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# INTRODUCTION TO COMMUNICATION SYSTEMS EE 511

UK

GPA 3.81

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This 12 page Class Notes was uploaded by Adaline Pollich on Friday October 23, 2015. The Class Notes belongs to EE 511 at University of Kentucky taught by Staff in Fall. Since its upload, it has received 14 views. For similar materials see /class/228328/ee-511-university-of-kentucky in Electrical Engineering at University of Kentucky.

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Date Created: 10/23/15

EE 422G Notes Preliminaries Instructor Cheung Overview EE422G Signal and Systems 11 1 Objective of the course Provide you with the necessary mathematical background to design analyze and model different kinds of signals and systems used in engineering 2 How does EE422G fit into your curriculum and professional career EE 5 l l 512 Communication Systems BB 586 Network Systems Communication EE422G BB 579 Neural BB 635 Engineering Image Processir BB 630 Digital Signal Processing EE 64o Stochastic System Data Analysis and Mode ling BB 571 572 Control Design i EB 61 l Deterministic System EE 6 l 3 Optimal Control BB 605 Discrete Event Systems System Design and Control Page 51 EE 422G Notes Preliminaries Instructor Cheung Some examples of jobs Position Digital Signal Processing Engineer Position will serve as a member of a wireless technology team Teams focus is low powered low cost embedded software radios General responsibilities will take place in the following areas Wireless Signal Processing System Engineering Waveform Development General Signal Processing This position involves the design and implementation of wireless modems This includes the design documentation simulation analysis and implementation of algorithms communications systems and protocols Position Image Processing Engineer Develop implement test debug and document automated machine vision inspection algorithms in CC Integrate motion control frame grabbers light control and camera control for specific applications Generate specifications for image acquisition systems Experience with CC computer vision image amp signal processing digital signal processing and system integration Position Video Processing Engineer Apple Computer is looking for a senior engineer architect to focus on the next generation video architectures with emphasis on digital video camera signal processing algorithms and software development Heshe will be responsible for design of most efficient software architecture for video processing will also ensure optimal and consistently improving video quality through the entire procession pipeline and help track and help select generations of video camera This individual should also have demonstrated expertise in the following areas of video and image processing fix pattern and temporal noise reduction bad pixel correction color correction Bayer demosaicing auto white balancing edge enhancement auto exposure auto focus 2 What will we cover in this course Four main topics Anal sis of ContinuousTime S stem usin La lace Transform and State Variable Techniques R 1F 59 o f9 n M l v Vv V 1F e YO X0 59 1F vt gt n v v Based on the techniques that you learnt from EE421G you should be able to compute the steady output of yt when Xt is a sinusoid But can you answer the following questions Page 52 EE 4226 Notes Preliminaries Instructor cheung a What is the output yt ifxt lote 5 cos 100mut Notnnusoidoz Input and vt 5 for t0 Initial Condition b bounded input signal will deliver a bounded output signal c Can you write a program to simulate this circuith any input called the Laplace Transform which is the rst topic ofthis course 39 39 tu an cl 4 L 39 we will introduce an advanced technique called State Variable Technique that is in u unlcnml JUI Crete rne Signals and stems not record CantmuaustmeL Cantmuaustxmi W mm 5 mm signal output retertxme Dismmw cantmuaustxme cantmlsigmzl WWW m meme record Compute 39 design tools are developed for discretetime system The major design tool We will 39 rate nllanti atinn 39 39 systems Page 573 EE 422G Notes Preliminaries Filter Design Low Pass Speci cation Pass Band 0 3 mg up a s Hja d8 s 0 Stop Band OX 3 a lHthB s b WW gm wp Instructor Cheung m L 7 60 The main design component of this course will focus on various approaches for designing analog continuoustime and discrete discretetime lters that satisfy a particular design specification Computational Signal Processing Analysis X jw J xte 139de Synthesis xt X jaej da Fourier Transform J i gt puma gn omx mu vrnzo SP mm EUNBI ma Mm 1m V mo 1 l rm 2 How do you build a digital spectrum analyzer We will learn how to sample Fourier Transform and how to compute it ef ciently The fundamental concept behind the Fast Fourier Transform is the cornerstone of many modern algorithms Page 54 EE 422G Notes Preliminaries Instructor Cheurig Introduction to Matlab l Starting Matlab File Edit View Web Windaw HElD DSlsiEEEnml l i ll a x L39san Taalbax yam Cache mus quothelp caalbaxlpanhicachequot m maze nfa Tu W scam an quotmum Helpquot m a gap mm This is the workspace which lists all the variables you are using You may type the commands after the quotgtgtquot symbol This is the command window you can enter commands and data and the results are displayed here Fzmmin mini 924u4 217 m 72 This is the command history window it displays a log of the commands used t 1 4 sun o It might be different if you use an older version of Matlab mine is 701 0 Make sure you have Signal Processing Toolbox Control System Toolbox and Symbolic Math Toolbox To check type gtgt e p and you should see these toolboxes listed among all the help pages signalsi nal Signal Processing Toolbox controlcontrol Control System Toolbox toolboxsymbolic Symbolic Math Toolbox 2 Numbers constants variables and data types 0 Numbers gtgt 4 ans Constants gtgt p i Page 55 EE 422G Notes Preliminaries Instructor Cheung ans 31416 gtgt 34i ans 3 400001 0 MATLAB variable names must begin with a letter which may be followed by any combination of letters digits and underscores MATLAB distinguishes between uppercase and lowercase characters so A and a are not the same variable 0 Vectors gtgt V 2 3 4 5 6 7 V 3 4 5 6 7 gtgt v4 ans 5 gtgt W 220527 w Columns 1 through 6 20000 25000 30000 35000 40000 45000 Columns 7 through 11 50000 55000 60000 65000 70000 Matrices the formal name of Matlab is MATriX LABoratory so Matlab is very ef cient in handling matrices gtgt A l 2 3 4 5 6 7 8 9 A l 2 3 4 5 6 7 8 9 gtgt Al2 ans 2 0 Strings gtgt w matlab is simple W matlab is simple Symbolic variables gtgt syms x y z gtgt X x X Page 56 EE 422G Notes Preliminaries Instructor Cheung 3 Operations and functions 0 Simple operations all work as they should be Type help ops for a list of operators and help elfun for a list of elementary mathematical functions Almost all of them can be applied to scalar vectors and matrices gtgt 345 451 A0 44 ans 16206 067431 gtgt sin1 2 3 4 ans 08415 09093 01411 07568 gtgt exp1 2 3 4 5 6 7 8 9 ans 10eOO3 00027 00074 00201 00546 01484 04034 10966 29810 81031 0 Entrywise operations are preceded with a gtgt a 1 2 3 4 5 6 7 8 9 lt comment Sign gtgt b 10 11 12 13 14 15 16 17 18 lt no echo gtgt ab ans 84 90 96 201 216 231 318 342 366 gtgt ab ans 10 22 36 52 7O 90 112 136 162 Function calls work pretty much the same way The most powerful aspect of Matlab is a large collection of functions commonly used in many engineering and scienti c communities Here are some of the signal processing commands we are going to use in this course We will discuss their usages later r e s 1 due Partialfraction expansion f our 1 e r i f ouri e r Symbolic forward and inverse Fourier Transform 1 ap 1 ac e 1 lap lac e Symbolic forward and inverse Laplace Transform t f Create transfer function for a system bode Magnitude and Phase response of a system p zmap Pole zero plot of a system s 8 Create statespace model for a system Page 57 EE 422G Notes Preliminaries Instructor Cheung s s 2 t f t f 2 s 8 Conversion between transfer function and state space representation 1 sim Simulate time response of LTI models e ig Eigenvalues of matrix expm Matrix exponential c 2 1 Continuous to discrete time z t rans i z t rans Symbolic forward and Inverse Ztransfrom re s i due z Partialfraction expansion in zdomain f i l t e r Discretetime filtering c onv Discretetime convolution but t e r Butterworth lter design chebyl Chebyshev 1 lter design imp i nva r Impulse invariance method for analogtodigital lter conversion b i l i ne a r Bilinear transformation method for analogto digital filter conversion 1 p 2 bp 1p 2 b s Frequency transformation 1 p 2 hp 1p 2 1p f irl fir2 FIR filter design f re q s f re q 8 Numerical Fourier transform f f t Fast Fourier Transform Symbolic operations most of the basic operations can be applied directly to symbolic variables To actual evaluate an expression of symbolic variables use the subs command gtgt syms a b c gtgt s sina S sinabexpc gtgt a05b9cl gtgt subss ans 117289 gtgt a0b0c0 gtgt subss ans O bexp c Page 58 EE 422G Notes Preliminaries Instructor Cheung 4 Miscallaneous Plotting gtgt xO00lzl yexpx gtgt xO00lzl gtgt plotxexpx r xexp2X39g39 gtgt xlabel x gtgt ylabel y gtgt title Simple plot mMemm 8 i i r Saving the workspace gtgt save everythingmat save workspace to everythingmat gtgt load everythingmat load everthingmat Saving what you type and the matlab output to a text le gtgt diary footxt output amp response goto footxt gtgt m gtgt diary off stop logging You can also save all your commands in a le and execute it later on The file should have a m extension Page 59 EE 4226 Notes Preliminaries Instructor cheung Quick Review of Con nuousr me Signal and System 1 Complex Numbers where 1 Basic operations 0 AdditionSubtratjon xxya 15 xaxyb Multiplication xxygtltaxb xaybxxbya Division xxy xaybxya7 re 7 2 b o 0 11 Conjugation 2 my o o Magnitude modulus wZImz2Rezz 0 Angle argument zztan l z M2 0 Euler Relation zzeoszzrsinzzMy 0 De Moivre s Formula 2quot We 2 eosnzzr sinnzz 2 Common Signal Representation sinusoid yt Asrnlt27yz 5 Aslnlit a where f in Hz or n in rads is e frequency A s the amplitude and a s the phase eg yt 3sln47l172 Complex sinusoid yt Aexpxlit a Acosa1 a 1Aslnlu 5 Page 5710 EE 422G Notes Preliminaries Instructor Cheung 0 Real Exponential 1 yexprt 2 x10 yexpt 09 08 2 07 06 15 gt 05 gt 04 1 03 02 05 01 0 5 10 0 5 10 o Singular functions 1 4305 0 Brick wall function Ht 0 otherw1se E o 6t is zero everywhere except at t0 which is infinity 0 Impulse function 6t1imH0 t s I6tdt 1 for any positive T o T6txtdt x0 0 Step function ut 600511 3 Systems xt input yt output Dynamic System H A processor which processes the input signal to produce the output 0 Properties 0 Linear Hax1t bx2 0 aHx1t bHx2 0 o TimeInvariant if ytHxt then yt TH yea 1 o Causal H xt0 depends only on xttSt0 Page 511 EE 422G Notes Preliminaries Instructor Cheung o The output of any Linear TimeInvariant System can be computed by convolVing Xt with a function ht called the impulse response which is the output of the system when using the impulse function as input yt xt ha Thaw 1 Examples of LTI systems include any system described by ordinary constant coefficient differential equations that includes all of the lumped electric circuits with resistors capacitors and inductors A Transform Methods methods that transform a system from one domain time domain to another domain frequencydomain in such a way that the analysis becomes easier In BB 421 you have learnt two transform domain methods 0 Fourier Series continuoustime periodic signals Mtlt2gt 11 m Periodic signalxt 4TET 275T 0 ZTET 4TET l L 716212 Analys1s Xk 1 xte j 7 dt 7 9 kg Synthesis xt ZXkej Tl k7m o Fourier Transform general continuoustime signals Wetw 4 X0 Analysis Xa xte dt Synthesis xt Xjae da derived from Fourier series by letting T goes to infinity and replacing the summation by integration Page 512

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