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ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14 th, 2007 1 ELE 532 – Signals and Systems Fall 2007 MATLAB Tutorial Raymond Phan Distributed.

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1 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14 th, ELE 532 – Signals and Systems Fall 2007 MATLAB Tutorial Raymond Phan Distributed Multimedia Computing Research (DMCR) Lab Ryerson University – EPH 237

2 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Outline of Tutorial – (1) Introduction Getting Started Variables and Starting Basics Vectors and Matrices Basic Operations Script Files Function Script Files

3 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Outline of Tutorial – (2) Flow Control Basic Graphics Commands Other Useful Commands Final Words

4 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Introduction – (1) So… what the hell is MATLAB and what’s it all about? –MATLAB: MATrix LABoratory Created in 1970 by a dude named Cleve Moler Was (and still is) used extensively at Stanford University and the University of New Mexico –Why? To make calculating the following things a lot easier! Matrix Theory Linear Algebra Numerical Analysis

5 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Introduction – (2) MATLAB is selected as a numerical analysis tool over languages like C and Java because: –Very EASY programming language –Powerful graphics capabilities –Very sleek and interactive interface –Great for general scientific and engineering computation Later in your courses, you’re going to start to use this heavily, especially in: –ELE 639: Control Systems –ELE 792: Digital Signal Processing –… any signal processing and controls course in 4 th year

6 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Outline of Tutorial – (1) Introduction Getting Started Variables and Starting Basics Vectors and Matrices Basic Operations Script Files Function Script Files

7 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Getting Started – (1) Where can I find and use MATLAB? Method #1: On the EE undergraduate network labs: –ENG 406, 407, 408 and 409 Log onto an EE undergraduate terminal A) Go to Applications – Accessories – Terminal and type in ‘matlab’ (without the quotes) B) Go to Applications – Math – MATLAB 2007a

8 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Getting Started – (2) Method #2: If you don’t feel like using the computers at school, you can install your own copy of MATLAB on your PC or laptop –There are many ways to obtain your own copy: Buy a student version at the Ryerson Bookstore Obtain a trial version online via: “Borrow” from a friend –Version of MATLAB needed for these labs: MATLAB 7.0 and up –NOTE!: You MUST have the Java Runtime Environment (JRE) installed on your system At LEAST 5.0 and up –MATLAB uses the JRE as a backbone to run the whole application

9 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Getting Started – (3) What happens next!? –MATLAB Interface: >> means it’s ready for input from you

10 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Outline of Tutorial – (1) Introduction Getting Started Variables and Starting Basics Vectors and Matrices Basic Operations Script Files Function Script Files

11 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Variables and Basic Commands – (1) One GREAT thing about MATLAB: –MATLAB is a programming language that is dynamically typed… what does this mean? –You can declare variables and initialize them without specifying what type they are MATLAB automatically figures this out for you, or you can choose to manually override the type –Example: C or Java way: int nikhil = 1, double jenny = 2 MATLAB way: nikhil = 1, jenny = 2

12 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Variables and Basic Commands – (2) When you want to assign something to a variable, use the = sign When you assign something to a variable, MATLAB initializes & automatically declares it Guidelines for variable names: –All must be single words, no spaces –Must begin with a letter, numbers or the underscore character ( _ ) –Variable names are case sensitive i.e nikhil is NOT the same as Nikhil i.e muffin is NOT the same as mUFfin –Names can be up to 19 characters in length

13 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Variables and Basic Commands – (3) Some valid variable names: –voltage –valueOfR1 –Ron_and_Mauro –_Alan2007_ Some invalid variable names (why are these invalid?): –123 –value of R1 –3v –X#*()$#$!!!

14 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Variables and Basic Commands – (4) Left panel: Current Directory / Workspace –A) Shows you directory structure to access working directory (more on this later) –B) Shows you all of the variables that have been created and can be accessed Right: Command Prompt –Enter commands and variable declarations here –Commands without a semicolon ( ; ) echo your command to screen –Commands with a semicolon suppress that output

15 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Variables and Basic Commands – (5) Can enter commands either: –One at a time: The end of each command, press ENTER (carriage return) –Multiple commands in one line: Suppress echoing: Use semicolons to separate each command on the line Enable echoing: Use commas (, ) to separate each command on the line Typing in a variable by itself and pressing ENTER will redisplay the variable Entering a value, pressing ENTER, and not assigning it to anything, the value will be automatically assigned to a variable called ans (answer)

16 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Variables and Basic Commands – (6)

17 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Variables and Basic Commands – (7) who command: Shows you all of the variables created by you –You can also check the workspace as well clear command: Clears all of the variables shown in the workspace, and you start from scratch clc command: Flushes the command prompt –Variables will still be in the workspace, but it clears the command prompt screen

18 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Variables and Basic Commands – (8)

19 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Variables and Basic Commands – (9) Can also declare complex numbers too: –Can add, subtract, multiply and divide You can use i or j to declare complex numbers Of course… you can also add, subtract, multiply and divide normal numbers too! –Too lazy to make a slide for it –However, we’ll get into addition, subtraction, multiplication and division in another way later

20 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Variables and Basic Commands – (10)

21 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Variables and Basic Commands – (11) Command History window: Used to keep track of the commands you ran recently You can also double click on any of the commands to re-run them again You can also press the up & down keys to cycle through the commands as well in the command prompt

22 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Outline of Tutorial – (1) Introduction Getting Started Variables and Starting Basics Vectors and Matrices Basic Operations Script Files Function Script Files

23 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (1) Unless otherwise defined, MATLAB treats ALL variables as 2D matrices… how is this possible? –Arrays and Vectors: N x 1 or 1 x N matrix –Single value: 1 x 1 matrix Why does MATLAB decide to handle it this way? –You’ll see later that handling variables as matrices makes things A LOT faster and easier to work with

24 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (2) How do you declare a vector / array in MATLAB? –C or Java way: int a[4] = {1, 2, 3, 4}; –MATLAB way: a = [ ] – row vector –Spaces mean to move to the next column a = [ ].’ – (.’ operator means to transpose a vector) - column vector a = [1;2;3;4] - column vector –Semicolon means to move to the next row You do not have to specify how big the vector is first before you make it –Beauty of dynamically typed languages! –MATLAB automatically figures out how big it is and you go from there

25 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (3) How do I access elements in a vector / array? –C or Java way: int jenny = a[0]; –MATLAB way: jenny = a(1); NOTE!: –No square brackets when accessing an element! Use round brackets! –Elements do not start at index 0, they start at index 1!

26 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vector and Matrices – (4)

27 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vector and Matrices – (5) How do I create a matrix in MATLAB? –C or Java way: int a[4][4] = {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}, {13, 14, 15, 16}}; –MATLAB way: #1: a = [ ; ; ; ]; #2: a = [ ; ; ; ];

28 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vector and Matrices – (6) How do I access elements in a matrix? –C or Java way: int alan = a[2][3]; –MATLAB way: alan = a(3,4); What’s the difference here? –No separate brackets for each dimension –Comma is used to separate the dimensions –All indices to access arrays are offset by 1! –Remember: 1 st parameter is the row, 2 nd parameter is the column

29 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vector and Matrices – (7) Here’s something to mess you up… how do I access a range of values in a matrix? Suppose I had a matrix already created called ray –How do I get all of the elements in the 1 st row? –C or Java way: int i; for(i = 0; i < 4; i++) ray[i] = a[0][i]; This is a pain in the butt!... There’s gotta be an easier way to do this!

30 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (8) MATLAB way: –ray = a(1, 1:4); –ray = a(1, :); What’s the difference here?! –NO for loop! –The colon ( : ) operator is used to access a range of values There is a more general use for this, but we’ll get into this later –1 : 4 means a range from 1 through 4 for a dimension –: by itself means give me all possible values in a dimension –Doing 1 : 4 in the 2 nd parameter means give me columns 1 through 4 –Doing : in the 2 nd parameter means give me all of the columns!

31 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (9)

32 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (10) Some more examples: –sally = a(2,3); –sally = a(1:3,3:4); –sally = a(:, 1:3); –sally = a(2:4,:); 1 st line: Access 2 nd row, 3 rd column element, and assign it to sally 2 nd line: Get a matrix with elements between rows 1 – 3, and columns 3 – 4 and assign this to sally 3 rd line: Get a matrix with elements between columns 1 – 3 and give me every possible row, and assign this to sally 4 th line: Get a matrix with elements between rows 2 – 4 and give me every possible column, and assign this to sally

33 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (11) Here’s a curve ball! –Joe = a(:,:); –Joe = a; What does this mean? Copy the entire matrix, a, and assign it to Joe You can also do the 2 nd line too. It’s exactly the same meaning

34 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (12) Example Time! 1) How do we define M in MATLAB syntax? 2) How do we execute a), b), c) and d)?

35 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (13)

36 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (14)

37 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (15) Example #2!

38 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (16) In other words, with matrices A, B and C, make me a matrix that looks like this! What do we need to do? –How do we define matrices A, B and C? –How do we create M?

39 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (17)

40 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (18) MATLAB has a really cool way of making vectors / arrays where consecutive elements are uniformly spaced Example: –Ray = 0 : 0.1 : 1.0; This generates a vector / array with 11 elements, such that –Ray = [ … 1.0];

41 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (19) General Form: –new_array = first_value : increment : last_value –Make note of the colons ( : )! first_value : The first value in the new vector / array last_value : The last value in the new vector / array increment : The step size –If you don’t include this value, it is automatically assumed to be 1

42 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (20) Examples: –jenny = 0 : 2 : 10; –eman = 3 : 3 : 30; –ron = 1 : 10; –mauro = 2.0 : -0.2 : 0.4; 1 st line: Creates a 6 element vector –jenny = [ ]; 2 nd line: Creates a 10 element vector –eman = [ … 27 30];

43 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (22) 3 rd line: Creates an 10 element vector –ron = [1 2 3 … 9 10]; 4 th line: Creates a 8 element vector –mauro = [ … ]; Pretty easy don’t you think!? Remember how I told you about that colon operator?... Well, here you go! To do this in C and Java, it requires a bit more work.

44 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (23) Some useful matrix and vector / array commands –eye(n): Creates an n x n identity matrix

45 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (24) Some useful matrix and vector / array commands –ones(n,m): Creates an n x m matrix full of ones –ones(1,n) or ones(n,1): Creates an array / vector that has n elements, full of ones

46 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (25) Some useful matrix and vector / array commands –zeros(n,m): Creates an n x m matrix full of zeros –zeros(1,n) or zeros(n,1) : Creates an array / vector that has n elements, full of zeros

47 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Vectors and Matrices – (26) Last important note: –MATLAB evaluates expressions to the right of the equals sign first –After, it assigns this result to the variable to the left of the equals sign –Here’s an example: sum = 2; sum = sum + 3; –What happens here? sum gets assigned the value of 2 first, then it gets added with 3, and stored back into sum … and that’s it for this section… whew!

48 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Outline of Tutorial – (1) Introduction Getting Started Variables and Starting Basics Vectors and Matrices Basic Operations Script Files Function Script Files

49 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Operations – (1) Let’s assume the following: –A and B : Are matrices or vectors / arrays of compatible dimensions Assume they can be added, subtracted, multiplied and divided properly –n is a scalar (single value number) Here’s a table that provides a good summary of all of the basic operations you can perform on matrices and vectors / arrays

50 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Operations – (2) Here, the elements in the matrices or vectors / arrays can be real or complex Addition and Subtraction will just add and subtract two matrices normally For vectors, each corresponding component gets added or subtracted

51 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Operations – (3)

52 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Operations – (4) Multiplication (this kind) only works for matrices –* is for matrix multiplication Division is a little bit more complicated –We have left division and right division Left Division == A -1 B Right Division == AB -1

53 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Operations – (5) Transposition: Transposes a matrix or vector –‘ operator Real valued entries: Normal Transpose Complex valued entries: Tranposes and performs complex conjugate –.’ operator Real and Complex valued entries: Normal Transpose

54 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Operations – (6)

55 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Operations – (7) Exponentiation multiplies a matrix with itself n times For calculations with *, /, \, and ^, there is something called element-by-element operations for vectors / arrays and matrices –You put a dot operator (. ) before the operation Example:.* or./ or.\ or.^ –The 1 st element of A is *, /, \ or ^ with the 1 st element of B, and that result gets stored –… don’t get it? Here’s an example

56 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Operations – (8)

57 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Operations – (9) Special Case: –If you wanted to multiply or divide every number in a matrix or vector / array by a constant, you can just simply do the following: Example: t = 0 : 2 : 20;  t = [0 2 4 … 18 20]; g = 2*t;  g = [0 4 8 … 36 40]; or g = 2.*t; h = t/4;  h = [ … 4.5 5]; or h = t./4; All you have to do is multiply or divide by the desired number –No need to create another matrix or vector / array and do point-by- point multiplication or division!

58 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Operations – (10) Special Case #2: –If you wanted to add or subtract every number in a matrix or vector / array by a constant, you can just simply do the following: Example: t = 0 : 20;  t = [0 2 4 … 18 20]; g = t + 2;  g = [2 4 6 … 20 22]; h = t - 4;  h = [ … 16 18]; All you have to do is add or subtract by the desired number –No need to create another matrix or vector / array and add or subtract that way!

59 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Operations – (10) Here are some useful commands for matrices and vectors / arrays: Assume that V is a vector of arbitrary length and M is a matrix of arbitrary size len = length(V); –Gives the number of elements the vector V has, and stores it into len [rows cols] = size(M); –Gives the number of rows and columns and stores them into rows and cols respectively –Don’t worry about the square braces for now, we’ll deal with them later.

60 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Operations – (11) sum(V) : Returns the sum of all elements contained in vector V sum(M) : Returns a row vector, where each element is the sum of the columns of matrix M … confused? Don’t worry, check out this example

61 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Operations – (12)

62 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Operations – (13) prod(V) : Returns the product of all elements contained in vector V –We multiply every single element in the vector with each other prod(M) : Returns a row vector, where each element is the product of the columns of matrix M … confused? Don’t worry, check out this example

63 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Operations – (14)

64 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Operations – (15) Quick quiz: –Suppose I perform this operation: V = n : -1 : 1; –n can be any number > 0 sum = prod(V); –What is the above operation equivalently called in mathematics? –…you’ve seen this before. Think MTH 314

65 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Operations – (16) It’s a factorial! Anyway, let’s keep going max(V) / min(V) : Returns the maximum / minimum of all elements contained in vector V max(M) / min(M) : Returns a row vector, where each element is the maximum / minimum of the columns of matrix M … confused again? No worries, here’s another example

66 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Operations – (17)

67 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Outline of Tutorial – (1) Introduction Getting Started Variables and Starting Basics Vectors and Matrices Basic Operations Script Files Function Script Files

68 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Script Files – (1) So far, you’ve seen that MATLAB can accept and execute commands interactively through the command prompt –… what happens if you’ve got A LOT of commands to execute? Think C or Java: You put all commands or syntax into a file and execute that file. You can do this with MATLAB, and you don’t have to input all of the commands individually.

69 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Script Files – (2) This kind of file is called a script file or M-file (M for MATLAB!) –You place all commands you want to execute in a file with extension.m at the end, and you run the script file –MATLAB will run all of these commands in sequence for you To execute a script file, make sure you set the working directory to be where the script file is located (remember I said we’d get back to this earlier?)

70 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Script Files – (3)

71 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Script Files – (4) MATLAB has a M-file editor that you can use where you can create your scripts –You can also use any other word processing editor. Just make sure the extension of the file is.m –It’s got: Some nice colour coding features Debugging Tools Interoperability with the MATLAB command prompt

72 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Script Files – (5)

73 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Script Files – (6) Once a script file has been created, type in the name of the file (without the.m) in the command prompt to execute the script –Make sure you set the proper working directory! When you execute a script file, all of the variables created in the script file get stored in the workspace for future use Let’s do an example: –Let’s make the factorial example into a script file

74 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Script Files – (7)

75 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Script Files – (8)

76 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Script Files – (9) The great thing about script files is that commands can be re-executed without having to enter them all again! –All you have to do is modify parts of the script file to give you the result you want The script file is now set to compute 4! What if I wanted to do 9!, or 12!, or 5! ? –Just change the n parameter accordingly

77 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Outline of Tutorial – (1) Introduction Getting Started Variables and Starting Basics Vectors and Matrices Basic Operations Script Files Function Script Files

78 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Function Script Files – (1) So, you’ve seen how script files work –So what are function script files? Think Java: These are methods –You send input variables into a function Difference: You don’t have to define what the variable types are. Remember: Dynamically Typed! –The function performs MATLAB commands with these input variables –The function returns output variables Difference: You can return more than one variable! You don’t have to define the variable type either! Unlike C or Java, you do not require return statements to return variables –All you have to do is assign something to the variable, and that’s it.

79 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Function Script Files – (2) Why would you want function script files? –Instead of changing some parts of a script file, you can do these changes by providing different variables to the input of the function –There may be a case where when you run a script, you don’t want variables created in the script to be saved to the workspace Function scripts only communicate with the MATLAB workspace with: –The variables that you pass to it –The variables that get sent to the output after it’s finished

80 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Function Script Files – (3) What does this mean? –Any variables you create within the function will be discarded after the function has finished executing –This is what we call local scope How do we create a function script file? –Pretty much the same as a normal script file.m as the extension to the file –Remember, with a script file, all you had to do was enter in the commands in sequence

81 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Function Script Files – (4) However, there are two differences between a script file, and a function script file –The file name of the function has to be the same as the function itself –The first line of a function script file must be the following: function [output1, output2,…] = function_name(input1, input2, …)

82 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Function Script Files – (5) The function keyword means that this script file is a function script file input1, input2, … represents the input variables going into the function output1, output2, … represents the output variables going into the function You may have noticed that there are square braces ( [ ] ) surrounding the output variables in the function header –In order to return more than one variable, MATLAB puts all of the variables into one vector and returns this vector, hence the [ ] … smart eh?

83 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Function Script Files – (6) Use the % operator to put in comments –If you want to perform the modulus, use the mod function –mod(x,y) == x % y in C or Java If you want to comment out a block of code, do the following: %{ … commands that are commented out … %} When you’re coding a function script file, it’s a good idea to put an author’s block at the beginning of the file, that tells someone how the function works, what inputs you need, what outputs come out, and how to use it

84 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Function Script Files – (7) Some examples of function script files that you have seen already: –eye(n) Input: number n, n > 0 Output: n x n identity matrix –prod(V), prod(M) Input: Vector V or Matrix M Output: A number or a vector –sum(V), sum(M) Input: Vector V or Matrix M Output: A number or a vector –max(V), max(M) Input: Vector V or Matrix M Output: A number or a vector –min(V), min(M) Input: Vector V or Matrix M Output: A number or a vector

85 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Function Script Files – (8) Here’s another one that you saw earlier: –[rows cols] = size(M) Input: Matrix M Output: 2 numbers, the rows and columns of the matrix –When you call this function script file in MATLAB, make sure the square braces are there –This is required if the function script file returns more than 1 variable –Failing to do this will result in the very last output variable to be saved instead

86 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Function Script Files – (9) So now with this, let’s go back to our factorial example and make this a function script file What do we need to do in order to make this a function script file? –Think back to the two differences that I said earlier about script files and function script files

87 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Function Script Files – (10)

88 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Function Script Files – (11)

89 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Function Script Files – (12) Some important things to be reminded of: –n in the function script file is not saved to the workspace n has a local scope! –Instead of changing the parameter n, as we did in a script file, we simply changed the input parameter of the function –If your function returns more than one variable, make sure you save them to a vector!

90 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Outline of Tutorial – (1) Introduction Getting Started Variables and Starting Basics Vectors and Matrices Basic Operations Script Files Function Script Files

91 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Outline of Tutorial – (2) Flow Control Basic Graphics Commands Other Useful Commands Final Words

92 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Flow Control – (1) You’ve seen this in C or Java many times Flow control allows your script or function script file to have decision making abilities …understand what I mean? If you don’t, MATLAB supports the following common flow control methods –for loop –while loop –if-else & else-if statements –switch-case-otherwise statements … now you see what I mean right?

93 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Flow Control – (2) for loops allow a group of commands to be executed a predetermined amount of times This loop has the following structure: for i = any_array … commands to be executed … end any_array is any valid array Can be any row or column vector

94 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Flow Control – (3) How this for loop works is as follows: –1 st iteration, i = any_array(1), then execute commands –2 nd iteration, i = any_array(2), then execute commands –… –n th iteration, i = any_array(n), then execute commands This can prove to be a very powerful mechanism –Your for loop indices never have to be in uniform steps! Don’t know what I mean?... Let’s do an example

95 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Flow Control – (4) First Example: for loop in uniform steps –f = 1; for i = 1:n f = f*i; end –Here, we’re computing our factorial function, but with the use of a for loop i is assigned 1 for the 1 st iteration, 2 for the 2 nd iteration, and n for the n th iteration For each iteration, we take the previous value of f and multiply by the current value of i

96 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Flow Control – (5) Second Example: for loop in non-uniform steps –val = 0; array = 1 : 20; for i = [ ] val = val + array(i); end –Here, we’re computing the sum of random elements in an array and storing them into val Take a close look at what I did in the for loop The 1 st iteration, i = 1, the 2 nd iteration, i = 4, the 3 rd iteration, i = 8, and so on Pretty cool eh!? You don’t have to have uniform steps in your for loops!

97 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Flow Control – (6) while loops let you execute a group of commands indefinitely until a condition is met The structure for this loop is as follows: while expression … commands to be executed … end

98 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Flow Control – (7) The commands between the while and the end statements are executed until expression is evaluated as false, or a zero (0) value You usually use relational or equality operators in the expression statement of the while loop A relational or equality expression is assigned a value of 1 if it’s true, and 0 if it’s false

99 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Flow Control – (8) Everything here is the same as C and Java, except for the not equals to operator. MATLAB has it as ~=, and C or Java has it as !=… be careful not to mix these up!

100 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Flow Control – (9) if-else & else-if statements help you execute blocks of commands when some condition is true Here’s the syntax for it… but I’m sure you already know this if exp_1 … commands to be executed if exp_1 is true … elseif exp_2 … commands to be executed if exp_2 is true … elseif exp_3 … commands to be executed if exp_3 is true … else … commands to be executed if none of the above is true … end

101 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Flow Control – (10) Note the following: –elseif and else operators are optional –You can have if statements by themselves as well without the above operators The break command: –Used often in for and while loops –When this command is encountered, the loop stops executing immediately and carries onto the next block of code –If you’re using this within nested loops, the inner most loop stops executing only

102 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Flow Control – (11) switch-case-otherwise statements are a special case (no pun intended) of the if-else & else-if statements You choose between a finite number of choices; each choice consists of a block of commands to be executed If the choice you make is none of the choices provided in this statement, we execute a default ( otherwise ) code block … so this is what this kind of statement looks like:

103 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Flow Control – (12) switch expr case value1, … commands to be executed if expr equals value1 … case value2, … commands to be executed if expr equals value2 … … otherwise, … commands to be executed if the value of expr is not equal to any of the above values … end You usually use switch statements when you want your program to run differently, based on the input parameters that are given to your function script file

104 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Flow Control – (13) Let’s do an example! –Let’s use the while and if-else statements to make a simple program –You all have studied logic gates in COE 328, so let’s use some simple facts from this –Let’s make a program that will classify a set of input voltages according to the following specs: If V out is between 0V and 0.5V, this is a logic 0 (0) If V out is between 2.7V and 5V, this is a logic 1 (1) All other voltages are classified as invalid (-1) –The program will read in an array of continuous input voltages, and output an array of the same size –Each element will take 1 of 3 possible values: 0, 1 and -1

105 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Flow Control – (14) What do I need to do? –Set up a function script file with the function keyword, and the appropriate inputs and outputs Let’s call this function: classify_TTL Inputs: V, an array of continuous input voltages Outputs: logic_levels, an classification array telling you whether you have logic 0, logic 1, or invalid voltages –Naturally, you want to use a for or while loop for this program because you want to check through every element in this input array –You use an if-else statement to check to see what the voltage inputs are, then you classify accordingly

106 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Flow Control – (15)

107 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Flow Control – (16)

108 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Flow Control – (17) Above, I declared an array of 7 input voltages and ran the function The 2 nd element is valid as logic 0 because it’s between 0V and 0.5V The 5 th and 6 th element is valid as logic 1 because they’re between 2.7V and 5V The rest are invalid

109 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Outline of Tutorial – (2) Flow Control Basic Graphics Commands Other Useful Commands Final Words

110 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (1) MATLAB provides a variety of sophisticated techniques for presenting and visualizing data Also, MATLAB makes it very easy to plot data! –I have never used MS Excel ever again because MATLAB makes it easy! The watered down version: –Provide an array of values for each set of axes –Run a function that plots things for you –Run a few more commands that will make a grid, set the title of the graph, the title of the axes and so on

111 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (2) 2D plotting: MATLAB makes this very easy! –If x and y are arrays of elements that are the same size, you can plot them using this data with the following command: plot(x, y); –This will bring up a window plotting a graph of y vs. x –To plot something simple, that’s just about it!

112 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (3) Here’s a basic example if you don’t believe me Let’s say I wanted to plot the line y = x Let’s choose 101 points between 0 to 10 in steps of 0.1 Here’s the syntax I’d use: … and that’s it! This is what the graph looks like…

113 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (4)

114 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (5) If you want to plot multiple plots on a single graph, you do the following: plot(x1,y1,x2,y2,…,xN,yN); N is the number of plots you want to appear on the single graph xi and yi are the points to the i th graph you want plotted on the single graph The number of elements between (x1,y1), (x2,y2), … (xN,yN) must all be the same!

115 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (6) Let’s do another example: –Let’s plot the following 5 lines: y1 = 0.1x y2 = 0.5x y3 = 2x y4 = 5x y5 = 10x –For now, let’s make them all go from 0 to 10 in step sizes of 0.1 –These plots don’t all have to have the same step size!

116 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (7) This is what I’d put into the command prompt in MATLAB –You can also make a script file too if you want! … and this is what the graph looks like!

117 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (8)

118 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (9) MATLAB automatically colour codes the different plots that are on the graph This graph looks pretty plain… there’s gotta be more that you can add, and yes you can You can add a title, label the axes, put a grid on and even a legend! –You can add these in the graph GUI that you’ve just seen, or do it through the command prompt

119 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (10) So let’s say I wanted to add a title, add a grid, label the axes and put up a legend, how would I do that?

120 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (11)

121 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (12) grid puts a grid on the graph –The spacing for the grid is automatically figured out by MATLAB title(‘…’) lets your graph have a title xlabel(‘…’), ylabel(‘…’) labels the x and y axes accordingly –Put the labels inside the quotations –Don’t forget the quotations ‘ ‘! legend(‘…’, ‘…’, …, ‘…’) produces a legend, labeling what each plot is on the graph

122 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (13) Remember, for the legend command, you label the plots the same order as how you plotted them! By default, MATLAB takes all points and connects them with a solid line, and it’s got its own way of determining which colour belongs to what plot Is there a way to control this?... Yes there is!

123 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (14) In addition to the x and y points, you specify an additional parameter: plot(x, y, ‘line_style’); line_style is a character string of 2 characters –The 1 st character specifies the colour of your plot –The 2 nd character specifies how your plot will be plotted on the graph, or the plot style

124 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (15) Supported colours: –blue, green, red, cyan, magenta, yellow, black Supported plot styles:

125 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (16) Examples: x = 0:0.1:10; y = x; –plot(x,y,’g.’); This will plot a green line with dots at each point –plot(x,y,’bo’); This will plot a blue line with circles at each point –plot(x,y,'rx’); This will plot a red line with crosses at each point

126 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (17) Like how we saw before, you can put multiple plots on a single graph, each with their own colour and plot styles with the following: plot(x1, y1, ’line_style1’, x2, y2, ’line_style2’,..., xN, yN, ’line_styleN’); N is the number of plots you want to appear on the single graph xi and yi are the points to the i th graph you want plotted on the single graph line_stylei is the plot style and colour of that i th graph The number of elements between (x1,y1), (x2,y2), … (xN,yN) must all be the same!

127 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (18) There is also a way to produce multiple graphs in one window –You can have more than 1 graph in one window at a time! You do this by using the subplot command The subplot command treats the window as if it had multiple slots –Each slot takes in a graph

128 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (19) How do we use the subplot command? –subplot(m,n,p) or subplot(mnp) –m and n you need to know before hand These determine the number of rows (m) and columns (n) for the amount of graphs you want p determines which location in the window you want the plot to go to The order is from left to right, top to bottom –In order to properly use subplot, you must call this function first –After, you code the syntax to plot something normally

129 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (20) Here’s a small example: –If I wanted to make a window that has 4 plots, 2 plots in each row  2 rows, here’s what I’d do Do subplot(221)  Specify that we want to work on the top left corner Next, code the syntax to plot normally. The plot will appear on the top left corner Do subplot(222)  Specify that we want to work on the top right corner Next, code the syntax to plot normally. The plot will appear on the top right corner Do subplot(223)  Specify that we want to work on the bottom left corner Next, code the syntax to plot normally. The plot will appear on the bottom left corner Do subplot(224)  Specify that we want to work on the bottom right corner Next, code the syntax to plot normally. The plot will appear on the bottom right corner

130 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (21) Let’s do another example… in case you didn’t get what I meant earlier Let’s make 4 graphs, have 2 rows and 2 columns for the window. Each graph will have one plot. –Let’s make each plot the following: 1. y1 = sin(x); 2. y2 = cos(x); 3. y3 = 3x; 4. y4 = 6x; –Let’s make the range of the plot go from: x = -10 : 0.1 : 10;… now what?

131 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (22)

132 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (23) 1 st step  Use the figure command –This produces a new, blank, window Use the subplot command to specify the number of rows and columns and which plot you want to draw first –Number ordering convention  Left to right, top to bottom Code the normal syntax you need to produce a plot. Use the plot command when you’re done Use the subplot command again to go to the next area, and code the plot syntax again Repeat until you’re done … and here’s what the window looks like!

133 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (24)

134 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Basic Graphics Commands – (25) Some functions, like cos and sin take in, not only single values, but vectors / arrays and matrices cos and sin apply their respective mathematical operations to every element if the input is a vector / array, or matrix The output will be a vector / array, or matrix, of the same size, with the function applied to each element in that memory chunk

135 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Outline of Tutorial – (2) Flow Control Basic Graphics Commands Other Useful Commands Final Words

136 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Other Useful Commands – (1) MATLAB has a great help facility, both through its interface and online If you need help regarding how a certain command works, type in the following in the command prompt: –help command command is the command you want to look up and to see how it works

137 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Other Useful Commands – (2) If you don’t know what a particular function is called, you can use the lookfor command It’s called the following way: –lookfor command Where command is the function you’re looking for MATLAB searches all of its libraries that are related to command

138 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Other Useful Commands – (3) A list of all of the MATLAB commands you have invoked in a session in the command prompt can be written into a file with the diary command You call this command this way in the command prompt diary diary_file diary_file is the name of the file where your commands you invoked in that session will be stored If the file already exists, your commands in the current session will be appended to the file Use diary off to turn off the diary command, and diary on to reactivate it

139 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Outline of Tutorial – (2) Flow Control Basic Graphics Commands Other Useful Commands Final Words

140 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Final Words – (1) This tutorial provided you the basics of how to use MATLAB and enough to get you started with these labs This tutorial, however, is not exhaustive –There are still a lot of commands out there that perform really cool stuff for you –Consider taking some time to look at them and see how cool MATLAB is Always use the help and lookfor commands when you’re learning a new function If all else fails, ask me!

141 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Final Words – (2) I adapted this tutorial from Dr. Y. C. Chen’s – “Introduction to MATLAB” tutorial and can be found here: –http://www.ee.ryerson.ca/~rphan/matlabtutorial.pdfhttp://www.ee.ryerson.ca/~rphan/matlabtutorial.pdf I also wrote a tutorial for the Ryerson IEEE Student Branch website 3 years ago, and can be found here: –http://www.ee.ryerson.ca/~ieee/articles/MATLAB.htmlhttp://www.ee.ryerson.ca/~ieee/articles/MATLAB.html

142 ELE 532 – Signals and Systems MATLAB Tutorial Friday, September 14th, Thanks For Listening! Any Questions?


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