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Introduction to MATLAB

Introduction to MATLAB. What is MATLAB?. MATLAB stands for MAT rix LAB oratory. MATLAB is a high-performance language for technical computing. Math and computation Algorithm development (optimized for DSP) Data acquisition Modeling, simulation, and prototyping

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Introduction to MATLAB

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  1. Introduction to MATLAB

  2. What is MATLAB? • MATLAB stands for MATrix LABoratory. • MATLAB is a high-performance language for technical computing. • Math and computation • Algorithm development (optimized for DSP) • Data acquisition • Modeling, simulation, and prototyping • Data analysis, exploration, and visualization • Scientific and engineering graphics • Application development, including graphical user interface building WWW.KAASHIVINFOTECH.COM

  3. Why Learn and Use MATLAB? • Heavily used in EET/CET courses with DSP content (CET311, EET350, EET453) • Extensive built-in commands for scientific and engineering mathematics • Easy way to generate class demonstrations and test examples • Simple and intuitive programming for more complex problems • Standard and widely-used computationalenvironment with many features, extensions, and links to other software. WWW.KAASHIVINFOTECH.COM

  4. MATLAB in DSP Product Development Develop and Test Algorithms in MATLAB SIMULINK Simulation DSP Processor Platform Code Composer MATLAB + PC = DSP Processor!! (just less efficient) WWW.KAASHIVINFOTECH.COM

  5. Why Learn MATLAB (and DSP)? • Digital Signal Processing (DSP) is the dominant technology today, and into the future, for small-signal electronic systems (i.e., just about everything) • MATLAB has become one of the standard design environments for DSP engineering • Our students need to be literate and skilled in this environment: knowledgeable in both DSP andMATLAB WWW.KAASHIVINFOTECH.COM

  6. How Can I Learn MATLAB? • Keep a copy of this presentation for reference (available on my Web Page) • Get MATLAB loaded on your PC • Read the “Getting Started” Users Guide at the MathWorks web site • Study some of the built-in help files and demos • Dive right in and use it! WWW.KAASHIVINFOTECH.COM

  7. This Presentation • The MATLAB System • The basics of MATLAB computation • The basics of MATLAB graphing • The basics of MATLAB programming • Various course examples • Mathematics • Electronics • Physics • Signal Processing(*) WWW.KAASHIVINFOTECH.COM

  8. The MATLAB System • Development Environment. • MATLAB desktop • Editor and debugger for MATLAB programs (“m-files”) • Browsers for help, built-in and on-line documentation • Extensive demos • The MATLAB Mathematical Function Library. • Elementary functions, like sum, sine, cosine, and complex arithmetic • More sophisticated functions like matrix inverse, matrix eigenvalues, Bessel functions, and fast Fourier transforms. • “Toolboxes” for special application areas such as Signal Processing • The MATLAB Language. • “Programming in the small" to rapidly create quick and dirty throw-away programs, or • “Programming in the large" to create large and complex application programs. • Graphics. • 2D and 3D plots • Editing and annotation features • The MATLAB Application Program Interface (API). • A library that allows you to write C and Fortran programs that interact with MATLAB. WWW.KAASHIVINFOTECH.COM

  9. MATLAB Development Environment (Workspace) WWW.KAASHIVINFOTECH.COM

  10. MATLAB “Help” Utilities • MATLAB is so rich that ‘help’ is essential • Command name and syntax • Command input/output parameters • Usage examples • Help command • help command_name • help [partial_name] tab • Help documents • Demos WWW.KAASHIVINFOTECH.COM

  11. MATLAB Function Library (A Subset) matlab\general - General purpose commands. matlab\ops - Operators and special characters. matlab\lang - Programming language constructs. matlab\elmat - Elementary matrices and matrix manipulation. matlab\elfun - Elementary math functions. matlab\specfun - Specialized math functions. matlab\matfun - Matrix functions - numerical linear algebra. matlab\datafun - Data analysis and Fourier transforms. matlab\polyfun - Interpolation and polynomials. matlab\funfun - Function functions and ODE solvers. matlab\sparfun - Sparse matrices. matlab\scribe - Annotation and Plot Editing. matlab\graph2d - Two dimensional graphs. matlab\graph3d - Three dimensional graphs. matlab\specgraph - Specialized graphs. matlab\graphics - Handle Graphics. WWW.KAASHIVINFOTECH.COM

  12. Some Elementary Functions Exponential. exp - Exponential. expm1 - Compute exp(x)-1 accurately. log - Natural logarithm. log1p - Compute log(1+x) accurately. log10 - Common (base 10) logarithm. log2 - Base 2 logarithm and dissect floating point number. pow2 - Base 2 power and scale floating point number. realpow - Power that will error out on complex result. reallog - Natural logarithm of real number. realsqrt - Square root of number greater than or equal to zero. sqrt - Square root. nthroot - Real n-th root of real numbers. nextpow2 - Next higher power of 2. WWW.KAASHIVINFOTECH.COM

  13. Some Specialized Functions Number theoretic functions. factor - Prime factors. isprime - True for prime numbers. primes - Generate list of prime numbers. gcd - Greatest common divisor. lcm - Least common multiple. rat - Rational approximation. rats - Rational output. perms - All possible permutations. nchoosek - All combinations of N elements taken K at a time. factorial - Factorial function. WWW.KAASHIVINFOTECH.COM

  14. The MATLAB Language (M-file example) function one_period(amp,freq,phase) % ONE_PERIOD(AMP,FREQ,PHASE) % This function plots one period of a sine wave with a given amplitude, % frequency (in Hz), and phase ( in degrees). T=1000/freq; % Compute the period in ms t=0:T/100:T; % Define a 100 point ms time vector 1 period long y=amp*sin(2*pi*t/T+phase*pi/180); % One period of the sine function plot(t,y) % Plot the result and format the axes and title xlabel('milliseconds') ylabel('amplitude') title(['One Period of a ',num2str(freq),' Hz Sinewave with ',num2str(phase), ' Degree phase']) WWW.KAASHIVINFOTECH.COM

  15. MATLAB Graphics:2D Functions (Physics Example) WWW.KAASHIVINFOTECH.COM

  16. MATLAB Graphics:2D Functions (Physics Example) WWW.KAASHIVINFOTECH.COM

  17. MATLAB Graphics:3D Functions (DSP Example) WWW.KAASHIVINFOTECH.COM

  18. Basic MATLAB Computation:Representation of Numbers and Variables • MATLAB operates on n row by m column matrices: • A n x m quantity is an array • A 1 x m or a n x 1 quantity is a vector [8 1 6] • A 1 x 1 quantity is a scalar [8] [8 1 6 3 5 7 4 9 2] WWW.KAASHIVINFOTECH.COM

  19. Basic MATLAB Computation:Basic Operations • Array manipulation (Magic Square example) • Sum, diag, transpose, colon operator, indexing • Array, vector, and scalar operators • Matrix and vector addition and multiplication • Element-by-element operations • Variable statements and definitions WWW.KAASHIVINFOTECH.COM

  20. MATLAB Plotting and Graphics • Rich set of commands for 2D and 3D plotting of functions • Command formatting and editing • GUI formatting and editing • Image display capabilities • Animation capabilities • Simple “copy and paste” for publishing generated figures WWW.KAASHIVINFOTECH.COM

  21. MATLAB PlottingBasic Commands • plot – x,y line plots • stem – n,y discrete plots (standard representation of digital signals) • bar – vertical bar plots • plot3 – 3D x,y,z line plots • mesh, surf, etc. – 3D surface plots • show_img – display matrix as an image • hold – hold current figure for multiple line plots • subplot – put multiple plots in one figure frame • Etc, etc. - See MATLAB help documentation WWW.KAASHIVINFOTECH.COM

  22. Basic Plotting - Examples • Plot of sin(x) function • Stem of sin(x) function • Bar of sin(x) function • Several sine functions with “hold” • Several sine functions with “subplot” • 2D plot of sinc(x) • 3D plot of sinc(x) [“plot_sinc” m-file] • GUI editing • View by rotation • Animation [“brownian_demo” m-file] WWW.KAASHIVINFOTECH.COM

  23. Basic MATLAB Programming • Scripts • String of MATLAB commands • Stored as m-file (*.m) • Use variables from command line • Variables have names consistent with script variable names • Used for “quick and dirty” programs • Example: “dydx_script” • Functions • String of MATLAB commands • Stored as m-file (*.m) • Use variables as function parameters • No restriction on parameter names • Can return variable results • Used for general purpose programs • Example: “yy=dydx(x,y) WWW.KAASHIVINFOTECH.COM

  24. Structure of m-file Functions:Examples • “one_period” • Use of “num2str” for variable formatting • “sumofsines” • Use of parameter-controlled data input loops • “fft_plot” • Use of MATLAB functions as subroutines • Use of “nargin” test and branch WWW.KAASHIVINFOTECH.COM

  25. Polynomial products and factoring: Mathematics Example:Polynomial Algebra (Convolution Operator) >> p1=[1,3,2]; >> p2=[1,5,4,4]; >> pc=conv(p1,p2) pc = 1 8 21 26 20 8 >> deconv(pc,p2) ans = 1 3 2 >> deconv(pc,p1) ans = 1 5 4 4 WWW.KAASHIVINFOTECH.COM

  26. Mathematics Example:Linear Systems • Solve the system: • A*S=B • MATLAB Code: >> A=[5,-2,-3;0,4,3;1,-1,9]; >> B=[-3,-2,60]'; % Note vector transpose (‘) >> S=linsolve(A,B) S = 1.0000 -5.0000 6.0000 WWW.KAASHIVINFOTECH.COM

  27. Mathematics Example:Polynomial Roots • Find the roots of the following system: • MATLAB code: >> roots([12 -1 -8]) ans = 0.8592 -0.7759 WWW.KAASHIVINFOTECH.COM

  28. Mathematics Example:Polynomial Roots • Graphical Solution: >> a=12; >> b=-1; >> c=-8; >> x=-1:0.1:1; >> y=a*x.^2+b*x+c; >> plot(x,y) WWW.KAASHIVINFOTECH.COM

  29. Electronic Circuits Example:Mesh Analysis (Linear System) Find the currents in each branch: I1, I2 -7I1 + 6I2 = 5 6I1 – 8I2 = -10 >> A=[-7,6;6,-8]; >> B=[5;-10]; >> X=linsolve(A,B) ans = 1.0000 2.0000 A*X = B WWW.KAASHIVINFOTECH.COM

  30. Electronic Circuits Example:FET Operating Point • Find the DC operating point of the following circuit: WWW.KAASHIVINFOTECH.COM

  31. Electronic Circuits Example:FET Operating Point • M-file: [Vgs_o,Id_o]=NFET_OP(Idss,Vp,Rs) • [v,id]=nfet_op(12,-4,1200); WWW.KAASHIVINFOTECH.COM

  32. Physics Example:Graphical Solution of a Trajectory • Problem: A football kicker can give the ball an initial speed of 25 m/s. Within what two elevation angles must he kick the ball to score a field goal from a point 50 m in front of goalposts whose horizontal bar is 3.44 m above the ground? WWW.KAASHIVINFOTECH.COM

  33. Physics Example:Field Goal Problem Solution: The general solution is the “trajectory equation.” where y = height, x = distance from goal, v0 = take-off speed, θ0 = take-off angle. Given the take-off speed of 25 m/s, the problem requires the solutions for θ0 that result in a minimum height of y = 3.44 m at a distance of x = 50 m from the goal post. Although an analytical solution is possible, a graphical solution provides more physical insight. WWW.KAASHIVINFOTECH.COM

  34. Physics Example:Field Goal Problem • MATLAB code for a graphical solution: >> v0=25; >> x=50; >> g=9.8; >> y=3.44; >> theta=5:.1:70; >> theta_r=theta*pi/180; >> z=y*ones(1,length(theta)); >> zz=x*tan(theta_r)-g*x^2./(2*v0^2*(cos(theta_r)).^2); >> plot(theta,zz) >> hold Current plot held >> plot(theta,z) WWW.KAASHIVINFOTECH.COM

  35. Physics Example:MATLAB Results WWW.KAASHIVINFOTECH.COM

  36. Signal Processing Examples • Fourier Synthesis and the Gibbs Phenomenon • “square_jms” m-file • Finite Impulse Response (FIR) Filter Design • Use of “fvtool” • Analog-to-Digital Converter Emulation • “adc” m-file • Digital Transfer Function in the Z-domain • “plotH” m-file WWW.KAASHIVINFOTECH.COM

  37. Thank U WWW.KAASHIVINFOTECH.COM

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