signals and systems matlab tutorial

ELE 532 – Signals and SystemsMATLAB Tutorial Friday, September 14th, 2007 5 Introduction – 2 • MATLAB is selected as a numerical analysis tool over languages like C and Java because: –

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ELE 532 – Signals and Systems

Raymond Phan

Distributed Multimedia Computing Research (DMCR) Lab

Ryerson University – EPH 237

rphan@ee.ryerson.ca

http://www.ee.ryerson.ca/~rphan/ele532/MATLABTutorial.ppt

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Outline of Tutorial – (1)

• Introduction

• Getting Started

• Variables and Starting Basics

• Vectors and Matrices

• Basic Operations

• Script Files

• Function Script Files

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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

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MATLAB Tutorial

Friday, September 14th, 2007

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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 4th year

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• 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

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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: http://www.mathworks.com

• “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

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MATLAB Tutorial

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Getting Started – (3)

– MATLAB Interface: >> means it’s ready for input from you

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– 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

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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

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(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

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– 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

pressing ENTER will redisplay the

variable

not assigning it to anything, the

value will be automatically assigned

to a variable called ans (answer)

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(6)

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• 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

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(8)

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– 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

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(10)

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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

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MATLAB Tutorial

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Vectors and Matrices – (1)

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

handle it this way?

– You’ll see later that handling variables as matrices

makes things A LOT faster and easier to work with

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MATLAB?

– C or Java way: int a[4] = {1, 2, 3, 4};

– MATLAB way:

• a = [1 2 3 4] – row vector

– Spaces mean to move to the next column

• a = [1 2 3 4].’ – (.’ operator means to transpose a

vector) - column vector

• a = [1;2;3;4] - column vector

– Semicolon means to move to the next row

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

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MATLAB Tutorial

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• How do I access elements

– No square brackets when accessing an

element! Use round brackets!

– Elements do not start at index 0, they start at

index 1!

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Vector and Matrices – (4)

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– C or Java way:

• int alan = a[2][3];

– MATLAB way:

• alan = a(3,4);

– 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

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MATLAB Tutorial

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• 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 1st row?

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• 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

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• Some more examples:

row, and assign this to sally

• 4th line: Get a matrix with elements between rows 2 – 4 and give me every possible

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MATLAB Tutorial

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– Joe = a(:,:);

– Joe = a;

entire matrix, a, and assign it

to Joe

• You can also do the 2 nd line

too It’s exactly the same

meaning

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• 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?

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making vectors / arrays where

consecutive elements are

uniformly spaced

• Example:

– Ray = 0 : 0.1 : 1.0;

with 11 elements, such that

– Ray = [0 0.1 0.2 0.3 … 1.0];

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– 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

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MATLAB Tutorial

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• 3 rd line: Creates an 10 element

vector

– ron = [1 2 3 … 9 10];

• 4 th line: Creates a 8 element vector

– mauro = [2.0 1.8 … 0.6 0.4];

• 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.

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vector / array

commands

– eye(n): Creates an n x n identity matrix

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MATLAB Tutorial

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• 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

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• 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

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MATLAB Tutorial

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• 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!

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MATLAB Tutorial

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Basic Operations – (1)

– 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)

a good summary of all of the basic operations you can

perform on matrices and

vectors / arrays

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vectors / arrays can be real or

complex

and subtract two matrices normally

component gets added or subtracted

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• 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 B

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• Real valued entries: Normal Transpose

• Complex valued entries: Tranposes and performs complex

conjugate

– ’ operator

• Real and Complex valued entries: Normal Transpose

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MATLAB Tutorial

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with itself n times

there is something called element operations for vectors /

element-by-arrays and matrices

– You put a dot operator ( ) before the operation

• Example: * or / or \ or ^

– The 1st element of A is *, /, \ or ^ with the 1st element of

B, and that result gets stored

– … don’t get it? Here’s an example

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– 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:

• 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!

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• 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

– No need to create another matrix or vector / array and add or

subtract that way!

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MATLAB Tutorial

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matrices and vectors / arrays:

length and M is a matrix of arbitrary size

– Gives the number of elements the vector V has, and

stores it into len

– 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.

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• 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

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• 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

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MATLAB Tutorial

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• 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

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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.

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MATLAB Tutorial

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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

you set the working directory to be where the script file is located

(remember I said we’d get back to

this earlier?)

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that you can use where you can create your scripts

editor Just make sure the extension of the file is m

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• 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

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