ECE 351

MATLAB INTRODUCTION(BY TEACHING ASSISTANTS)

WHY MATLAB? The name MATLAB (matrix laboratory), is

Developed by Mathworks.http://www.mathworks.com/products/matlab/index.html

While the software has progressed well beyond its original goal as a tool dedicated to performing matrix computations, it is still based on the notation of arrays and matrices.

The latest version is R2013b

MATLAB is a high-level language and interactive environment that enables you to perform computationally intensive tasks.

High-level language for technical computing Development environment for managing

code, files, and data

Interactive tools for iterative exploration, design, and problem solving

Mathematical functions for linear algebra, statistics, Fourier analysis, filtering, optimization, and numerical integration

2-D and 3-D graphics functions for visualizing data

MATRICES, ARRAYS AND VECTORS A matrix is simply a rectangular list of

numbers The "size" of a matrix is given as two numbers,

the first is traditionally the number of rows in the matrix while the second is the number of columns in the matrix.

Matrices are usually written in tabular form contained between two large parentheses or square brackets.

Arrays/vectors: matrices with only ONE row or column

Example A 2×3 （ two by three）matrix 34 56 31 -45 6 43

A 1×3 row vector 34 56 31

A 2×1 column vector 34 -45

TO START MATLAB Command window Single line commands, results Editor Edit scripts Workspace Store variables Current Folder Store files

TO START MATLAB

TO START MATLAB Command window Only one line a time Create a new .m file File->New->Script Check the usage of ‘;’, ‘%’, ‘%%’ Save and Run

PRESENT MATRICES IN MATLAB >> a=[1 2 3; 4 5 6]Or>> a=[1, 2, 3; 4, 5, 6]

Try on your own computer if you haven’t done so.

ARITHMETIC OPERATIONS Scalar operations: There are four scalar operations

addition: + subtraction: - multiplication: * division: /

Example>> a=[1 2 3; 4 5 6]>> b=3*a>> b=[3 6 9; 12 15 18]

Matrix Addition and Subtraction For two matrices to be added or

subtracted they must be of the same size. The entries are computed by adding or

subtracting the corresponding entries in the two original matrices.

Example >> a=[1 2 3; 4 5 6] >> b=[2 4 6; 3 5 7] >> c=a-b c=[-1 -2 -3; 1 0 -1]

Multiplication and Division 2 different types: componentwise and

conventional

Recall: How to multiply matrices?

2 1 1 03 0 4 2

Normal multiplication: A, B, C is n by n

In MATLAB >> C=A*B

A B C

1

n

jk ji iki

c a b

Componentwise multiplication: Same problem as before,

In MATLAB >> C=A.*B

jk jk jkc a b

FUNCTIONS AND SHORTCUTS

Functions: operations that can be called in a scripts

Zeros() Ones() Eye() Diag() Linspace() …

Zeros(n) to create an n by n matrix with all entries

zero. Zeros(n, m) create an n by m one. Ones(n) to create an n by n matrix with all entries 1.

Used as the same fashion as zeros(n) Eye(n) to create an n by n identity matrix. Diag([]) to create a diagonal matrix. Vector given

shows as diagonal elements.

Two shortcuts for row vectors:1. vector=a:n:bthe vector starts with a and end with b, n is the

step sizeExample>> t=1:0.5:3 t=1 1.5 2 2.5 3

If n is not given, default value is 1>> t=1:3 t=1 2 3

2 linspace(a, b, n) to create a row matrix with n elements, start

from a and end with b, with equal step size.Example: >> t=linspace(0,10,11)t=0 1 2 3 4 5 6 7 8 9 10

size() inv() []’ fft()

Functions can be self defined. Most functions work componentwise

SELF-DEFINED FUNCTION File->New->Function Input arguments Output arguments Function name How to call function

HOW TO PLOT FIGURES?Plot(x,y):2 vector input, x will be horizontal axis and y

be the vertical one.x, y must be the same size

s: applicable parameters: color, plot symbol, line type used as character strings.

t=0:0.1:5 y=sin(2*pi*t) Plot(t,y)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

t=0:0.001:5 y=sin(2*pi*t) Plot(t,y)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

plot(t,y,'--')

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

plot(t,y,'g')

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Legend, title and label

legend(‘strings1’,’strings2’…..’location’,’orientation’)

e.g legend('sin function') TitleTitle(‘text’) e.g title('function') LabelXlabel(‘text’) e.g xlabel('time')Similar: ylabel, zlabel

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

time

Am

plitu

de

function

sin function

Example 1 t=0:0.001:5 x=cos(2*pi*t) y=sin(2*pi*t) plot(t,x,'g') hold on plot(t,y,'r')

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Example 2 t=0:0.001:5 x=cos(2*pi*t) y=sin(2*pi*t) subplot(2,1,1) plot(t,x,'g') subplot(2,1,2) plot(t,y,'r')

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1

-0.5

0

0.5

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1

-0.5

0

0.5

1

HW1 t = (-2:0.01:2)/1000; a1 = 500; x1 = 20 * sin(2*pi*1000*t - pi/3) .* exp(-a1*t); a2 = 750; x2 = 20 * sin(2*pi*1000*t - pi/3) .* exp(-a2*t); a3 = 1000; x3 = 20 * sin(2*pi*1000*t - pi/3) .* exp(-a3*t); %Plot Resutls figure(1); clf; plot(t,x1,'b'); hold on plot(t,x2,'k:'); plot(t,x3,'r--'); hold off xlabel('time (sec)') ylabel('Amplitude') title('Exponentially Damped Sinusoid') axis([-2/1000 2/1000 -120 120]) legend('a = 500','a = 750','a = 1000')

HW1

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

x 10-3

-100

-50

0

50

100

time (sec)

Am

plitu

de

Exponentially Damped Sinusoid

a = 500a = 750a = 1000

2. semilogy(x, y, s) logarithmic (base 10) scale is used for the Y-

axis. Used as the same fashion as plot. Similar: semilogx, loglog.

Example:

BASIC PROGRAMMING SYNTAX FOR ‘for’ is used for repeating statements Example: t=0; for i=1:5 t=t+i; end

Also see WHILE

IF If Conditionally execute statements. Example t=0; for i=1:5 if i>3 t=t+i; end end

QUESTIONOS