This document provides an overview of basic MATLAB concepts including: 1. Creating variables and performing basic arithmetic operations 2. Generating and manipulating matrices using built-in functions 3. Plotting graphs of simple functions like sine and cosine waves 4. Solving linear equations and finding the inverse and determinant of matrices It includes sample exercises demonstrating these MATLAB skills.

1. SIGNALS AND SYSTEMS
BY
LIM, JONATHAN G.
Getting Started with MATLAB
Arrays and Matrices
Digital Image Processing
Audio Signal Processing

2. BASIC MATLAB OPERATOR
Basic Arithmetic Operators
Operation Symbol
Addition +
Subtraction -
Multiplication *
Division /
Power ^

3. MATLAB variables are created with an assignment statement. The syntax of
variable assignment is
variable name = a value (or an expression)
For example,
>> addition = 25 + 75;
>> y = (900 / 300) + 2*5
CREATING MATLAB VARIABLES

4. SAMPLE EXERCISES
• Calculate the expression using the MatLab

5. ELEMENTARY FUNCTIONS
Example:
let a = 5 ;b = 2 ;y = 8
>> a = 5;
>>b = 2;
>>y = 8;
>>y = exp(-a)*sin(x)+10*sqrt(y);
>>y
y =
28.2904

6. BASIC PLOTTING
The MATLAB command to plot a graph is plot(x,y). The vectors x
= (1; 2; 3; 4; 5; 6) and y = (3; -1; 2; 4; 5; 1)
>> x = [1 2 3 4 5 6];
>> y = [3 -1 2 4 5 1];
>> plot(x,y)

8. PLOTTING SINE WAVE SIGNAL
>> x = 0: pi/100 : 2*pi; % 0-2π with increment of
π
100
>> y = sin(x); % starts at 0,
>> plot(x,y) % takes steps (or increments) of
π
100
,
% stops when 2¼ is reached.

10. ADDING INFORMATION
>>xlabel('x = 0:2pi')
>> ylabel('Sine of x')
>> title('Plot of the Sine function')

11. MULTIPLE DATA SETS
>> x = 0:pi/100:2*pi;
>> y1 = 2*cos(x);
>> y2 = cos(x);
>> y3 = 0.5*cos(x);
>> plot(x, y1, x, y2, x, y3)
>> xlabel(‘x: 0 - 2pi')
>> ylabel('Cosine functions')
>>
legend('2*cos(x)','cos(x)','0.5*cos(x
)')
>> title('Typical example of multiple
plots')
>> axis([0 2*pi -3 3])

12. 0 1 2 3 4 5 6 7
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
x: 0 - 2
Cosinefunctions
2*cos(x)
cos(x)
0.5*cos(x)
>>plot(x,y1,'--',x,y2,'-',x,y3,':')

13. EXERCISES
Plot the following y1 = 2sin(x), y2 = cos(x) , y3 = 0.6cos(0.5x)
0 1 2 3 4 5 6 7
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Cosinefunctions
x: 0-2
Exercise 1
2*sin(x)
cos(x)
0.6*cos(.5*x)

14. • x = 0:pi/100:2*pi;
• y1 = 2*sin(x);
• y2 = cos(x);
• y3 = 0.6*cos(.5*x);
• plot(x,y1,‘:',x,y2,‘:',x,y3,':')
• xlabel(‘x: 0 - 2pi')
• ylabel('Cosine functions')
• legend('2*sin(x)','cos(x)','0.6*cos(.5*x)')
• title(‘Exercise 1’)
• axis([0 2*pi -3 3])

15. MATRIX GENERATION
• Matrices are fundamental to MATLAB. Therefore, we need to
become familiar with matrix generation and manipulation.
Matrices can be generated in several ways.
• A vector is a special case of a matrix.

16. An array of dimension (1x n) is called a row vector, whereas an
array of dimension (m x1) is called a column vector.
>> row = [1 4 7 10 13] % row vector
>> column = [1;4;7;10;13] % column vector
Converting Row Vector to Column Vector or Vice Versa using Transpose. The
transpose operation is denoted by an apostrophe or a single quote (').
>> row = row’
>>column = column’

17. ENTERING A MATRIX
A matrix is an array of numbers. To type a matrix into MATLAB you
must
1. Begin with a square bracket, [
2. Separate elements in a row with spaces or commas (,)
3. Use a semicolon (;) to separate rows
4. End the matrix with another square bracket, ].
>> A = [1 2 3; 4 5 6; 7 8 9]A =
1 2 3
4 5 6
7 8 9

18. Transpose a Matrix:
>> A = [1 2 3; 4 5 6; 7 8
9]
>> A’
ans =
1 4 7
2 5 8
3 6 0

19. COLON OPERATOR
>>x = 1: .5: 5; %1-5 with increment of 0.5
>>x
x =
1.0000 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000 4.5000
5.0000

20. SAMPLE EXERCISES
• Find Matrix C if C = A x B and D = AB
C =
300 360 420
660 810 960
1020 1260 1500
D =
10 40 90
160 250 360
490 640 810

21. SOLVING LINEAR EQUATION
Example:
Find the value of x,y
and z
Solution:

22. INVERSE AND DETERMINANT
Consider the matrix: find the inverse and determinants

23. EXERCISES
1. Solve for the value of x, the inverse and determinants. Store in
variable X, INV and DET respectively

24. EXERCISES
2. Liz buys three apples, a dozen bananas, and one cantaloupe
for $2.36. Bob buys a dozen apples and two cantaloupe for
$5.26. Carol buys two bananas and three cantaloupe for $2.77.
How much do single pieces of each fruit cost?