FDP on Electronic Design Tools - Fundamentals of MATLAB 12/12/2017. A hands-on training session on. Fundamentals of MATLAB

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1 A hands-on training session on Fundamentals of MATLAB in connection with the FDP on Electronic Design GCE Kannur 11 th 15 th December 2017 Resource Person : Dr. A. Ranjith Ram Associate Professor, ECE Dept. Govt. College of Engineering Kannur Cell : arr@gcek.ac.in Objective : Getting familiarized with MATLAB 62 Slides & 180 Minutes (9:00 AM 12:30 PM) Outline Introduction MATLAB and Simulink Toolboxes & Built-in Functions Help & Documentation Matrix Algebra Polynomials and Roots Trigonometric Functions One Dimensional Plots Developing and running MATLAB scripts Dr. A. Ranjith Ram arr@gcek.ac.in 1

2 Introduction to MATLAB & Simulink 30 Minutes About MATLAB MATLAB MATrix LABoratory a product by MathWorks Inc., USA High Performance Computing Environment Completely written using C Language Unlike C, it is a Column Major Language Available for both Windows and Linux Version : R2013a or R Release 2013 Year a First half; b Second Half Dr. A. Ranjith Ram arr@gcek.ac.in 2

3 The Company MathWorks Founded in 1984 by Jack Little (President) and Cleve Moler (Chief Scientist) at Natick, USA In addition to MATLAB, Jack Little Cleve Moler MathWorks develops Simulink, a product for simulating linear and nonlinear dynamic systems Website : MATLAB & Simulink MATLAB uses an algorithmic approach for programming and is a CUI based computing environment Simulink, on the other hand, uses block diagram based approach and hence, is a GUI based one. One can say that Simulink is built on MATLAB However, one has to purchase Simulink along with MATLAB, if he/she requires Simulink MATLAB functions resides in the respective Toolboxes Simulink boxes are residing in the respective Blocksets Dr. A. Ranjith Ram arr@gcek.ac.in 3

4 Where we fit MATLAB? MATLAB High Level Languages such as Pascal, C, C++ etc. Assembly Language Machine Language Features of MATLAB MATLAB treats every data as a matrix! MATLAB is an interpreted language, not a compiler based one MATLAB does not need any variable declarations MATLAB does not require any dimension statements MATLAB has no packaging MATLAB does not need any storage allocation MATLAB does not require any pointers MATLAB programs can be run step by step, with full access to all variables, functions etc. Dr. A. Ranjith Ram arr@gcek.ac.in 4

5 Why it is different from C? No need for defining the data types, i.e., int a; double b; float c; All variables are created with double precision unless specified otherwise Example: >> A = 10; >> f = 1.0; After these statements, the variables A and w are 1 x 1 matrices with double precision Programming Environment 60 Minutes Dr. A. Ranjith Ram arr@gcek.ac.in 5

6 How to Open Double Clicking the emblem Version Product Company MATLAB Desktop Current Folder Command Window Workspace Command History Dr. A. Ranjith Ram 6

7 MATLAB Desktop Ready or Not Ready? Ready Not Ready! Using the Command Window A = 10 Assignment f = 1.0; Putting a semicolon will suppress the output in the command window b = (pi/180) * theta theta should be defined! name = Sachin ; If there is not an assignment, MATLAB character array (string) c = f < 1 ; logical variable will automatically assign the value to a default ans variable! Dr. A. Ranjith Ram arr@gcek.ac.in 7

8 Using Command Window (Contd ) Clearing commands clc ; clears the command window clear ; clears the workspace Use the up-arrow ( ) for fetching the previous command Preferences Creating a Row Vector r = [ ] or [1, 0, 3, 2] Delimiter is a space or comma Enclosed in square braces MATLAB takes the above as r = [ ] n = [1:10] or 1:10 MATLAB takes the above as n = [ ] k = [3:2:15] or 3:2:15 MATLAB takes the above as k = [ ] Dr. A. Ranjith Ram arr@gcek.ac.in 8

9 Creating a Row Vector linspace Suppose we want N number of data points in the interval (x 1, x 2 ) The previous method fails here as one has to compute the step size explicitly, and one is advised to use linspace function here. linspace linearly spaced vector take care of this situation in MATLAB linspace(x1, X2) generates a row vector of 100 linearly equally spaced points between X1 and X2. linspace(x1, X2, N) generates N points between X1 and X2. For N = 1, linspace returns X2 linspace is useful in many signal processing and plotting situations. linspace(1,10,13); Creating a Column Vector c = [1; 0; 3; 2] Delimiter is a semicolon Enclosed in square braces MATLAB takes the above as 1 0 c = 3 2 Transposing operation : using r = 2:3:10 ; c = r ; Dr. A. Ranjith Ram arr@gcek.ac.in 9

10 Creating an M x N Matrix m = [1 0 3; 4 2 0; 0 1 5]; Delimiters are spaces and semicolons Enclosed in square braces MATLAB takes the above as c = A semicolon inside the square bracket means an end of a row Semicolon outside the square bracket has a different meaning! m = [1:3; 4:6; 7:9]; MATLAB is Simple Powerful! Dealing with matrices is very easy in MATLAB We can concatenate matrices without using a for loop! a = [1; 2; 3; 4]; b = [5; 7; 8; 9] c = [a b]; Guess c = [a ; b] here! In a similar way, a = [ ]; b = [ ] c = [a ; b]; Guess c = [a b] here! Dr. A. Ranjith Ram arr@gcek.ac.in 10

11 Variable Classes or Data Types MATLAB supports several classes of variables (or data types) Numeric Character Logical Structure Cell array Data Types (Contd ) Dr. A. Ranjith Ram arr@gcek.ac.in 11

12 MATLAB Toolboxes Aerospace Toolbox Image Processing Toolbox Bioinformatics Toolbox Instrument Control Toolbox Communications System Toolbox Mapping Toolbox Computer Vision System Toolbox Model Predictive Control Toolbox Control System Toolbox Model-Based Calibration Toolbox Curve Fitting Toolbox Neural Network Toolbox Data Acquisition Toolbox Optimization Toolbox Database Toolbox Parallel Computing Toolbox DSP System Toolbox Partial Differential Equation Toolbox Econometrics Toolbox Phased Array System Toolbox Financial Toolbox RF Toolbox Fuzzy Logic Toolbox Robust Control Toolbox Image Acquisition Toolbox Signal Processing Toolbox Some Built-in Functions sin() plot() cos() stem() inv() surf() eye() mesh() rand() fft() ones() abs() zeros() eig() size() rank() length() ceil() max() round() min() sum() fliplr() prod() flipud() linspace() Dr. A. Ranjith Ram 12

13 Help / Documentation help function_name or doc function_name Help Menu Search Tea Break! 10 Minutes Dr. A. Ranjith Ram arr@gcek.ac.in 13

14 Matrix Algebra 40 Minutes Matrix Addition & Subtraction Matrix addition : + a = [ ]; b = [ ]; c = a + b yields c = [ ] Matrix subtraction : a = [ ]; b = [ ]; c = a - b yields c = [ ] Both the matrices should be of the same dimensions. Equivalent to addition and subtraction of two signals Dr. A. Ranjith Ram arr@gcek.ac.in 14

15 Matrix Multiplication Matrix multiplication : * a = [ ; ]; b = [3 1; 1 2; 0 1; 2 3]; c = a * b yields c = [ ] Both a & b should be conformable to multiplication a should be of dimension M x N and b should be of N x K The result will be of M x K dimension Multiplication by a scalar is also done using * The function equivalent to * is mtimes() c = mtimes(a, b) Signal Product Signal multiplication is done using.*.* will compute the element-by-element product a = 1:5; b = 2:6; c = a.* b will yield c = [ ] Matrix dimensions must match. Will output a signal of same dimension Is useful is many signal processing operations The function equivalent to.* is times() Check: pow = a.* a; and pow = a.^ 2; Dr. A. Ranjith Ram arr@gcek.ac.in 15

16 Matrix Division (?) 1. Matrix division using / a = [1 2 3; 0 1 2; 3 0 4]; b = [3 0 1; 1 2 0; 0 1 3]; c = a / b yields c = [ ] a / b computes a * inv(b) 2. Matrix division using \ a \ b computes inv(a) * b Find the inverse of a using \ a \ eye(size(a)) Matrix Indexing and Addressing In MATLAB, the indexing is from 1 to N, unlike from 0 to N 1 in DSP theory or C Language This practicality is to be taken care of when the an algorithm in theoretical DSP is getting implemented using MATLAB normal braces ( ) are used for addressing elements of a matrix temp(5,10) selects the element in the 5 th row and 10 th column of the matrix temp marks(:,3) selects the third column of the matrix marks marks(2,:) selects the second raw of the matrix marks lena(:,:,2) selects the green component of the colour image lena face(20:50,30:60,:) will select a rectangular region of the colour image face Dr. A. Ranjith Ram arr@gcek.ac.in 16

17 Other Methods of Indexing In MATLAB, indexing has more advanced features One can use a vector for indexing another vector. For example, >> a = [ ]; >> b = [2 4 6]; >> a(b) will yield >> ans = This is a powerful indexing method in MATLAB Another type of indexing is logical indexing, which would be covered later, in a higher level of this training Functions for Matrices inv(a) inverse of the matrix a eye(n) identity matrix of dimension, N x N rand(n) a square matrix of dimension N x N ones(n) and zeros(n) square matrices of 0 s & 1 s size(a) and length(a) length = max(size(a)) max() and min() max & min of the columns fliplr() and flipud() flipping left-right & up-down eig(a) eigen values of the matrix a rank(a) rank of the matrix a sum(a) sum of the elements of a prod(a) product of the elements of a power() matrix power Dr. A. Ranjith Ram arr@gcek.ac.in 17

18 Methods of Data Input & Output 10 Minutes Data Input Generally there are three ways of inputting data into MATLAB directly entering in the command line from memory read an excel file read a speech file read an image file from I/O devices input from a sensor input from a microphone input from a camera Dr. A. Ranjith Ram arr@gcek.ac.in 18

19 Data Input Examples fc = input('enter the carrier frequency: '); x = xlsread( table.xlsx'); wavread( aud.wav ); imread( lena.jpg ); S=load( filemname ); import menu import a file Data Output Generally there are three ways of outputting data from MATLAB directly flashing to command line to memory write an excel file write a speech file write an image file to I/O devices output to a DAC output to a loudspeaker output to a display Dr. A. Ranjith Ram arr@gcek.ac.in 19

20 Data Output Examples sprintf( The bandwidth is %d', bw) or display(bw) fid = fopen('exp.txt','w'); fprintf(fid,'%6.2f %12.8f\n',y); fclose(fid); xlswrite( t.xlsx,m) wavwrite(s,fs, au.wav ) / sound(s,fs) imwrite(y, img.jpg ) save( filename, var) / imshow(y) save menu Reserved Characters / Words 10 Minutes Dr. A. Ranjith Ram arr@gcek.ac.in 20

21 Characters and Meaning ; suppressing output in the command window = assignment + addition - subtraction * matrix product / post multiply with inverse \ pre multiply with inverse < less than > greater than ~ logical not & logical and logical or Characters and Meaning (Contd ). element wise operation, decimal point, structure field access.. parent directory continuation : range [ ] matrix entry ( ) addressing array elements, function { } cell array addressing % commenting ^ power string entity complex conjugate function handle Dr. A. Ranjith Ram arr@gcek.ac.in 21

22 Reserved Characters / Words i imaginary notation j do pi Inf infinity NaN not a number eps spacing of floating point numbers who prints variables in work space why answers to such a question. Do chat with MATLAB! beep produces a beep sound Basic Computing and Plotting 40 Minutes Dr. A. Ranjith Ram arr@gcek.ac.in 22

23 Roots of a Polynomial roots(c) computes the roots of the polynomial whose coefficients are the elements of the vector C If C has N+1 components, the polynomial is C(1) * X^N C(N) * X + C(N+1). C = [ ]; r = roots(c) yields r = [-2 1 1] p = poly(r) converts the roots to its polynomial yields p = [ ] One Dimensional Plots plot(x, y) plots vector y versus vector x If x or y is a matrix, then the vector is plotted versus the rows or columns of the matrix, whichever line up plot(y) plots the columns of y versus their index if y is complex, plot(y) is equivalent to plot(real(y), imag(y)) in all other uses of plot, the imaginary part is ignored stem() plots a signal in a sampled fashion bar() plots a signal in bar form stairs() plots a signal in staircase form scatter() plots in the form of scatter diagram Dr. A. Ranjith Ram arr@gcek.ac.in 23

24 Plotting Trigonometric Functions Let the time duration of the waveform be one second i.e., 0 1 second Let the amplitude be 10 and frequency be one Hertz. t = 0 : 0.01 : 1; f = 1; A = 10 ; x = A*sin(2*pi*f*t); plot(t, x); stem(t,x) This yields an output figure : Use close command to close a figure (close all : closes all figures) Ensure sufficient samples! t = 0:0.1:1; t = 0:0.01:1; Dr. A. Ranjith Ram arr@gcek.ac.in 24

25 Plotting More features Choosing colour and line width Adding title, x-label & y-label, grid lines and legends Choice of range of the independent and dependent variable axes plot(t,x, r, LineWidth,2); grid on; axis([ ]) title( The Sine Wave ); Amplitude xlabel( Time ); ylabel( Amplitude ); legend( Sin(2pift) ) \pi Multiple Plots in a Window Using subplot() function subplot initializes a tiled space in a figure window After subplot, a plot function is to be used for subplot(221) subplot(222) actual plotting subplot(223) subplot(224) Dr. A. Ranjith Ram arr@gcek.ac.in 25

26 Multiple Plots in a Window (Contd ) t = 1:200; subplot(221) plot(exp(-0.01*t), r ); subplot(222) plot(exp(-0.02*t), g ); subplot(223) plot(exp(-0.03*t), b ); subplot(224) plot(exp(-0.04*t), k ); Plots in Different Windows figure(1) plot(exp(-0.01*t), r ); figure(2) plot(exp(-0.02*t), g ); figure(3) plot(exp(-0.03*t), b ); figure(4) plot(exp(-0.04*t), k ); Dr. A. Ranjith Ram arr@gcek.ac.in 26

27 Plots on the Same Axes plot(exp(-0.01*t), r ); hold on; plot(exp(-0.02*t), g ); hold on; plot(exp(-0.03*t), b ); hold on; plot(exp(-0.04*t), k ); legend( e^{-0.01t}, e^{-0.02t}, e^{-0.03t},... e^{-0.04t} ) hold off; M-Files / Script Files 10 Minutes Dr. A. Ranjith Ram arr@gcek.ac.in 27

28 When to Create a Script File t = 0:0.01:1; f = 1.0; Command line based computation has x = 10*cos(2*pi*f*t); its own limitations plot(t, x, r ); title( The Sine Wave ); xlabel( Sampling Instants ); ylabel( Amplitude ); If one has to find/plot a function after changing the value of one of the variable, he/she has to execute all the subsequent commands one by one At this point, script files or m-files need to be created It is created using an editor which is having all the features like cut/copypaste, undo, indent, insert, save as, etc. Creating a Script File Click on the New Script menu on the MATLAB Desktop Dr. A. Ranjith Ram arr@gcek.ac.in 28

29 Developing a script file Enter all the instructions line-by-line in the editor Or, Select the group of commands from the command history and rightclick on the selection to create script Running a Script File Click on the Run Button on the Editor Menu Dr. A. Ranjith Ram arr@gcek.ac.in 29

30 Few Points on Script Files A script is to be saved before running it (for the first time) MATLAB saves the script is the current directory by default If the user saves the script in another folder, MATLAB will ask for the options of Change Folder or Set Path while running Opt Change Folder. Then you will be using MATLAB from your folder Care should be given on aming the script file : The filename should always start with an alphabet! The filename should not be the same as any of the built-in functions! Spaces can not appear in between! One can use underscore (_) or hyphen ( ) to connect words Adopt your own policy when naming script files. It may be better to reflect the purpose for which the program is developed. Exercises 1) Plot the function x(t) = e at 2) Plot the function x(t) = 1 e at 3) Plot the function x(t) = 6 Sin(at) 4 Cos(bt) 4) Plot the function x(t) = Cos(bt) e at 5) Plot the function f(x) = sinc(x) 6) Plot the function f(x) = (1/ 2πσ) e (x μ)2 / 2σ 2 7) Plot the function x(n) = e an 8) Plot the function x(n) = 6 Sin(an) 4 Cos(bn) Dr. A. Ranjith Ram arr@gcek.ac.in 30

31 Part I : Summary Familiarized with MATLAB desktop, toolboxes, variable classes and some built-in functions Performed simple computations using the command prompt, reviewed fundamentals of linear algebra using MATLAB Differentiated the matrix product from signal product Studied how to seek help in the command prompt and how to use the help menu Learnt the various methods of data input and output Computed the roots of a polynomial and obtained the polynomial from a root set Learnt how to plot one dimensional (1-D) curves Studied how to create and run the MATLAB script files Thanks Courtesy : 1. MathWorks Training & Services, Bengaluru 2. TEQIP Project Phase-II, GCE Kannur arr@gcek.ac.in Mob : Dr. A. Ranjith Ram arr@gcek.ac.in 31