FDP on Electronic Design Tools - Computing with MATLAB 13/12/2017. A hands-on training session on. Computing with MATLAB

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1 A hands-on training session on Computing with 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 : Creating functions, 2-D, and 3-D plots 48 Slides & 90 Minutes Outline Logical operations & Logical indexing Cell arrays The for loop, while, if-else, break etc. Commenting and publishing MATLAB script files Standard AM and FM Simulation, computing the execution time Developing user-defined functions Global variables, current directory & path Plotting 2-D and 3-D figures in MATLAB 2 Dr. A. Ranjith Ram arr@gcek.ac.in 1

2 Logical & Relational Operators 20 Minutes Relational Operators Equals : == or eq Greater than : > or gt Less than : < and lt Greater than or equal : >= or ge Less than or equal : <= or le Not equal : ~= or ne Whether numerically equal : isequal 4 Dr. A. Ranjith Ram arr@gcek.ac.in 2

3 Logical Operations and : & not : ~ or : exor : xor Determine if all array elements are nonzero : all Determine if any array elements are nonzero : any Find indices and values of nonzero elements : find Determine if input is logical array : islogical 5 Logical Indexing One can use logical indexing to extract portions of data according to a logical criterion. Comparisons using relational operators such as < and == return a logical array. Eg., marks = [ ]; idx = marks >= 35; creates a logical variable idx of the same size as marks One can use a logical variable as an index to any other variable The result will be the array elements where the index is true passed = marks(idx); Note that the result of logical indexing will be a smaller array (possibly even empty if the index contains no true values). It is therefore important to be careful to keep dimensions consistent when indexing to multiple variables. 6 Dr. A. Ranjith Ram arr@gcek.ac.in 3

4 Cell Arrays Cell arrays are a MATLAB data type that can contain data of different types and dimensions. Each cell in a cell array contains data in the form of any possible MATLAB data type, including other cell arrays. The contents of the cells in cell array need not be of the same size, dimensions or even type. For example, in a 2-element cell array data, the content of the first cell can be another cell array and that of the second cell be a numeric array Cell arrays are very powerful in coping with data using MATLAB, in the sense it greatly simplifies processing using structured data features. 7 Cell Array Indexing We can index a cell array using standard MATLAB indexing. This returns a portion of the original cell array, and so, itself a cell array. data(1) returns the first cell of the cell array data MATLAB will display only the data type and size of the cell, not its contents We can access the contents of cells in a cell array by indexing with curly braces { } rather than parentheses. name = data{2} assigns the contents of the first cell of the cell array data to name What will be the outputs of data(1:4) and data{1:4}? >> data{1:4} is equivalent to >> data{1}, data{2}, data{3}, data{4} 8 Dr. A. Ranjith Ram arr@gcek.ac.in 4

5 Cell Array Indexing (Contd..) >> data = {12 2 1;'Sachin a<1 20 ;23 a>=1 'Sharukh'} Try name1 = data{2,1} name2 = data(2,1) data1 = data{1:3} data2 = data(1:3) row1 = data{1,1:3} row2 = data(1,1:3) 9 Iterative Constructs 30 Minutes Dr. A. Ranjith Ram arr@gcek.ac.in 5

6 The for Loop for i=1:1:10 pow = i*i end for should always be closed with end for nested for loops, there should be sufficient number of end s for i=1:1:20 for j=1:1:10 prod = i*j end end Default increment of the index is unity The drawback of using for loops in MATLAB is the computational delay 11 While Performs a group of operations when a condition is satisfied a = 1 while length(a) < 10 a = [0 a] + [a 0] end produces the Pascal s Triangle : Dr. A. Ranjith Ram arr@gcek.ac.in 6

7 if - else if else also should be closed with end if expression statements else if expression statements else statements end for i=0:1:10 if rem(i,2) ~= 0 odd = i else even = i end end 13 Break & Continue break terminates the execution of a for or while loop. Statements in the loop after the break statement do not execute. In nested loops, break exits only from the loop in which it occurs. Control passes to the statement that follows the end of that loop. continue passes control to the next iteration of a for or while loop. It skips any remaining statements in the body of the loop for the current iteration. The program continues execution from the next iteration. continue applies only to the body of the loop where it is called. In nested loops, continue skips remaining statements only in the body of the loop in which it occurs 14 Dr. A. Ranjith Ram arr@gcek.ac.in 7

8 Commenting & Publishing 50 Minutes Making the Script User-friendly By inserting comments at appropriate positions in the script Commenting in MATLAB is by putting % There is no need to enclose the comment inside two % s All the text portion to the right side of a % until a line feed will be treated as a comment The commented portion would be automatically displayed in green fonts in the MATLAB editor The process of commenting not only for making the script user-friendly, but also to serve for additional features on publishing the script. 16 Dr. A. Ranjith Ram arr@gcek.ac.in 8

9 Standard AM An example MATLAB program Equation : v(t) = V c [1 + k a v m (t)] cos (2πf c t) Single tone : v(t) = V c [1 + m.cos (2πf m t) ] cos (2πf c t) f1 = 2; f2 = 80; fs = 10000; t = 0:(1/fs):1; m = 0.8; vm = cos(2*pi*f1*t); vc = cos(2*pi*f2*t); sam = (1+m*vm).*vc; plot(t,sam) % Baseband frequency % Carrier frequency % Sampling Rate % Sampling instants % Modulation Index % Baseband Signal % Carrier Signal % Standard AM 17 Standard AM Spectra & Complete Waveforms Spectra computation in MATLAB : fft X = fft(sam,fs); % N-point Spectra subplot(411); plot(t,vm); subplot(412); plot(t,vc, r ); subplot(413); plot(t,sam, g ); subplot(414); stem([1:fs]-1,abs(x), k ); axis([ ]); 18 Dr. A. Ranjith Ram arr@gcek.ac.in 9

10 FM Another example program Equation : v = V cos (ω c t + m f sin ω m t) f1 = 2; % Baseband frequency f2 = 80; % Carrier frequency fs = 10000; t = 0:(1/fs):1; % Sampling instants m = 4; % Modulation Index vm = sin(2*pi*f1*t); % Baseband Signal vc = cos(2*pi*f2*t); % Carrier Signal fm = cos(2*pi*f2*t + m*vm); % FM plot(t,fm) (Find spectra and plot all waveforms and spectra using subplot) 19 Publishing a MATLAB script Publishing : 20 Dr. A. Ranjith Ram arr@gcek.ac.in 10

11 Publishing Options Output file format Appropriate placing of %% effects the generation of section titles and table of content in the published file. 21 Repeating % has Meaning! Only error-free codes can be published This is because MATLAB always runs the codes before publishing A double % comment in the top means the title in publishing! A single % comment after this will be published as text lines in the document Subsequent double % effects the table of content & section headings! Comments in line with the commands will be maintained as such in the document The figures will be inserted soon after the codes for plotting. 22 Dr. A. Ranjith Ram arr@gcek.ac.in 11

12 Tea Break! 10 Minutes Creating Functions 40 Minutes Dr. A. Ranjith Ram 12

13 Creating User-defined Functions One can modularize the code by creating his/her own functions in MATLAB A main script file may call these functions by passing appropriate arguments to them. All the concepts like arguments, local and global variables etc., concerned with C programming is applicable here also. Hence at the function call, arguments are passed to the function The function performs the necessary computation and returns values to the calling program The returned values are used in the main script 25 Form of MATLAB Functions The first command line should be of the form function [v1 v2] = funct_name(a1, a2,..., an) v1 & v2 return values funct_name name given to the function (Should not be a built-in function) a1, a2,..., an arguments passed Care should be taken : The script file itself should be named with funct_name.m and it should reside in the current directory Then one can use the user-defined function, func_name by typing [p q] = func_name(i, j, l,... n) 26 Dr. A. Ranjith Ram arr@gcek.ac.in 13

14 Current Directory Current Directory 27 An Example Function function v = sam(t,f1,f2,m) % Function definition vm = cos(2*pi*f1*t); % Baseband Signal vc = cos(2*pi*f2*t); % Carrier Signal v = (1+m*vm).*vc; % Standard AM Main Program : time = 0:0.001:1; % Time duration bf = 2; % Baseband frequency cf = 80; % Carrier frequency mi = 0.8; % Modulation Index x = sam(time,bf,cf,mi); % Function Call plot(time,x) % Plot AM 28 Dr. A. Ranjith Ram arr@gcek.ac.in 14

15 Local & Global Variables function g = game(p,q,r,s) global a b; % global variables t=p*q/a; u=r*s/b; g = t.^2 + u.^2; % return value If not defined as global, all the variables are local to the function Interestingly, one can note that the local variables will not be displayed in the workspace Unlike C, the functions are not to be written in the same file as the main program A function can also be passed as an argument to another function In this is to be used as the argument 29 More about MATLAB functions If the function is not in the current directory, one can Set Path for calling the function The comments inserted in the beginning of MATLAB function script bear additional information than simple comment lines They serve as the information to be displayed on the screen when the user seeks help First few lines of comments until two line breaks will be thrown for display on help This is how comment lines are placed in a MATLAB function 30 Dr. A. Ranjith Ram arr@gcek.ac.in 15

16 Setting Path Setting a path 31 Setting Path (Contd..) Saving the set path will permanently add the new folder to MATLAB software! By this you can add your own toolboxes to MATLAB, i.e., you can customize it. 32 Dr. A. Ranjith Ram arr@gcek.ac.in 16

17 Commenting in the Function % SAM computes the standard am function % sam(a,b,c,d) returns the standard am samples in % which a is the time span, b is the baseband % frequency, c is the carrier frequency and d is the % modulation index in the range (0,1) % Developed by Ranjith Ram on 18 th August function v = sam(t,f1,f2,m) % Function Definition vm = cos(2*pi*f1*t); % Baseband Signal vc = cos(2*pi*f2*t); % Carrier Signal v = (1+m*vm).*vc; % Standard AM 33 The Execution Time Avoid using for loops as much as possible since it consumes time. If logical indexing is used, the code becomes faster! tic & toc functions work together to measure elapsed time. toc, by itself, displays the elapsed time, in seconds, since the most recent execution of the tic command. T = toc saves the elapsed time in T as a double scalar. toc(tstart) measures the time elapsed since the tic command that generated TSTART. Example code is >> tic >> E = sum(abs(x).^2)/8; >> toc 34 Dr. A. Ranjith Ram arr@gcek.ac.in 17

18 Deliberate Delay Pause One can deliberately delay the computation by inserting a pause command in MATLAB pause(n) pauses for n seconds before continuing, where n can also be a fraction. For example, pause(2) delays the execution of the next command by 2 seconds A simple pause without any argument causes a procedure to stop and wait for the user to strike any key before continuing. Example code is >> tic >> E = sum(abs(x).^2)/8; >> pause(2) >> toc 35 2-D & 3-D Visualizations 60 Minutes Dr. A. Ranjith Ram arr@gcek.ac.in 18

19 2-D and 3-D plots in MATLAB One can have higher dimensional plots in MATLAB using appropriate functions For this, the first task is to select the two dimensional data points The corresponding task in 1-D case was achieved by using t = 1 : 200 or t = linspace(1,200,200) Here t would serve as the index for the placement of 1-D samples In 2-D, an extended spatial arrangement is required to initialize a plot The MATLAB function meshgrid will serve this purpose 37 Making data points for 2-D plots The meshgrid function converts vectors of points into matrices that can represent a grid of points in the x-y plane >> x = 1:7; >> y = 2:2:12; >> [X,Y] = meshgrid(x,y); x : 1 x 7 vector y : 1 x 6 vector Grid is formed with 6 x 7 points Here X contains the x coordinates of all points in the 6-by-7 grid and Y contains the corresponding y coordinates. These matrices of coordinates can be used in calculations, interpolation of scattered data and visualization. 38 Dr. A. Ranjith Ram arr@gcek.ac.in 19

20 Mesh Grid (1,2) (4,2) (7,2) (1,8) (7,8) (1,12) (4,12) (7,12) 39 Two Dimensional Plots contour(z) plot of matrix z treating the values in z as heights above a plane are the level curves of z for some values v. The values v are chosen automatically contour(x, y, z) x and y specify the (x, y) coordinates of the surface fill(x, y, c) fills the 2-D polygon defined by vectors x and y with the color specified by c The vertices of the polygon are specified by pairs of components of x and y c is a single character string chosen from the list 'r', 'g', 'b', 'c', 'm', 'y', 'w', 'k'. 40 Dr. A. Ranjith Ram arr@gcek.ac.in 20

21 2-D Plot Example contour [x y] = meshgrid(-3:0.1:+3, -3:0.1:+3); contour(x,y,x.^2 + y.^2); axis square This yields an output figure : Three Dimensional Plots plot3(x, y, z) if x, y, and z are vectors, it plots a line in 3D space through the points whose coordinates are the elements of x, y and z. if x, y, and z are matrices, it plots several lines obtained from the columns of x, y and z. contour3(x, y, z) 3D contour plot mesh(x, y, z) plots the colored parametric mesh defined by the arguments surf(x, y, z) plots the colored parametric surface defined by the arguments colour is proportional to the height of the surface 42 Dr. A. Ranjith Ram arr@gcek.ac.in 21

22 3-D Plot Example plot3 t=-2:0.01:2; Plot3(cos(2*pi*t),sin(2*pi*t),t); This yields an output figure : D Plot Example mesh [x y] = meshgrid(-2:0.1:2,-2:0.1:2); z = x.^2 - y.^2; Saddle Point mesh(x,y,z); 4 2 Z 0 This yields an output figure : Y X Dr. A. Ranjith Ram arr@gcek.ac.in 22

23 3-D Plot Example surf [z theta] = meshgrid(-1:0.1:1, (0:0.1:2)*pi); x=sqrt(1-z.^2).*cos(theta); 1 y=sqrt(1-z.^2).*sin(theta); 0.5 surf(x,y,z); axis square -1 1 This yields an output figure : Graphics Objects & Properties A plot in MATLAB is a collection of there graphics objects : 1. a figure window 2. axes 3. plot elements (such as lines and bars) The commands are >> figure; >> axes; >> plot(t,x); Each graphics object has properties that govern its appearance and behavior. Different types of objects have different properties, although there are some properties that are universal. One can interact with graphics object by obtaining a handle to it. 46 Dr. A. Ranjith Ram arr@gcek.ac.in 23

24 Graphics Object Hierarchy The axes labels and title are described by text objects that are a part of the axes, their handles being stored in the X/Y/Zlabels and Title properties of the axes object, rather than as children Figure = Axes Plot objects 47 Part II : Summary Studied logical operations and logical indexing Familiarized with cell arrays, for and while loops and if-else construct Learnt how to make the code user-friendly through commenting Studied how to publish a MATLAB script Simulated AM and FM, computed the execution time Studied how to create user-defined functions Earned the notion of global variables, current directory & path Learnt how to plot 2-D and 3-D figures in MATLAB 48 Dr. A. Ranjith Ram arr@gcek.ac.in 24

25 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 25