Biomedical Engineering Reference
In-Depth Information
Appendix
John D. Enderle, PhD
A.1 MATLAB
MATLAB is a high-level computer program that performs technical computing and plot-
ting based on matrices. It is a programming language that has many of the same capabilities
as FORTRAN, C and other programming languages, but is much easier to use. This section
introduces the reader to MATLAB in sufficient detail so that the program can be used to
solve relevant problems in this topic. Other MATLAB features are introduced in later chap-
ters as needed.
A.1.1 Matrix Basics
MATLAB was originally developed as MATrix LABoratory, with most commands stated
in terms of matrices. A matrix is a rectangular array consisting of
n
rows and
m
columns of
elements. The array
A
, denoted with a bold uppercase letter, is denoted as
. . .
a
11
a
12
a
1
m
. . .
a
21
a
22
a
2
m
A
=
ð
A
:
1
Þ
a
n
1
a
n
2
. . .
a
nm
where each element of the array,
a
ij
, is a constant or a function. The order of array
A
is
referred to as
. For our purposes,
the matrix
A
usually stores the parameters for a system, such as values for resistors,
capacitors and inductors.
An array of one column is referred to as a column vector, that is, an array of order
n
m
.If
n
¼
m
,
A
is called a square matrix of order
n
n
1.
We typically denote a column vector with a bold lowercase letter, such as
x
1
x
2
x
ð
A
:
2
Þ
=
x
n
where each element
x
i
is a variable, constant or a function of time. The column vector is useful
for representing variables and inputs for a system. An array of one row is referred to as a row
vector, that is, an array of order 1
. The row vector is useful for representing a polynomial
of the characteristic function (defined later) for a system. A matrix of order 1
n
1 is a scalar.
