicatio of DSP i FDM, sub carriers are chose to esure that the spectra of the modulated sigal do ot overlap to avoid Cross talk b) Cross modulatio c) Aliasig d) Noise or Distortio As: 78. QMF stads for Quatizig Multiple Frequecy b) Quality measuremet factor c) Quadrature Mirror Filter d) Noe As: c) 79. Filters desiged by selectig fiite umber of samples of impulse respose are called Fiite Impulse Respose Filters b) Ifiite Impulse Respose Filters c) Impulse Ivariat Trasformatio d) Noe As: 80. The coditios to be satisfied for costat phase delay i liear phase FIR filters are N 1 / 2, h() h(n 1 ) b) 2 N 1, h() h N 1 / 2 c) N 1/ 2, h() hn 1/ 2 d) Noe As: Choose Hd ; 2. Fid hd from Hd T ; 3. Trucate hd to h 4. Take Z-trasform of h for H(z); Idetify the Desig techique suitable for the above steps Frequecy samplig Method b) Widow Method c) Fourier Series Mehod d) Optimal Filter Desig Method As: c) 82. The abrupt trucatio of impulse respose itroduces oscillatios i the pass bad ad stop bad. This effect is kow as Kaiser Oscilatios b) Aliasig c) Gibb s Pheomeo d) Noe As: c) 83. I Rectagle Widow, the mai lobe width is equal to 4 / N b) 2 / N c)8 / N d) 16 / N As: 84. I Rectagle Widow, Maximum side lobe magitude is equal to -3 db b) -13 db c) -23 db d) Noe As: b)

15 85. I triagular widow, the mai lobe width is equal to 4 / N b) 8 / N c) 2 / N d) 16 / N As: b) 86. I triagular widoe, the maximm side lobe magitude is equal to -5 db b) -15 db c) -25 db d) -35 db As: c) 87. I Hammig widow, the maximum side lobe magitude is equal to -4 db b) -4.1 db c) -31 db d) Noe As: b) 88. I Haig widow, the maximum side lobe magitude is -3 db b) -13 db c) -41 db d) -31 db As: d) 89. I Blackma widow, the mai lobe width is 2 / N b) 8 / N c) 4 / N d) 12 / N As: d) 90. I Blackma widow, maximum side lobe magitude is -8 db b) -31 db c) -41 db d) -58 db As: d) 91. The frequecy respose of digial filter is periodic with period equal to Samplig frequecy b) cut-off frequecy c) Phase delay d) group delay As: 92. Oscillatios ca be reduced by multiplyig the impulse respose by a appropriatewidow fuctio Gibb s b) Laplace s c) siusoidal d) Noe As: 93. Ideal filters are causal b) No- causal c) stable d) Ustable As: b) 94. The phase distortio is due to characteristics of the filter No liear phase b) Liear phase c) curviliear phase d) Mootoic As: 95. I Blackma widow spectrum, the width of mai lobe is that of Rectagular widow for some value of N Same as b) double c) ripple d) four times As: c) 96. The vocal tract has certai ormal resoat modes of vibratio called as Articulators b) Formats c) glottis Vibrators d) Noe As: b)

16 97. The term homomorphic processig is applied to a class of systems that obey a geeralized priciple of superpositio b) Time Ivariat c) Liearity d) Causality As: 98. Appedig zeros to a sequece i order to icrease is legth is called Overlappig zeros b) overflowig zeros c) Paddig zeros d) Noe As: c) 99. I magitude respose of the DFT of a sigal, the bi crossover the result i a sigal loss at frequecy poits off the DFT bi ceters. This is referred to as Scallopig Loss b) Picket-fece effect C) ad b) d) Noe As: c) 100. The Z-Trasform of * * * X z b) * x () is X z c) * X z d) Noe As :

17

18

19

Analog and Digital Signals. Introduction to Digital Signal Processing. Discrete-time Sinusoids. Analog and Digital Signals

Analog and Digital Signals. Introduction to Digital Signal Processing. Discrete-time Sinusoids. Analog and Digital Signals Itroductio to Digital Sigal Processig Chapter : Itroductio Aalog ad Digital Sigals aalog = cotiuous-time cotiuous amplitude digital = discrete-time discrete amplitude cotiuous amplitude discrete amplitude

More information

11. What are energy and power signals? (April/may 2011, Nov/Dec 2012) Energy signal: The energy of a discrete time signal x(n) is defined as

11. What are energy and power signals? (April/may 2011, Nov/Dec 2012) Energy signal: The energy of a discrete time signal x(n) is defined as DHAALAKSHMI COLLEGE OF EGIEERIG, CHEAI DEPARTMET OF COMPUTER SCIECE AD EGIEERIG IT650 DIGITAL SIGAL PROCESSIG UIT - I : SIGALS AD SYSTEMS PART A MARKS. Defie Sigal ad Sigal Processig. A sigal is defied

More information

Solution of EECS 315 Final Examination F09

Solution of EECS 315 Final Examination F09 Solutio of EECS 315 Fial Examiatio F9 1. Fid the umerical value of δ ( t + 4ramp( tdt. δ ( t + 4ramp( tdt. Fid the umerical sigal eergy of x E x = x[ ] = δ 3 = 11 = ( = ramp( ( 4 = ramp( 8 = 8 [ ] = (

More information

A. Basics of Discrete Fourier Transform

A. Basics of Discrete Fourier Transform A. Basics of Discrete Fourier Trasform A.1. Defiitio of Discrete Fourier Trasform (8.5) A.2. Properties of Discrete Fourier Trasform (8.6) A.3. Spectral Aalysis of Cotiuous-Time Sigals Usig Discrete Fourier

More information

Practical Spectral Anaysis (continue) (from Boaz Porat s book) Frequency Measurement

Practical Spectral Anaysis (continue) (from Boaz Porat s book) Frequency Measurement Practical Spectral Aaysis (cotiue) (from Boaz Porat s book) Frequecy Measuremet Oe of the most importat applicatios of the DFT is the measuremet of frequecies of periodic sigals (eg., siusoidal sigals),

More information

M2.The Z-Transform and its Properties

M2.The Z-Transform and its Properties M2.The Z-Trasform ad its Properties Readig Material: Page 94-126 of chapter 3 3/22/2011 I. Discrete-Time Sigals ad Systems 1 What did we talk about i MM1? MM1 - Discrete-Time Sigal ad System 3/22/2011

More information

x[0] x[1] x[2] Figure 2.1 Graphical representation of a discrete-time signal.

x[0] x[1] x[2] Figure 2.1 Graphical representation of a discrete-time signal. x[ ] x[ ] x[] x[] x[] x[] 9 8 7 6 5 4 3 3 4 5 6 7 8 9 Figure. Graphical represetatio of a discrete-time sigal. From Discrete-Time Sigal Processig, e by Oppeheim, Schafer, ad Buck 999- Pretice Hall, Ic.

More information

Chapter 7: The z-transform. Chih-Wei Liu

Chapter 7: The z-transform. Chih-Wei Liu Chapter 7: The -Trasform Chih-Wei Liu Outlie Itroductio The -Trasform Properties of the Regio of Covergece Properties of the -Trasform Iversio of the -Trasform The Trasfer Fuctio Causality ad Stability

More information

Chapter 2 Systems and Signals

Chapter 2 Systems and Signals Chapter 2 Systems ad Sigals 1 Itroductio Discrete-Time Sigals: Sequeces Discrete-Time Systems Properties of Liear Time-Ivariat Systems Liear Costat-Coefficiet Differece Equatios Frequecy-Domai Represetatio

More information

ADVANCED DIGITAL SIGNAL PROCESSING

ADVANCED DIGITAL SIGNAL PROCESSING ADVANCED DIGITAL SIGNAL PROCESSING PROF. S. C. CHAN (email : sccha@eee.hku.hk, Rm. CYC-702) DISCRETE-TIME SIGNALS AND SYSTEMS MULTI-DIMENSIONAL SIGNALS AND SYSTEMS RANDOM PROCESSES AND APPLICATIONS ADAPTIVE

More information

Finite-length Discrete Transforms. Chapter 5, Sections

Finite-length Discrete Transforms. Chapter 5, Sections Fiite-legth Discrete Trasforms Chapter 5, Sectios 5.2-50 5.0 Dr. Iyad djafar Outlie The Discrete Fourier Trasform (DFT) Matrix Represetatio of DFT Fiite-legth Sequeces Circular Covolutio DFT Symmetry Properties

More information

Signal Processing in Mechatronics. Lecture 3, Convolution, Fourier Series and Fourier Transform

Signal Processing in Mechatronics. Lecture 3, Convolution, Fourier Series and Fourier Transform Sigal Processig i Mechatroics Summer semester, 1 Lecture 3, Covolutio, Fourier Series ad Fourier rasform Dr. Zhu K.P. AIS, UM 1 1. Covolutio Covolutio Descriptio of LI Systems he mai premise is that the

More information

EE123 Digital Signal Processing

EE123 Digital Signal Processing EE123 Digital Sigal Processig Lecture 20 Filter Desig Liear Filter Desig Used to be a art Now, lots of tools to desig optimal filters For DSP there are two commo classes Ifiite impulse respose IIR Fiite

More information

Chapter 7 z-transform

Chapter 7 z-transform Chapter 7 -Trasform Itroductio Trasform Uilateral Trasform Properties Uilateral Trasform Iversio of Uilateral Trasform Determiig the Frequecy Respose from Poles ad Zeros Itroductio Role i Discrete-Time

More information

Linear time invariant systems

Linear time invariant systems Liear time ivariat systems Alejadro Ribeiro Dept. of Electrical ad Systems Egieerig Uiversity of Pesylvaia aribeiro@seas.upe.edu http://www.seas.upe.edu/users/~aribeiro/ February 25, 2016 Sigal ad Iformatio

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science. BACKGROUND EXAM September 30, 2004.

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science. BACKGROUND EXAM September 30, 2004. MASSACHUSETTS INSTITUTE OF TECHNOLOGY Departmet of Electrical Egieerig ad Computer Sciece 6.34 Discrete Time Sigal Processig Fall 24 BACKGROUND EXAM September 3, 24. Full Name: Note: This exam is closed

More information

Discrete-Time Signals and Systems. Discrete-Time Signals and Systems. Signal Symmetry. Elementary Discrete-Time Signals.

Discrete-Time Signals and Systems. Discrete-Time Signals and Systems. Signal Symmetry. Elementary Discrete-Time Signals. Discrete-ime Sigals ad Systems Discrete-ime Sigals ad Systems Dr. Deepa Kudur Uiversity of oroto Referece: Sectios. -.5 of Joh G. Proakis ad Dimitris G. Maolakis, Digital Sigal Processig: Priciples, Algorithms,

More information

Module 18 Discrete Time Signals and Z-Transforms Objective: Introduction : Description: Discrete Time Signal representation

Module 18 Discrete Time Signals and Z-Transforms Objective: Introduction : Description: Discrete Time Signal representation Module 8 Discrete Time Sigals ad Z-Trasforms Objective:To uderstad represetig discrete time sigals, apply z trasform for aalyzigdiscrete time sigals ad to uderstad the relatio to Fourier trasform Itroductio

More information

Frequency Response of FIR Filters

Frequency Response of FIR Filters EEL335: Discrete-Time Sigals ad Systems. Itroductio I this set of otes, we itroduce the idea of the frequecy respose of LTI systems, ad focus specifically o the frequecy respose of FIR filters.. Steady-state

More information

Solutions. Number of Problems: 4. None. Use only the prepared sheets for your solutions. Additional paper is available from the supervisors.

Solutions. Number of Problems: 4. None. Use only the prepared sheets for your solutions. Additional paper is available from the supervisors. Quiz November 4th, 23 Sigals & Systems (5-575-) P. Reist & Prof. R. D Adrea Solutios Exam Duratio: 4 miutes Number of Problems: 4 Permitted aids: Noe. Use oly the prepared sheets for your solutios. Additioal

More information

The z-transform can be used to obtain compact transform-domain representations of signals and systems. It

The z-transform can be used to obtain compact transform-domain representations of signals and systems. It 3 4 5 6 7 8 9 10 CHAPTER 3 11 THE Z-TRANSFORM 31 INTRODUCTION The z-trasform ca be used to obtai compact trasform-domai represetatios of sigals ad systems It provides ituitio particularly i LTI system

More information

The z-transform. 7.1 Introduction. 7.2 The z-transform Derivation of the z-transform: x[n] = z n LTI system, h[n] z = re j

The z-transform. 7.1 Introduction. 7.2 The z-transform Derivation of the z-transform: x[n] = z n LTI system, h[n] z = re j The -Trasform 7. Itroductio Geeralie the complex siusoidal represetatio offered by DTFT to a represetatio of complex expoetial sigals. Obtai more geeral characteristics for discrete-time LTI systems. 7.

More information

Z - Transform. It offers the techniques for digital filter design and frequency analysis of digital signals.

Z - Transform. It offers the techniques for digital filter design and frequency analysis of digital signals. Z - Trasform The -trasform is a very importat tool i describig ad aalyig digital systems. It offers the techiques for digital filter desig ad frequecy aalysis of digital sigals. Defiitio of -trasform:

More information

Discrete-Time Signals and Systems. Signals and Systems. Digital Signals. Discrete-Time Signals. Operations on Sequences: Basic Operations

Discrete-Time Signals and Systems. Signals and Systems. Digital Signals. Discrete-Time Signals. Operations on Sequences: Basic Operations -6.3 Digital Sigal Processig ad Filterig..8 Discrete-ime Sigals ad Systems ime-domai Represetatios of Discrete-ime Sigals ad Systems ime-domai represetatio of a discrete-time sigal as a sequece of umbers

More information

ECE-S352 Introduction to Digital Signal Processing Lecture 3A Direct Solution of Difference Equations

ECE-S352 Introduction to Digital Signal Processing Lecture 3A Direct Solution of Difference Equations ECE-S352 Itroductio to Digital Sigal Processig Lecture 3A Direct Solutio of Differece Equatios Discrete Time Systems Described by Differece Equatios Uit impulse (sample) respose h() of a DT system allows

More information

Digital Signal Processing

Digital Signal Processing Digital Sigal Processig Z-trasform dftwave -Trasform Backgroud-Defiitio - Fourier trasform j ω j ω e x e extracts the essece of x but is limited i the sese that it ca hadle stable systems oly. jω e coverges

More information

The Discrete Fourier Transform

The Discrete Fourier Transform The iscrete Fourier Trasform The discrete-time Fourier trasform (TFT) of a sequece is a cotiuous fuctio of!, ad repeats with period. I practice we usually wat to obtai the Fourier compoets usig digital

More information

Exam. Notes: A single A4 sheet of paper (double sided; hand-written or computer typed)

Exam. Notes: A single A4 sheet of paper (double sided; hand-written or computer typed) Exam February 8th, 8 Sigals & Systems (5-575-) Prof. R. D Adrea Exam Exam Duratio: 5 Mi Number of Problems: 5 Number of Poits: 5 Permitted aids: Importat: Notes: A sigle A sheet of paper (double sided;

More information

Question1 Multiple choices (circle the most appropriate one):

Question1 Multiple choices (circle the most appropriate one): Philadelphia Uiversity Studet Name: Faculty of Egieerig Studet Number: Dept. of Computer Egieerig Fial Exam, First Semester: 2014/2015 Course Title: Digital Sigal Aalysis ad Processig Date: 01/02/2015

More information

COMM 602: Digital Signal Processing

COMM 602: Digital Signal Processing COMM 60: Digital Sigal Processig Lecture 4 -Properties of LTIS Usig Z-Trasform -Iverse Z-Trasform Properties of LTIS Usig Z-Trasform Properties of LTIS Usig Z-Trasform -ve +ve Properties of LTIS Usig Z-Trasform

More information

Digital signal processing: Lecture 5. z-transformation - I. Produced by Qiangfu Zhao (Since 1995), All rights reserved

Digital signal processing: Lecture 5. z-transformation - I. Produced by Qiangfu Zhao (Since 1995), All rights reserved Digital sigal processig: Lecture 5 -trasformatio - I Produced by Qiagfu Zhao Sice 995, All rights reserved DSP-Lec5/ Review of last lecture Fourier trasform & iverse Fourier trasform: Time domai & Frequecy

More information

2D DSP Basics: 2D Systems

2D DSP Basics: 2D Systems - Digital Image Processig ad Compressio D DSP Basics: D Systems D Systems T[ ] y = T [ ] Liearity Additivity: If T y = T [ ] The + T y = y + y Homogeeity: If The T y = T [ ] a T y = ay = at [ ] Liearity

More information

Spring 2014, EE123 Digital Signal Processing

Spring 2014, EE123 Digital Signal Processing Aoucemets EE3 Digital Sigal Processig Last time: FF oday: Frequecy aalysis with DF Widowig Effect of zero-paddig Lecture 9 based o slides by J.M. Kah Spectral Aalysis with the DF Spectral Aalysis with

More information

Definition of z-transform.

Definition of z-transform. - Trasforms Frequecy domai represetatios of discretetime sigals ad LTI discrete-time systems are made possible with the use of DTFT. However ot all discrete-time sigals e.g. uit step sequece are guarateed

More information

Ch3 Discrete Time Fourier Transform

Ch3 Discrete Time Fourier Transform Ch3 Discrete Time Fourier Trasform 3. Show that the DTFT of [] is give by ( k). e k 3. Determie the DTFT of the two sided sigal y [ ],. 3.3 Determie the DTFT of the causal sequece x[ ] A cos( 0 ) [ ],

More information

Signals & Systems Chapter3

Signals & Systems Chapter3 Sigals & Systems Chapter3 1.2 Discrete-Time (D-T) Sigals Electroic systems do most of the processig of a sigal usig a computer. A computer ca t directly process a C-T sigal but istead eeds a stream of

More information

Generalizing the DTFT. The z Transform. Complex Exponential Excitation. The Transfer Function. Systems Described by Difference Equations

Generalizing the DTFT. The z Transform. Complex Exponential Excitation. The Transfer Function. Systems Described by Difference Equations Geeraliig the DTFT The Trasform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl 1 The forward DTFT is defied by X e jω = x e jω i which = Ω is discrete-time radia frequecy, a real variable.

More information

Chapter 8. DFT : The Discrete Fourier Transform

Chapter 8. DFT : The Discrete Fourier Transform Chapter 8 DFT : The Discrete Fourier Trasform Roots of Uity Defiitio: A th root of uity is a complex umber x such that x The th roots of uity are: ω, ω,, ω - where ω e π /. Proof: (ω ) (e π / ) (e π )

More information

Fall 2011, EE123 Digital Signal Processing

Fall 2011, EE123 Digital Signal Processing Lecture 5 Miki Lustig, UCB September 14, 211 Miki Lustig, UCB Motivatios for Discrete Fourier Trasform Sampled represetatio i time ad frequecy umerical Fourier aalysis requires a Fourier represetatio that

More information

EE422G Homework #13 (12 points)

EE422G Homework #13 (12 points) EE422G Homework #1 (12 poits) 1. (5 poits) I this problem, you are asked to explore a importat applicatio of FFT: efficiet computatio of covolutio. The impulse respose of a system is give by h(t) (.9),1,2,,1

More information

Introduction to Digital Signal Processing

Introduction to Digital Signal Processing Fakultät Iformatik Istitut für Systemarchitektur Professur Recheretze Itroductio to Digital Sigal Processig Walteegus Dargie Walteegus Dargie TU Dresde Chair of Computer Networks I 45 Miutes Refereces

More information

DIGITAL SIGNAL PROCESSING LECTURE 3

DIGITAL SIGNAL PROCESSING LECTURE 3 DIGITAL SIGNAL PROCESSING LECTURE 3 Fall 2 2K8-5 th Semester Tahir Muhammad tmuhammad_7@yahoo.com Cotet ad Figures are from Discrete-Time Sigal Processig, 2e by Oppeheim, Shafer, ad Buc, 999-2 Pretice

More information

Block-by Block Convolution, FFT/IFFT, Digital Spectral Analysis

Block-by Block Convolution, FFT/IFFT, Digital Spectral Analysis Lecture 9 Outlie: Block-by Block Covolutio, FFT/IFFT, Digital Spectral Aalysis Aoucemets: Readig: 5: The Discrete Fourier Trasform pp. 3-5, 8, 9+block diagram at top of pg, pp. 7. HW 6 due today with free

More information

EE Midterm Test 1 - Solutions

EE Midterm Test 1 - Solutions EE35 - Midterm Test - Solutios Total Poits: 5+ 6 Bous Poits Time: hour. ( poits) Cosider the parallel itercoectio of the two causal systems, System ad System 2, show below. System x[] + y[] System 2 The

More information

3. Z Transform. Recall that the Fourier transform (FT) of a DT signal xn [ ] is ( ) [ ] = In order for the FT to exist in the finite magnitude sense,

3. Z Transform. Recall that the Fourier transform (FT) of a DT signal xn [ ] is ( ) [ ] = In order for the FT to exist in the finite magnitude sense, 3. Z Trasform Referece: Etire Chapter 3 of text. Recall that the Fourier trasform (FT) of a DT sigal x [ ] is ω ( ) [ ] X e = j jω k = xe I order for the FT to exist i the fiite magitude sese, S = x [

More information

Chapter 3. z-transform

Chapter 3. z-transform Chapter 3 -Trasform 3.0 Itroductio The -Trasform has the same role as that played by the Laplace Trasform i the cotiuous-time theorem. It is a liear operator that is useful for aalyig LTI systems such

More information

Lecture 3. Digital Signal Processing. Chapter 3. z-transforms. Mikael Swartling Nedelko Grbic Bengt Mandersson. rev. 2016

Lecture 3. Digital Signal Processing. Chapter 3. z-transforms. Mikael Swartling Nedelko Grbic Bengt Mandersson. rev. 2016 Lecture 3 Digital Sigal Processig Chapter 3 z-trasforms Mikael Swartlig Nedelko Grbic Begt Madersso rev. 06 Departmet of Electrical ad Iformatio Techology Lud Uiversity z-trasforms We defie the z-trasform

More information

Olli Simula T / Chapter 1 3. Olli Simula T / Chapter 1 5

Olli Simula T / Chapter 1 3. Olli Simula T / Chapter 1 5 Sigals ad Systems Sigals ad Systems Sigals are variables that carry iformatio Systemstake sigals as iputs ad produce sigals as outputs The course deals with the passage of sigals through systems T-6.4

More information

ECE 308 Discrete-Time Signals and Systems

ECE 308 Discrete-Time Signals and Systems ECE 38-5 ECE 38 Discrete-Time Sigals ad Systems Z. Aliyazicioglu Electrical ad Computer Egieerig Departmet Cal Poly Pomoa ECE 38-5 1 Additio, Multiplicatio, ad Scalig of Sequeces Amplitude Scalig: (A Costat

More information

Discrete-Time Systems, LTI Systems, and Discrete-Time Convolution

Discrete-Time Systems, LTI Systems, and Discrete-Time Convolution EEL5: Discrete-Time Sigals ad Systems. Itroductio I this set of otes, we begi our mathematical treatmet of discrete-time s. As show i Figure, a discrete-time operates or trasforms some iput sequece x [

More information

ELEG3503 Introduction to Digital Signal Processing

ELEG3503 Introduction to Digital Signal Processing ELEG3503 Itroductio to Digital Sigal Processig 1 Itroductio 2 Basics of Sigals ad Systems 3 Fourier aalysis 4 Samplig 5 Liear time-ivariat (LTI) systems 6 z-trasform 7 System Aalysis 8 System Realizatio

More information

The z Transform. The Discrete LTI System Response to a Complex Exponential

The z Transform. The Discrete LTI System Response to a Complex Exponential The Trasform The trasform geeralies the Discrete-time Forier Trasform for the etire complex plae. For the complex variable is sed the otatio: jω x+ j y r e ; x, y Ω arg r x + y {} The Discrete LTI System

More information

6.003 Homework #3 Solutions

6.003 Homework #3 Solutions 6.00 Homework # Solutios Problems. Complex umbers a. Evaluate the real ad imagiary parts of j j. π/ Real part = Imagiary part = 0 e Euler s formula says that j = e jπ/, so jπ/ j π/ j j = e = e. Thus the

More information

FIR Filter Design: Part II

FIR Filter Design: Part II EEL335: Discrete-Time Sigals ad Systems. Itroductio I this set of otes, we cosider how we might go about desigig FIR filters with arbitrary frequecy resposes, through compositio of multiple sigle-peak

More information

Frequency Domain Filtering

Frequency Domain Filtering Frequecy Domai Filterig Raga Rodrigo October 19, 2010 Outlie Cotets 1 Itroductio 1 2 Fourier Represetatio of Fiite-Duratio Sequeces: The Discrete Fourier Trasform 1 3 The 2-D Discrete Fourier Trasform

More information

Introduction to Signals and Systems, Part V: Lecture Summary

Introduction to Signals and Systems, Part V: Lecture Summary EEL33: Discrete-Time Sigals ad Systems Itroductio to Sigals ad Systems, Part V: Lecture Summary Itroductio to Sigals ad Systems, Part V: Lecture Summary So far we have oly looked at examples of o-recursive

More information

Written exam Digital Signal Processing for BMT (8E070). Tuesday November 1, 2011, 09:00 12:00.

Written exam Digital Signal Processing for BMT (8E070). Tuesday November 1, 2011, 09:00 12:00. Techische Uiversiteit Eidhove Fac. Biomedical Egieerig Writte exam Digital Sigal Processig for BMT (8E070). Tuesday November, 0, 09:00 :00. (oe page) ( problems) Problem. s Cosider a aalog filter with

More information

ELEG 4603/5173L Digital Signal Processing Ch. 1 Discrete-Time Signals and Systems

ELEG 4603/5173L Digital Signal Processing Ch. 1 Discrete-Time Signals and Systems Departmet of Electrical Egieerig Uiversity of Arasas ELEG 4603/5173L Digital Sigal Processig Ch. 1 Discrete-Time Sigals ad Systems Dr. Jigxia Wu wuj@uar.edu OUTLINE 2 Classificatios of discrete-time sigals

More information

Spring 2014, EE123 Digital Signal Processing

Spring 2014, EE123 Digital Signal Processing Aoucemets EE3 Digital Sigal Processig Lecture 9 Lab part I ad II posted will post III today or tomorrow Lab-bash uesday -3pm Cory hree shorter Midterms: / i class / i class /3 (or BD) i class / or / (BD)

More information

Digital Signal Processing

Digital Signal Processing Digital Sigal Processig EC5 SUBJECT CODE : EC5 IA ARKS : 5 O. OF LECTURE HRS/WEEK : 4 EXA HOURS : 3 TOTAL O. OF LECTURE HRS. : 5 EXA ARKS : UIT - PART - A DISCRETE FOURIER TRASFORS DFT: FREQUECY DOAI SAPLIG

More information

Signal Processing. Lecture 02: Discrete Time Signals and Systems. Ahmet Taha Koru, Ph. D. Yildiz Technical University.

Signal Processing. Lecture 02: Discrete Time Signals and Systems. Ahmet Taha Koru, Ph. D. Yildiz Technical University. Sigal Processig Lecture 02: Discrete Time Sigals ad Systems Ahmet Taha Koru, Ph. D. Yildiz Techical Uiversity 2017-2018 Fall ATK (YTU) Sigal Processig 2017-2018 Fall 1 / 51 Discrete Time Sigals Discrete

More information

Time-Domain Representations of LTI Systems

Time-Domain Representations of LTI Systems 2.1 Itroductio Objectives: 1. Impulse resposes of LTI systems 2. Liear costat-coefficiets differetial or differece equatios of LTI systems 3. Bloc diagram represetatios of LTI systems 4. State-variable

More information

Advanced Training Course on FPGA Design and VHDL for Hardware Simulation and Synthesis

Advanced Training Course on FPGA Design and VHDL for Hardware Simulation and Synthesis 265-25 Advaced Traiig Course o FPGA esig ad VHL for Hardware Simulatio ad Sythesis 26 October - 2 ovember, 29 igital Sigal Processig The iscrete Fourier Trasform Massimiliao olich EEI Facolta' di Igegeria

More information

EE / EEE SAMPLE STUDY MATERIAL. GATE, IES & PSUs Signal System. Electrical Engineering. Postal Correspondence Course

EE / EEE SAMPLE STUDY MATERIAL. GATE, IES & PSUs Signal System. Electrical Engineering. Postal Correspondence Course Sigal-EE Postal Correspodece Course 1 SAMPLE STUDY MATERIAL Electrical Egieerig EE / EEE Postal Correspodece Course GATE, IES & PSUs Sigal System Sigal-EE Postal Correspodece Course CONTENTS 1. SIGNAL

More information

Run-length & Entropy Coding. Redundancy Removal. Sampling. Quantization. Perform inverse operations at the receiver EEE

Run-length & Entropy Coding. Redundancy Removal. Sampling. Quantization. Perform inverse operations at the receiver EEE Geeral e Image Coder Structure Motio Video (s 1,s 2,t) or (s 1,s 2 ) Natural Image Samplig A form of data compressio; usually lossless, but ca be lossy Redudacy Removal Lossless compressio: predictive

More information

Discrete-time signals and systems See Oppenheim and Schafer, Second Edition pages 8 93, or First Edition pages 8 79.

Discrete-time signals and systems See Oppenheim and Schafer, Second Edition pages 8 93, or First Edition pages 8 79. Discrete-time sigals ad systems See Oppeheim ad Schafer, Secod Editio pages 93, or First Editio pages 79. Discrete-time sigals A discrete-time sigal is represeted as a sequece of umbers: x D fxœg; <

More information

FIR Filter Design: Part I

FIR Filter Design: Part I EEL3: Discrete-Time Sigals ad Systems FIR Filter Desig: Part I. Itroductio FIR Filter Desig: Part I I this set o otes, we cotiue our exploratio o the requecy respose o FIR ilters. First, we cosider some

More information

FIR Filter Design by Windowing

FIR Filter Design by Windowing FIR Filter Desig by Widowig Take the low-pass filter as a eample of filter desig. FIR filters are almost etirely restricted to discretetime implemetatios. Passbad ad stopbad Magitude respose of a ideal

More information

EE123 Digital Signal Processing

EE123 Digital Signal Processing Aoucemets HW solutios posted -- self gradig due HW2 due Friday EE2 Digital Sigal Processig ham radio licesig lectures Tue 6:-8pm Cory 2 Lecture 6 based o slides by J.M. Kah SDR give after GSI Wedesday

More information

Signal Processing in Mechatronics

Signal Processing in Mechatronics Sigal Processig i Mechatroics Zhu K.P. AIS, UM. Lecture, Brief itroductio to Sigals ad Systems, Review of Liear Algebra ad Sigal Processig Related Mathematics . Brief Itroductio to Sigals What is sigal

More information

PRELIM PROBLEM SOLUTIONS

PRELIM PROBLEM SOLUTIONS PRELIM PROBLEM SOLUTIONS THE GRAD STUDENTS + KEN Cotets. Complex Aalysis Practice Problems 2. 2. Real Aalysis Practice Problems 2. 4 3. Algebra Practice Problems 2. 8. Complex Aalysis Practice Problems

More information

Chapter 4 : Laplace Transform

Chapter 4 : Laplace Transform 4. Itroductio Laplace trasform is a alterative to solve the differetial equatio by the complex frequecy domai ( s = σ + jω), istead of the usual time domai. The DE ca be easily trasformed ito a algebraic

More information

Module 11: Applications : Linear prediction, Speech Analysis and Speech Enhancement Prof. Eliathamby Ambikairajah Dr. Tharmarajah Thiruvaran School

Module 11: Applications : Linear prediction, Speech Analysis and Speech Enhancement Prof. Eliathamby Ambikairajah Dr. Tharmarajah Thiruvaran School Module : Applicatios : Liear predictio, Speech Aalysis ad Speech Ehacemet Prof. Eliathamby Ambiairajah Dr. Tharmarajah Thiruvara School of Electrical Egieerig & Telecommuicatios The Uiversity of New South

More information

Professor: Mihnea UDREA DIGITAL SIGNAL PROCESSING. Grading: Web: MOODLE. 1. Introduction. General information

Professor: Mihnea UDREA DIGITAL SIGNAL PROCESSING. Grading: Web:   MOODLE. 1. Introduction. General information Geeral iformatio DIGITL SIGL PROCESSIG Profeor: ihea UDRE B29 mihea@comm.pub.ro Gradig: Laboratory: 5% Proect: 5% Tet: 2% ial exam : 5% Coure quiz: ±% Web: www.electroica.pub.ro OODLE 2 alog igal proceig

More information

Mathematical Description of Discrete-Time Signals. 9/10/16 M. J. Roberts - All Rights Reserved 1

Mathematical Description of Discrete-Time Signals. 9/10/16 M. J. Roberts - All Rights Reserved 1 Mathematical Descriptio of Discrete-Time Sigals 9/10/16 M. J. Roberts - All Rights Reserved 1 Samplig ad Discrete Time Samplig is the acquisitio of the values of a cotiuous-time sigal at discrete poits

More information

Lecture 2 Linear and Time Invariant Systems

Lecture 2 Linear and Time Invariant Systems EE3054 Sigals ad Systems Lecture 2 Liear ad Time Ivariat Systems Yao Wag Polytechic Uiversity Most of the slides icluded are extracted from lecture presetatios prepared by McClella ad Schafer Licese Ifo

More information

EECE 301 Signals & Systems

EECE 301 Signals & Systems EECE 301 Sigals & Systems Prof. Mark Fowler Note Set #8 D-T Covolutio: The Tool for Fidig the Zero-State Respose Readig Assigmet: Sectio 2.1-2.2 of Kame ad Heck 1/14 Course Flow Diagram The arrows here

More information

FIR Filters. Lecture #7 Chapter 5. BME 310 Biomedical Computing - J.Schesser

FIR Filters. Lecture #7 Chapter 5. BME 310 Biomedical Computing - J.Schesser FIR Filters Lecture #7 Chapter 5 8 What Is this Course All About? To Gai a Appreciatio of the Various Types of Sigals ad Systems To Aalyze The Various Types of Systems To Lear the Skills ad Tools eeded

More information

CS2403 DIGITAL SIGNAL PROCESSING L T P C

CS2403 DIGITAL SIGNAL PROCESSING L T P C CS403 DIGITAL SIGNAL PROCESSING L T P C 3 0 0 3 UNIT I SIGNALS AND SYSTEMS 9 Basic elemets of DSP cocepts of frequecy i Aalog ad Digital Sigals samplig theorem Discrete time sigals, systems Aalysis of

More information

The Z-Transform. (t-t 0 ) Figure 1: Simplified graph of an impulse function. For an impulse, it can be shown that (1)

The Z-Transform. (t-t 0 ) Figure 1: Simplified graph of an impulse function. For an impulse, it can be shown that (1) The Z-Trasform Sampled Data The geeralied fuctio (t) (also kow as the impulse fuctio) is useful i the defiitio ad aalysis of sampled-data sigals. Figure below shows a simplified graph of a impulse. (t-t

More information

T Signal Processing Systems Exercise material for autumn Solutions start from Page 16.

T Signal Processing Systems Exercise material for autumn Solutions start from Page 16. T-6.40 P (Problems&olutios, autum 003) Page / 9 T-6.40 P (Problems&olutios, autum 003) Page / 9 T-6.40 igal Processig ystems Exercise material for autum 003 - olutios start from Page 6.. Basics of complex

More information

Signals and Systems. Problem Set: From Continuous-Time to Discrete-Time

Signals and Systems. Problem Set: From Continuous-Time to Discrete-Time Sigals ad Systems Problem Set: From Cotiuous-Time to Discrete-Time Updated: October 5, 2017 Problem Set Problem 1 - Liearity ad Time-Ivariace Cosider the followig systems ad determie whether liearity ad

More information

The Z-Transform. Content and Figures are from Discrete-Time Signal Processing, 2e by Oppenheim, Shafer, and Buck, Prentice Hall Inc.

The Z-Transform. Content and Figures are from Discrete-Time Signal Processing, 2e by Oppenheim, Shafer, and Buck, Prentice Hall Inc. The Z-Trasform Cotet ad Figures are from Discrete-Time Sigal Processig, e by Oppeheim, Shafer, ad Buck, 999- Pretice Hall Ic. The -Trasform Couterpart of the Laplace trasform for discrete-time sigals Geeraliatio

More information

Solutions of Chapter 5 Part 1/2

Solutions of Chapter 5 Part 1/2 Page 1 of 8 Solutios of Chapter 5 Part 1/2 Problem 5.1-1 Usig the defiitio, compute the -trasform of x[] ( 1) (u[] u[ 8]). Sketch the poles ad eros of X[] i the plae. Solutio: Accordig to the defiitio,

More information

MAXIMALLY FLAT FIR FILTERS

MAXIMALLY FLAT FIR FILTERS MAXIMALLY FLAT FIR FILTERS This sectio describes a family of maximally flat symmetric FIR filters first itroduced by Herrma [2]. The desig of these filters is particularly simple due to the availability

More information

Difference Equation Construction (1) ENGG 1203 Tutorial. Difference Equation Construction (2) Grow, baby, grow (1)

Difference Equation Construction (1) ENGG 1203 Tutorial. Difference Equation Construction (2) Grow, baby, grow (1) ENGG 03 Tutorial Differece Equatio Costructio () Systems ad Cotrol April Learig Objectives Differece Equatios Z-trasform Poles Ack.: MIT OCW 6.0, 6.003 Newto s law of coolig states that: The chage i a

More information

Discrete-Time Filters

Discrete-Time Filters Discrete-Time Filters Puttig LTI Systems to Work x h y y[] = x[] h[] = h[ m] x[m] m= Y (z) = H(z) X(z), Y (ω) = H(ω) X(ω) Goal: Desig a LTI system to perform a certai task i some applicatio Key questios:

More information

Exponential Moving Average Pieter P

Exponential Moving Average Pieter P Expoetial Movig Average Pieter P Differece equatio The Differece equatio of a expoetial movig average lter is very simple: y[] x[] + (1 )y[ 1] I this equatio, y[] is the curret output, y[ 1] is the previous

More information

2D DSP Basics: Systems Stability, 2D Sampling

2D DSP Basics: Systems Stability, 2D Sampling - Digital Iage Processig ad Copressio D DSP Basics: Systes Stability D Saplig Stability ty Syste is stable if a bouded iput always results i a bouded output BIBO For LSI syste a sufficiet coditio for stability:

More information

PAPER : IIT-JAM 2010

PAPER : IIT-JAM 2010 MATHEMATICS-MA (CODE A) Q.-Q.5: Oly oe optio is correct for each questio. Each questio carries (+6) marks for correct aswer ad ( ) marks for icorrect aswer.. Which of the followig coditios does NOT esure

More information

Digital Signal Processing, Fall 2006

Digital Signal Processing, Fall 2006 Digital Sigal Processig, Fall 26 Lecture 1: Itroductio, Discrete-time sigals ad systems Zheg-Hua Ta Departmet of Electroic Systems Aalborg Uiversity, Demark zt@kom.aau.dk 1 Part I: Itroductio Itroductio

More information

Mechatronics. Time Response & Frequency Response 2 nd -Order Dynamic System 2-Pole, Low-Pass, Active Filter

Mechatronics. Time Response & Frequency Response 2 nd -Order Dynamic System 2-Pole, Low-Pass, Active Filter Time Respose & Frequecy Respose d -Order Dyamic System -Pole, Low-Pass, Active Filter R 4 R 7 C 5 e i R 1 C R 3 - + R 6 - + e out Assigmet: Perform a Complete Dyamic System Ivestigatio of the Two-Pole,

More information

Web Appendix O - Derivations of the Properties of the z Transform

Web Appendix O - Derivations of the Properties of the z Transform M. J. Roberts - 2/18/07 Web Appedix O - Derivatios of the Properties of the z Trasform O.1 Liearity Let z = x + y where ad are costats. The ( z)= ( x + y )z = x z + y z ad the liearity property is O.2

More information

Review of Discrete-time Signals. ELEC 635 Prof. Siripong Potisuk

Review of Discrete-time Signals. ELEC 635 Prof. Siripong Potisuk Review of Discrete-time Sigals ELEC 635 Prof. Siripog Potisuk 1 Discrete-time Sigals Discrete-time, cotiuous-valued amplitude (sampled-data sigal) Discrete-time, discrete-valued amplitude (digital sigal)

More information

Digital Signal Processing, Fall 2010

Digital Signal Processing, Fall 2010 Digital Sigal Processig, Fall 2 Lecture : Itroductio, Discrete-time sigals ad sstems Zheg-Hua Ta Departmet of Electroic Sstems alborg Uiversit, Demar zt@es.aau.d Digital Sigal Processig, I, Zheg-Hua Ta

More information

: Transforms and Partial Differential Equations

: Transforms and Partial Differential Equations Trasforms ad Partial Differetial Equatios 018 SUBJECT NAME : Trasforms ad Partial Differetial Equatios SUBJECT CODE : MA 6351 MATERIAL NAME : Part A questios REGULATION : R013 WEBSITE : wwwharigaeshcom

More information

Wavelet Transform and its relation to multirate filter banks

Wavelet Transform and its relation to multirate filter banks Wavelet Trasform ad its relatio to multirate filter bas Christia Walliger ASP Semiar th Jue 007 Graz Uiversity of Techology, Austria Professor Georg Holzma, Horst Cerja, Christia 9..005 Walliger.06.07

More information

from definition we note that for sequences which are zero for n < 0, X[z] involves only negative powers of z.

from definition we note that for sequences which are zero for n < 0, X[z] involves only negative powers of z. We ote that for the past four examples we have expressed the -trasform both as a ratio of polyomials i ad as a ratio of polyomials i -. The questio is how does oe kow which oe to use? [] X ] from defiitio

More information

EEO 401 Digital Signal Processing Prof. Mark Fowler

EEO 401 Digital Signal Processing Prof. Mark Fowler EEO 40 Digital Sigal Processig Prof. Mark Fowler Note Set #3 Covolutio & Impulse Respose Review Readig Assigmet: Sect. 2.3 of Proakis & Maolakis / Covolutio for LTI D-T systems We are tryig to fid y(t)

More information

School of Mechanical Engineering Purdue University. ME375 Frequency Response - 1

School of Mechanical Engineering Purdue University. ME375 Frequency Response - 1 Case Study ME375 Frequecy Respose - Case Study SUPPORT POWER WIRE DROPPERS Electric trai derives power through a patograph, which cotacts the power wire, which is suspeded from a cateary. Durig high-speed

More information