Transcript DISP-2003: Introduction to Digital Signal Processing

INTRODUCTION TO
MATLAB
Dr. Hugh Blanton
ENTC 4347
TOPICS
1.
2.
3.
4.
5.
6.
Basic MATLAB
Matrices
Operators
Script and function files
Flow control
Plotting
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MATLAB
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Basic MATLAB
optional windows
workspace
current directory
type commands here
command window
screen shot of the Matlab window
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Matlab’s help features
type “help” at the command prompt
and Matlab returns a list of help topics
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Matlab’s help features
>> help lang
Matlab’s language constructs
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Matlab’s help features
>> help for
how to use Matlab’s “for” statement
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Matlab’s help features
you can also access “on-line” help by clicking the
question mark in the toolbar
separate window
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MATLAB Variables
all variables are stored in 32bit floating point format
no distinction between real and integer
>>a = 3;
same assignment for “a”
>>a = 3.0;
Matlab is case sensitive
>>A=3;
Aa
>>a=2;
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MATLAB Variables
can use numbers and underscore in variable names
>>case34=6.45;
OK
>>case_34=6.45;
names must start with a letter
>>34case=23.45;
results in a syntax error
string (text) variables enclosed in single quotes.
The variable is stored as array of characters
>>title=‘This is the title’;
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MATLAB Variables
if a variable is defined,
typing the variable name returns its value
>>a=45.57;
>>a
a=
45.57
Matlab returns the value
to clear a variable from memory
>>a=4
>>clear a
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MATLAB Variables
Matlab will “echo” commands unless a semi-colon is used
>>a=23.2;
>>
>>a=23.2
a=
23.2
>>
Matlab echoes the command
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MATLAB Variables
column vectors
Vectors
1 
 
a  2 
3 
 
a  1 2 3
>>a=[1;2;3];
>>a
a=
1
2
3
>>a=[1,2,3];
>>a
a=
1 2 3
use comma
to separate columns
use semi-colon
to separate rows
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row vectors
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MATLAB Variables
Matrices
2-dimensional matrices
1 2 3
a

4
5
6


>>a=[1,2,3;4,5,6];
>>a
a=
1 2 3
4 5 6
again, separate columns with commas and rows with semi-colons
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MATLAB Variables
Indexing Matrix elements
A vector is a special type of matrix
row vector is a 1 x n matrix, 1 row n columns
column vector is a n x 1 matrix, n rows 1 column
>>a=[1,2,3];
>>a(2)
ans =
2
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could also reference by a(1,2)
note, a(2,1) would produce an error
because “a” only has one row
MATLAB
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MATLAB Variables
Indexing Matrix elements
more examples
1 2 3
a

4
5
6


>>a=[1,2,3;4,5,6];
assigning
addressing
>>a(2,2)=9;
>>a
a=
1 2 3
4 9 6
>>a(2,3)
ans =
6
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MATLAB Variables
complex-valued numbers
Typically, the variable “i” or “j” is used to represent the
complex variable; e.g.
i  1
Then, a complex number is represented as
z = a + ib
Re(z) = a
Im(z) = b
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MATLAB Variables
complex-valued numbers
Unless i or j has been previously defined, Matlab assigns
i and j the complex variable value
In Matlab, a complex variable is represented in the
following format
(assuming all variables are cleared)
>>z=23+i*56;
>>z=23+j*56;
>>z
>>z
z=
z=
23.00 + 56.00i
23.00 + 56.00i
Matlab always uses the symbol “i” to represent a complex number
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MATLAB Variables
complex-valued numbers
What happens in this case?
What happens in this case?
>>i=3;
>> z=23+i*56;
>>z
z=
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>>a=sqrt(-1);
>>z=23+a*56;
>>z
z=
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MATLAB Variables
complex-valued numbers
Note, a real-valued number is a special case of a
complex-valued number
assigning any element of a matrix as complex-valued
makes the entire matrix complex-valued
>>a=[1,2];
>>a
a=
1 2
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>>a(1)=1+i*5;
>>a
a=
1.00+5.00i
MATLAB
2.00+0.00i
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MATLAB Variables
Advanced data types
n-dimensional arrays
structures
cell arrays
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MATLAB Variables
Basic operations
addition
subtraction
multiplication
division
right division
left division
>>a=3;b=4;
>>c1=a/b;
>>c2=a\b;
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+
*
/
\
c1=0.75
c2=1.3333….
MATLAB
?
so, be careful!
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MATLAB Variables
Mixed Real and Complex valued Variables
if both variables are real-valued, a real-valued result is obtained
if one variable is complex-valued, Matlab recasts the real
variable as complex and then performs the operation. The
result is complex-valued
however, the type casting is done internally, the real-valued
variable remains real after the operation
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MATLAB Variables
Other (Scalar) Operations
Math representation
Matlab interpretation
z  yx
>>z=y^x;
y  ex
>>y=exp(x);
y  ln(x)
>>y=log(x);
y  log(x)
>>y=log10(x)
y  sin(x) y  sin 1 (x)
>>y=sin(x);
>>y=asin(x);
y  cos(x) y  cos 1 (x)
>>y=cos(x);
>>y=acos(x);
y  tan(x) y  tan 1 (x)
>>y=tan(x);
>>y=atan(x);
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MATLAB Variables
Examples
>>y=x^0.5;
>>y=x^(1/2);
>>y=sqrt(x);
y x
All variables in the preceding operations can be
real or complex, negative or positive
for x < 0, y is complex. Matlab assumes you allow complex
valued numbers. If y is not to be complex, you must
provide error checking.
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MATLAB Variables
Matrices
•Only matrices of the same dimension can be added and subtracted
•For multiplication, the inner dimensions must be the same
4 5
1 2 3
2 3 4
6 7 
A
C

B




4
5
6
5
6
7




 8 9 
Error
No error
>>D=A+C;
>>D=A*B;
>>D=A+B;
>>D=B*A;
>>D=A-B; Matrix multiplication
>>D=A*C; not commutative
>>D=C*A;
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MATLAB Variables
Left(\) and Right(/) Matrix “division”
Math representation
Matlab interpretation
C  A 1B
>>C=A\B;
C  BA 1
>>C=B/A;
Remember, A must be square and full rank
(linearly independent rows/columns)
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MATLAB Variables
Matrix Transpose
Math representation
Matlab interpretation
>>C=A’;
C  AT
For complex-valued matrices, complex conjugate transpose
1 2 3
A

4
5
6


a  1  j2 3  j4
>>B=A’;
>>b=a’;
1 4
B  2 5


 3 6 
1  j2 
b

3

j4


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MATLAB m-files
Two types of m-files
script files
collection of commands that Matlab executes
when the script is “run”
function files
collection of commands which together
represent a function, a procedure or a method
Both types are separate files with a “.m” extension
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MATLAB m-files
To create an m-file, open the Matlab text editor
Click on the “page” icon
The Matlab text editor window will open
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MATLAB m-files
Script Files
On the command line
In the script file named test.m
>>x=3.0;
>>y=x^2;
>>y
y =
9.0
>>
On the command line
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>>test
y =
9.0
>>
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MATLAB m-files
Script Files
script files share the workspace memory
test.m script
>>x=5.0;
>>test
>>y
y =
25.0
>>
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MATLAB m-files
Script Files
script files can call other script files
inner.m script
>>outter
y =
36.0
>>
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outter.m script
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MATLAB m-files
Function Files
Matlab identifies function files from script files by
using the “function” and “return” keywords
the name of the function file must be
the same name as the function
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MATLAB m-files
Function Files
The function file x2.m
Dr. Blanton
>>r=3;
>>d=x2(r);
>>d
d =
9.0
>>
- ENTC 4347 MATLAB
>>h=x2(4.2);
>>h
h =
17.64
>>
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MATLAB m-files
Function Files
Multiple Inputs and Outputs
outputs in square brackets, [ ]
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inputs in parentheses ( )
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MATLAB m-files
Function Files
variables created in the function are not retained
in the workspace, except for the output variables
the function does not have access to workspace
variables, except for the inputs
variables passed to the function are “copies” of the
workspace variables. Changing their value inside the
function has no effect on their value in the workspace.
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MATLAB Flow Control
The “while” and “if” statements
while expression
statements
end
if expression
statements
end
if expression
statements1
else
statements2
end
Matlab evaluates expression as logical “true” or “false”
“false” equivalent to zero
“true” equivalent to any non-zero number
statements, any valid Matlab command
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MATLAB Flow Control
evaluating expression
conditional operators
==
equal to
<
less than
>
greater than
<= less than or equal to
>= greater than or equal to
~= not equal to
any valid equation
a=4;
b=5;
c=5;
if a+b “True”
if b-c “False”
watch out for round-off
and word length error
logical operators
& and
| or
if sin(0) “False”
if sin(pi) “True”
sin(pi) = 1.22e-16
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while(3<=a)&(a<=5)
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MATLAB Flow Control
The “for” statement
for index = start : [increment :] end
statements
end
index, start, increment, and end do not need to be integer valued
increment is optional, if increment is not specified
increment defaults to 1
index can be incremented positive (increment > 0) or
negative (increment < 0)
loop stops when index > end (or index < end)
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MATLAB Flow Control
example
script file to cycle through x values
function file to generate the y values
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MATLAB PLOTTING
Basic 2D plotting functions
plot(x1,y1[,x2,y2,x3,y3.....])
xlabel(‘x axis name’)
ylabel(‘y axis name’)
title(‘graph name’)
Additional functions
grid on
grid off
axis([xmin,xmax,ymin,ymax])
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MATLAB PLOTTING
example y = sin(t)
the “plot” function alone
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MATLAB PLOTTING
example y = sin(t)
script file to generate
a graph of y = sin(t)
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MATLAB PLOTTING
example y = sin(t)
function file to generate
a graph of y = sin(t)
>>graphsin
>>
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MATLAB PLOTTING
Adding a Legend for multiple graphs
“legend” remembers
the order the graphs
were plotted
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