INTRODUCTION TO MATLAB

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• MATLAB is originally designed for matrix manipulation
• Many signal processing functions available, eg. convolution, Fourier Transform, …
• MATLAB environment symbol: ‘>>’
• Data represented in matrix/vector form

• Defining a vector of linear elements

>>b=0:0.2:1;

% b=[0 0.2 0.4 0.6 0.8 1]

• Defining a matrix

>>A=[1 2 3; 4 5 6; 7 8 9];

‘;’ : end of row indicator

A is a 3x3 matrix, A(1,1)=1, A(1,3)=3, A(3,2)=8, etc.

• Appending a matrix

>>r=[10 11 12];

>>A=[A;r];

A is now a 4x3 matrix, A(4,1)=10, etc.

• Arithmetric operations

+, -	:	matrix addition and subtraction
*	:	matrix multiplication
^	:	matrix power, A^3=A*A*A
‘	:	matrix transpose
.*	:	element by element multiplication
./	:	element by element division

• Complex number

by default

>>z=9+7*i;

% define a complex number, real(z)=9, imag(z)=7

• Control flow:

>>for i=1:10,	% for loop
x(i)=i;
end;	% x=[1 2 3 4 5 6 7 8 9 10]
>>
>>i=1;	% while loop
>>while i<=10,
x(i)=i;
i=i+1;
end;	% x=[1 2 3 4 5 6 7 8 9 10]
>>if (x(1)= =1)	% if statement
x=x*2;
else
x=x/2;
end;	% x=[2 4 6 8 10 12 14 16 18 20]

• Relational operator

&	:	logical and
|	:	logical or
~	:	not
= =	:	equal
~=	:	not equal

• Built-in functions

sin(x), cos(x), sqrt(x), length(x), log(x), …

• User defined function

example:

% a function that computes the mean and standard deviation

% of the elements in a vector x

% function name is stat

% must be saved using the function name with extension .m,

% i.e. stat.m

function [mean,stdev] = stat(x)

L=length(x);

mean=sum(x)/L;

stdev=sqrt(sum(x.^2)/L-mean^2);

• Script file

a text file that contains MATLAB commands, must be saved with extension ".m"

key in filename without extension in MATLAB executes the commands in the scrip file

example:

% a script file that calls function stat

% script file saved as test.m

x=41:50;	% define data
time=1:10;
plot(time,x);	% plot the data vector x
[mean,stdev] = stat(x);	% call function stat, returned
	% values in mean and stdev
fprintf('mean: %3.2f\n',mean);
fprintf('standard deviation: %2.4f\n',stdev);
>>test	% run the commands in test.m
>>mean: 45.50
>>standard deviation: 2.8722

• Data I/O

>>save abc.mat	% save the whole workspace
>>load abc	% load entire workspace
>>save xy.dat x y -ascii	% save variables x and y in xy.dat
>>load xy.dat	% load the data stored in the file
	% result in vector xy

• Online help in Matlab

>>help zeros

% explain how ‘zeros’ works