Using MATLAB

Summary: This module covers basic use of MATLAB, and you will be up and running on variables, matrices, mathematical operations and the built-in help system in just a few minutes.

MATLAB has a great on-line help system accessible using the help command. Typing

help <function>

will return text information about the chosen function. For example to get information about the built-in function sum type:

help sum

To list the contents of a toolbox type help <toolbox>, e.g. to show all the functions of the signal processing toolbox enter

help signal processing

If you don't know the name of the function but a suitable keyword use the lookfor followed by a keyword string, e.g.

lookfor 'discrete fourier'

To explore the extensive help system use the "Help menu" or try the commands helpdesk or demo.

Matrices, vectors and scalars

MATLAB uses matrices as the basic variable type. Scalars and vectors are special cases of matrices having size 1x1, 1xN or Nx1. In MATLAB, there are a few conventions for entering data:

Elements of a row are separated with blanks or commas.
Each row is ended by a semicolon, ;.
A list of elements must be surrounded by square brackets, [ ]

EXAMPLE 1

It is easy to create basic variables.

x = 1 (scalar)

y = [2 4 6 8 10] (row vector)

z = [2; 4; 6; 8; 10] (column vector)

A = [4 3 2 1 0; 1 3 5 7 9] (2 x 5 matrix)

Regularly spaced values of a vector can be entered using the following compact notation

start:skip:end

EXAMPLE 2

A more compact way of entering variables than in Example 1 is shown here:

y= 2 : 2 : 10

A=[4:-1:0;1:2:9]

If the skip is omitted it will be set to 1, i.e., the following are equivalent

start:1:end and start:end

To create a string use the single quotation mark " ' ", e.g. by entering x = 'This is a string'.

Indexing matrices and vectors

Indexing variables is straightforward. Given a matrix M the element in the i'th row, j'th column is given by M(i,j). For a vector v the i'th element is given by v(i). Note that the lowest allowed index in MATLAB is 1. This is in contrast with many other programming languages (e.g. JAVA and C), as well as the common notation used in signal processing, where indexing starts at 0. The colon operator is also of great help when accessing specific parts of matrices and vectors, as shown below.

EXAMPLE 3

This example shows the use of the colon operator for indexing matrices and vectors.

A(1,:) returns the first row of the matrix A.

A(:,3) returns the third column of the matrix A.

A(2,1:5) returns the first five elements of the second row.

x(1:2:10) returns the first five odd-indexed elements of the vector x.

Basic operations

MATLAB has built-in functions for a number of arithmetic operations and functions. Most of them are straightforward to use. The Table below lists the some commonly used functions. Let x and y be scalars, M and N matrices.

TABLE 1: **Common mathematical operations in MATLAB**
	MATLAB
xy	`x*y`
x^y	`x^y`
e^x	`exp(x)`
log(x)	`log10(x)`
ln(x)	`log(x)`
log2(x)	`log2(x)`
MN	`M*N`
M^-1	`inv(M)`
M^T	`M'`
det(M)	`det(M)`

Dimensions - MATLAB functions length and size are used to find the dimensions of vectors and matrices, respectively.
Elementwise operations - If an arithmetic operation should be done on each component in a vector (or matrix), rather than on the vector (matrix) itself, then the operator should be preceded by ".", e.g .*, .^ and ./.

EXAMPLE 4

Elementwise operations, part I

Let A=(

1	1
1	1

). Then A^2 will return AA=(

2	2
2	2

), while A.^2 will return (

1²	1²
1²	1²

)=(

1	1
1	1

EXAMPLE 5

Elementwise operations, part II

Given a vector x, and a vector y having elements y(n)=

sin(x(n))

. This can be easily be done in MATLAB by typing y=1./sin(x) Note that using / in place of ./ would result in the (common) error Matrix dimensions must agree.

Complex numbers

MATLAB has excellent support for complex numbers with several built-in functions available. The imaginary unit is denoted by i or (as preferred in electrical engineering) j. To create complex variables z₁=7+ⅈ and z₂=2e^ⅈπ simply enter z1 = 7 + j and z2 = 2*exp(j*pi)

The Table below gives an overview of the basic functions for manipulating complex numbers, where z is a complex number.

TABLE 2:**Manipulating complex numbers in MATLAB**
	MATLAB
Re(z)	`real(z)`
Im(z)	`imag(z)`
\|z\|	`abs(z)`
Angle(z)	`angle(z)`
z^*	`conj(z)`

Other Useful Details

A semicolon added at the end of a line tells MATLAB to suppress the command output to the display.
MATLAB and case sensitivity. For variables MATLAB is case sensitive, i.e., b and B are different. For functions it is case insensitive, i.e., sum and SUM refer to the same function.
Often it is useful to split a statement over multiple lines. To split a statement across multiple lines, enter three periods "..." at the end of the line to indicate that it continues on the next line.