1. INTRODUCTION TO MATLAB
Dr. Hugh Blanton
ENTC 4347

2. TOPICS Basic MATLAB Matrices Operators Script and function files
DISP-2003
TOPICS
Basic MATLAB
Matrices
Operators
Script and function files
Flow control
Plotting
Dr. Blanton - ENTC MATLAB / 45
Introduction to Digital Signal Processing

3. Basic MATLAB optional windows workspace current directory
type commands here
command window
screen shot of the Matlab window
Dr. Blanton - ENTC MATLAB / 45

4. Matlab’s help features
type “help” at the command prompt
and Matlab returns a list of help topics
Dr. Blanton - ENTC MATLAB / 45

5. Matlab’s help features
>> help lang
Matlab’s language constructs
Dr. Blanton - ENTC MATLAB / 45

6. Matlab’s help features
>> help for
how to use Matlab’s “for” statement
Dr. Blanton - ENTC MATLAB / 45

7. Matlab’s help features
you can also access “on-line” help by clicking the
question mark in the toolbar
separate window
Dr. Blanton - ENTC MATLAB / 45

8. 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;
Dr. Blanton - ENTC MATLAB / 45

9. 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’;
Dr. Blanton - ENTC MATLAB / 45

10. 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
Dr. Blanton - ENTC MATLAB / 45

11. 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
Dr. Blanton - ENTC MATLAB / 45

12. MATLAB Variables Vectors column vectors row vectors >>a=[1;2;3];
use semi-colon
to separate rows
use comma
to separate columns
Dr. Blanton - ENTC MATLAB / 45

13. MATLAB Variables Matrices 2-dimensional matrices
again, separate columns with commas and rows with semi-colons
Dr. Blanton - ENTC MATLAB / 45

14. 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
could also reference by a(1,2)
note, a(2,1) would produce an error
because “a” only has one row
Dr. Blanton - ENTC MATLAB / 45

15. MATLAB Variables Indexing Matrix elements more examples
assigning
addressing
>>a(2,2)=9;
>>a
a =
>>a(2,3)
ans = 6
Dr. Blanton - ENTC MATLAB / 45

16. MATLAB Variables complex-valued numbers
Typically, the variable “i” or “j” is used to represent the complex variable; e.g.
Then, a complex number is represented as
z = a + ib
Re(z) = a
Im(z) = b
Dr. Blanton - ENTC MATLAB / 45

17. 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
z = i
>>z=23+j*56;
>>z
z = i
Matlab always uses the symbol “i” to represent a complex number
Dr. Blanton - ENTC MATLAB / 45

18. MATLAB Variables complex-valued numbers What happens in this case?
>> z=23+i*56;
>>z
z =
>>a=sqrt(-1);
>>z=23+a*56;
>>z
z =
Dr. Blanton - ENTC MATLAB / 45

19. 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
>>a(1)=1+i*5;
>>a
a =
i i
Dr. Blanton - ENTC MATLAB / 45

20. MATLAB Variables Advanced data types n-dimensional arrays structures
cell arrays
Dr. Blanton - ENTC MATLAB / 45

21. MATLAB Variables Basic operations addition + subtraction -
multiplication *
division
right division /
left division \ ?
>>a=3;b=4;
>>c1=a/b;
>>c2=a\b;
c1=0.75
so, be careful!
c2=1.3333….
Dr. Blanton - ENTC MATLAB / 45

22. 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
Dr. Blanton - ENTC MATLAB / 45

23. MATLAB Variables Other (Scalar) Operations Math representation
Matlab interpretation
>>z=y^x;
>>y=exp(x);
>>y=log(x);
>>y=log10(x)
>>y=sin(x);
>>y=cos(x);
>>y=tan(x);
>>y=asin(x);
>>y=acos(x);
>>y=atan(x);
Dr. Blanton - ENTC MATLAB / 45

24. MATLAB Variables Examples >>y=x^0.5; >>y=x^(1/2);
>>y=sqrt(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.
Dr. Blanton - ENTC MATLAB / 45

25. MATLAB Variables Matrices
Only matrices of the same dimension can be added and subtracted
For multiplication, the inner dimensions must be the same
No error
Error
>>D=A+C;
>>D=A*B;
>>D=B*A;
>>D=A+B;
>>D=A-B;
>>D=A*C;
>>D=C*A;
Matrix multiplication not commutative
Dr. Blanton - ENTC MATLAB / 45

26. MATLAB Variables Left(\) and Right(/) Matrix “division”
Math representation
Matlab interpretation
>>C=A\B;
>>C=B/A;
Remember, A must be square and full rank (linearly independent rows/columns)
Dr. Blanton - ENTC MATLAB / 45

27. MATLAB Variables Matrix Transpose Math representation
Matlab interpretation
>>C=A’;
For complex-valued matrices, complex conjugate transpose
>>b=a’;
>>B=A’;
Dr. Blanton - ENTC MATLAB / 45

28. 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
Dr. Blanton - ENTC MATLAB / 45

29. 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
Dr. Blanton - ENTC MATLAB / 45

30. 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
>>test
y =
9.0
>>
Dr. Blanton - ENTC MATLAB / 45

31. MATLAB m-files Script Files script files share the workspace memory
test.m script
>>x=5.0;
>>test
>>y
y =
25.0
>>
Dr. Blanton - ENTC MATLAB / 45

32. MATLAB m-files Script Files script files can call other script files
inner.m script
>>outter
y =
36.0
>>
outter.m script
Dr. Blanton - ENTC MATLAB / 45

33. 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
Dr. Blanton - ENTC MATLAB / 45

34. MATLAB m-files Function Files The function file x2.m >>r=3;
>>d=x2(r);
>>d
d =
9.0
>>
>>h=x2(4.2);
>>h
h =
17.64
>>
Dr. Blanton - ENTC MATLAB / 45

35. MATLAB m-files Function Files Multiple Inputs and Outputs
outputs in square brackets, [ ]
inputs in parentheses ( )
Dr. Blanton - ENTC MATLAB / 45

36. 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.
Dr. Blanton - ENTC MATLAB / 45

37. MATLAB Flow Control The “while” and “if” statements while expression
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
Dr. Blanton - ENTC MATLAB / 45

38. MATLAB Flow Control evaluating expression any valid equation
conditional operators
== equal to
< less than
> greater than
<= less than or equal to
>= greater than or equal to
~= not equal to
a=4;
b=5;
c=5;
if a+b
if b-c
“True”
“False”
watch out for round-off
and word length error
logical operators
& and
| or
if sin(0)
if sin(pi)
sin(pi) = 1.22e-16
“False”
“True”
while(3<=a)&(a<=5)
Dr. Blanton - ENTC MATLAB / 45

39. 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)
Dr. Blanton - ENTC MATLAB / 45

40. MATLAB Flow Control example script file to cycle through x values
function file to generate the y values
Dr. Blanton - ENTC MATLAB / 45

41. 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])
Dr. Blanton - ENTC MATLAB / 45

42. MATLAB PLOTTING example y = sin(t) the “plot” function alone
Dr. Blanton - ENTC MATLAB / 45

43. MATLAB PLOTTING example y = sin(t)
script file to generate a graph of y = sin(t)
Dr. Blanton - ENTC MATLAB / 45

44. MATLAB PLOTTING example y = sin(t)
function file to generate a graph of y = sin(t)
>>graphsin
>>
Dr. Blanton - ENTC MATLAB / 45

45. MATLAB PLOTTING Adding a Legend for multiple graphs
“legend” remembers the order the graphs were plotted
Dr. Blanton - ENTC MATLAB / 45