1. An Introduction to MATLAB M File, Simulink and GUI
Dr. Mohamed Ibrahim

2. Introduction to MATLAB and Simulink
What can you gain from the course ?
Know what M File/Simulink/GUI is
Know how to get started with M File/Simulink/GUI
Know basics of M File/Simulink/GUI
know how to solve simple problems
Know how to built application (Fuzzy Controller)

3. Simmilation Package Circuit Analysis Saber Pspice Finite Element Ansys
Control Orientation
Matlab
Lab View
Why Matlab?
User Friendly (GUI)
Easy to work with
Powerful tools for complex mathematics

4. Introduction to MATLAB
Contents
M File
Introduction
Math Function
Vectors and Matrices
Built in functions
M–files : script and/functions
Symbolic
Control
Signal processing
Image
Hardware
Examples
Application
GUI
Components
Examples
Application
Simulink
Components
Modeling examples
Application

5. History MATLAB – MATrix LABoratory
In 1970s – Dr.Cleve Moler
Based on Fortran on EISPACK and LINPACK
Only solve basic matrix calculation and graphic
1984 – MathWorks Company by Cleve Moler and Jack Little
Matlab 1.0 based on C
Included image manipulations, multimedia etc. toolboxes
In 1990 – run on Windows
Simulink, Notebook, Symbol Operation, etc.
21 Century

6. Files in the working Folder
Getting Started
Run MATLAB from Start  Programs  MATLAB
Depending on version used, several windows appear
For example in (R2011b), there are several windows – command history, command, workspace, etc
Command History
Workspace
Command Window
Files in the working Folder

7. Ask more information about software
contacting the company
eg. Technique support, bugs.
>> ver
version of matlab and its toolboxes
licence number
>> whatsnew
what’s new of the version

8. • Where to get help? 1) In MATLAB’s prompt type: help lookfor helpwin
helpdesk
demos.
2) On the Web:

9. MATLAB’s Workspace Data files save filename var1 var2 … load filename
• who,whos - current variables in workspace
• save - save workspace variables to *.mat file
• load - load variables from *.mat file
• clear all - clear workspace variables
Data files
save filename var1 var2 …
>> save myfile.mat x y  binary
>> save myfile.dat x –ascii  ascii
load filename
>> load myfile.mat  binary
>> load myfile.dat –ascii  ascii

10. Special Values pi:  value up to 15 significant digits i, j: sqrt(-1)
Inf: infinity (such as division by 0)
NaN: Not-a-Number (division of zero by zero)
clock: current date and time in the form of a 6-element row vector containing the year, month, day, hour, minute, and second
date: current date as a string such as 16-Feb-2004
eps: epsilon is the smallest difference between two numbers
ans: stores the result of an expression
; surpress output
, separation of commands in one line

11. Special command help command  Online help
lookfor keyword  Lists related commands
which  Version and location info
clear  Clears the workspace
clc  Clears the command window
diary filename  Sends output to file
diary on/off  Turns diary on/off
who, whos  Lists content of the workspace
more on/off  Enables/disables paged output
Ctrl+c  Aborts operation
…  Continuation
%  Comments

12. Basic Operations variable_name = expression; addition a + b  a + b
subtraction a - b  a - b
multiplication a x b  a * b
division a / b  a / b
exponent ab  a ^ b

13. Working with complex numbers
real and imaginary
real % real part of complex number
imag % imaginary part of complex number
magnitude and phase
abs % magnitude of complex number
angle % phase of complex number
Examples during Matlab demo

14. Built in functions (commands)
Scalar functions – used for scalars and operate element-wise when applied to a matrix or vector
e.g. sin cos tan atan asin log
abs angle sqrt round floor
At any time you can use the command help to get help
e.g. >>>help sin

15. Built in functions (commands)
>>> a=linspace(0,(2*pi),10)
a =
Columns 1 through 7
Columns 8 through 10
>>> b=sin(a)
b =
Columns 1 through 7
Columns 8 through 10
>>>

16. Built in functions (commands)
Vector functions – operate on vectors returning scalar value
e.g. max min mean prod sum length
>>> a=linspace(0,(2*pi),10)
>>> b=sin(a);
>>> max(b)
ans =
0.9848
>>> max(a)
6.2832
>>> length(a) 10

17. Data >> A=[ 2 5 8 9 6 7] A = 2 5 8 9 6 7 >> x=1:2:10 x =
[x1 x2 … ; x3 x4 …] input of matrices and vectors
x1:x2 creation of a line vector [x1 x1+1 x1+2…x2]
x1:d:x2 creation of a line vector [x1 x1+d x1+2*d…x2]
linspace(x1,x2,n) line vector, start val x1, end val x2, size n, equally distributed
logspace(x1,x2,n) line vector, start val x1, end val x2, size n, logarithmically distributed
>> A=[ ]
A =
>> x=1:2:10
x =

18. How do we assign values to vectors?
Vectors and Matrices
How do we assign values to vectors?
If we want to construct a vector of, say, 100 elements between 0 and 2 – linspace
>>> c1 = linspace(0,(2*pi),100);
>>> whos
Name Size Bytes Class
c x double array
Grand total is 100 elements using 800 bytes
>>>

19. How do we assign values to vectors?
Vectors and Matrices
How do we assign values to vectors?
If we want to construct an array of, say, 100 elements between 0 and 2 – colon notation
>>> c2 = (0:0.0201:2)*pi;
>>> whos
Name Size Bytes Class
c x double array
c x double array
Grand total is 200 elements using 1600 bytes
>>>

20. Built-in MATLAB Functions
result = function_name( input );
abs, sign
log, log10, log2
exp
sqrt
sin, cos, tan/sind,cosd,tand
asin, acos, atan
max, min
round, floor, ceil, fix
mod, rem
Real,imag,abs,angle
>>> help elmat  help for elementary math functions

21. Basic Operations on Matrices
• All the operators in MATLAB defined on
matrices : +, -, *, /, ^, sqrt, sin, cos etc.
• Element wise operators defined with
preceding dot : .*, ./, .^ .
• size(A) - size vector
• sum(A) - columns sums vector
• sum(sum(A)) - all the elements sum

22. Basic Mathematical Operations
Addition:
>> C = A + B
Subtraction:
>> D = A – B
Multiplication:
>> E = A * B (Matrix multiplication)
>> E = A .* B (Element wise multiplication)
Division:
Left Division and Right Division
>> F = A . / B (Element wise division)
>> F = A / B (A * inverse of B)
>> F = A . \ B (Element wise division)
>> F = A \ B (inverse of A * B)
Examples during Matlab demo

23. Built-in MATLAB Functions
eye(n) nxn identity matrix
ones(n) nxn matrix with all entries equal to 1
zeros(n) nxn matrix with all entries equal to 0
rand(x) nxn matrix with random entries between 0 and 1
randn(x) nxn matrix with normally distributed random entries
magic(x) nxn matrix constructed from the integers 1 through n^2 with equal row and column sums
min, max, mean, std, sum, prod ,Diag
Inv, Det, Eig, Rank, Cumsum, Cumprod
matrix .’, matrix ’, diff, conv
Size, length
>>> help matfun

24. Built-in MATLAB Functions
min, max, mean, std, sum, prod ,Diag
Inv, Det, Eig, Rank, Cumsum, Cumprod
matrix .’, matrix ’, diff, conv

25. Changing the data format
>> value = ;
format short 
format long 
format short e  e+001
format long e  e+001
format short g 
format long g 
format rat  1000/81

26. Matrices in Matlab To enter a matrix >> A = [3 1 ; 6 4]
3 1
6 4
>> A = [3 1 ; 6 4]
>> A = [3, 1 ; 6, 4]
>> B = [3, 5 ; 0, 2]
Examples during Matlab demo

27. How do we assign values to matrices ?
Vectors and Matrices
How do we assign values to matrices ?
>>> A=[1 2 3;4 5 6;7 8 9]
A =
>>>
Columns separated by space or a comma
Rows separated by semi-colon

28. Generating basic matrices
Matrix with ZEROS:
>> Z = ZEROS (r, c)
Matrix with ONES:
>> O = ONES (r, c)
IDENTITY Matrix:
>> I = EYE (r, c)
r  Rows
c  Columns
zeros, ones, eye  Matlab functions
Examples during Matlab demo

29. Variables – Vectors and Matrices –
ALL variables are matrices
Variables
They are case–sensitive i.e x  X
Their names can contain up to 31 characters
Must start with a letter
e.g x x x x 4
Variables are stored in workspace

30. How do we assign values to vectors?
Vectors and Matrices
How do we assign values to vectors?
A row vector – values are separated by spaces
>>> A = [ ]
A =
>>>
>>> B = [10;12;14;16;18]
B = 10 12 14 16 18
>>>
A column vector – values are separated by semi–colon (;)

31. How do we assign values to matrices ?
Vectors and Matrices
How do we assign values to matrices ?
>>> A=[1 2 3;4 5 6;7 8 9]
A =
>>>
Columns separated by space or a comma
Rows separated by semi-colon

32. How do we access elements in a matrix or a vector?
Vectors and Matrices
How do we access elements in a matrix or a vector?
Try the followings:
>>> A(2,3)
ans = 6
>>> A(:,3)
ans = 3 6 9
>>> A(2,:)
ans =
>>> A(1,:)
ans =

33. Arithmetic operations – Matrices
Vectors and Matrices
Arithmetic operations – Matrices
Performing operations to every entry in a matrix
Add and subtract
>>> A=[1 2 3;4 5 6;7 8 9]
A =
>>>
>>> A+3
ans =
>>> A-2
ans =

34. Arithmetic operations – Matrices
Vectors and Matrices
Arithmetic operations – Matrices
Performing operations to every entry in a matrix
Multiply and divide
>>> A=[1 2 3;4 5 6;7 8 9]
A =
>>>
>>> A*2
ans =
>>> A/3
ans =

35. Arithmetic operations – Matrices
Vectors and Matrices
Arithmetic operations – Matrices
Performing operations to every entry in a matrix
Power
>>> A=[1 2 3;4 5 6;7 8 9]
A =
>>>
To square every element in A, use the element–wise operator .^
>>> A.^2
ans =
>>> A^2
ans =
A^2 = A * A

36. Arithmetic operations – Matrices
Vectors and Matrices
Arithmetic operations – Matrices
Performing operations between matrices
>>> A=[1 2 3;4 5 6;7 8 9]
A =
>>> B=[1 1 1;2 2 2;3 3 3]
B = =
A*B =
A.*B

37. ? (matrices singular) Arithmetic operations – Matrices
Vectors and Matrices
Arithmetic operations – Matrices
Performing operations between matrices
? (matrices singular)
A/B =
A./B

38. Arithmetic operations – Matrices
Vectors and Matrices
Arithmetic operations – Matrices
Performing operations between matrices
??? Error using ==> ^
At least one operand must be scalar
A^B =
A.^B

39. Vectors and Matrices
Ex 1.1
Solve the following Equation
4x1 - 2x2 - 10x3=-10
2x1 + 10x2- 12x3=32
-4x1- 6x2 + 16x3=-10
For the matrix equation below, AX = B, determine the vector X.

40. Vectors and Matrices
solution
 a=[ ; ; ];
b=[-10;32;-10];
c=inv(a);
z=c*b;
x1=z(1)
x2=z(2)
x3=z(3)
   
x1 =  
 x2 =  
 x3 =  

41. Arithmetic operations – Matrices
Vectors and Matrices
Arithmetic operations – Matrices
Example:
-j5
j10
10
1.50o
2-90o
Solve for V1 and V2

42. Arithmetic operations – Matrices
Vectors and Matrices
Arithmetic operations – Matrices
Example (cont)
(0.1 + j0.2)V1 – j0.2V = -j2
- j0.2V j0.1V = 1.5 = A x y =

43. Arithmetic operations – Matrices
Vectors and Matrices
Arithmetic operations – Matrices
Example (cont)
>>> A=[( j) -0.2j;-0.2j 0.1j]
A =
i i
i i
>>> y=[-2j;1.5]
y = i
1.5000
>>> x=A\y
x = i i
>>>
* A\B is the matrix division of A into B, which is roughly the same as INV(A)*B *

44. Arithmetic operations – Matrices
Vectors and Matrices
Arithmetic operations – Matrices
Example (cont)
>>> V1= abs(x(1,:))
V1 =
>>> V1ang= angle(x(1,:))
V1ang =
0.5191
V1 = 16.1229.7o V

45. Built in functions (commands)
Matrix functions – perform operations on matrices
>>> x*xinv
ans =
>>>
>>> x=rand(4,4)
x =
>>> xinv=inv(x)
xinv =

46. Built in functions (commands)
From our previous example, = y x A =
>>> x=inv(A)*y
x = i i

47. Polynomial Example 1.1 Find the roots of the following polynomial.
 s6 + 9s s s s s + 15
 The polynomial coefficients are entered in a row vector in descending powers.
The roots are found using roots.
p = [ ]
r = roots(p)    i i i i

48. The coefficients of the polynomial equation
Example 1.2
The roots of a polynomial are i i i i
. Determine the polynomial equation.
Complex numbers may be entered using function i or j. The roots are then
entered in a column vector. The polynomial equation is obtained using poly as follows
i = sqrt(-1)
r = [ *i -1-2*I 0.5*i -0.5*i ]
p = poly(r)
The coefficients of the polynomial equation

49. Find a polynomial of degree 3 to fit the following data
Example 1.3
Find a polynomial of degree 3 to fit the following data
x = [ ];
y = [ ];
c = polyfit(x,y,3) x y

50. Partial Fraction a=[2 0 9 1] b=[1 1 4 4 ] [r,p,k]=residue(a,b) Example
Determine the partial fraction expansion for
 a=[ ]
b=[ ]
[r,p,k]=residue(a,b)
r =
  i i
 p =
  i i
 k =
  2

51. Plotting / displaying 3D plots: PLOT(x,y) IMAGE(x) MESH MESHGRID
Plots y versus x.
Linear plot
XLABEL(‘label’)
YLABEL(‘label’)
TITLE(‘title’)
IMAGE(x)
Displays image
3D plots:
MESH
3D mesh surface (Ex. filters)
MESHGRID
Useful in 3D plots
SURF
3D colored surface (Ex. filters)
Examples during Matlab demo

52. Built in functions (commands)
Data visualisation – plotting graphs
>>> help graph2d
>>> help graph3d
e.g. plot polar loglog mesh semilog plotyy surf
Visualization and Graphics
• plot(x,y), plot(x,sin(x)) - plot 1-D function
• figure , figure(k) - open a new figure
• hold on, hold off - refreshing
• mesh(x_ax,y_ax,z_mat) - view surface
• contour(z_mat) - view z as top. map
• subplot(3,1,2) - locate several plots in figure
• axis([xmin xmax ymin ymax]) - change axes
• title(‘figure title’) - add title to figure

53. Example 1
Fit a polynomial of order 2 to the following data Plot the given data point with
symbol x, and the fitted curve with a solid line. Place a boxed legend on the graph.
The command p = polyfit(x, y, 2) is used to find the coefficients of a polynomial
of degree 2 that fits the data, and the command yc = polyval(p, x) is used to evaluate
the polynomial at all values in x. We use the following command.
x=[ ]
y=[ ]

54. x=[ ]
y=[ ]
p = polyfit(x,y,2)
yc=polyval(p,x)
plot(x,y,'r*',x,yc)
title('graph title')
xlabel('xlable')
ylabel('ylable')
grid
legend('point','curve',4)

55. Data visualisation – plotting graphs
Example on plot – 2 dimensional plot
title xlabel ylabel legend
Use ‘copy’ and ‘paste’ to add to your window–based document, e.g. MSword
Example
Plot sine wave from –pi to pi and write on axis
'-pi','-pi/2','0','pi/2','pi'

56. x = -pi:.1:pi;
y = sin(x);
plot(x,y)
set(gca,'XTick',-pi:pi/2:pi)
set(gca,'XTickLabel',{'-pi','-pi/2','0','pi/2','pi'})
xlabel('-\pi \leq \Theta \leq \pi')
ylabel('sin(\Theta)')
title('Plot of sin(\Theta)')
text(-pi/4,sin(-pi/4),'\leftarrow sin(-\pi\div4)',...
'HorizontalAlignment','left')

57. Multi Figures x = -pi:.1:pi; y = sin(x); subplot(2,3,1),plot(x,y)

58. MATLAB supports many types of graph and surface plots:
line plots (x vs. y),
filled plots,
bar charts,
pie charts,
parametric plots,
polar plots,
contour plots,
density plots,
log axis plots,
surface plots,
parametric plots in 3 dimensions and spherical plots.

59. Z = 10e(–0.4a) sin (2ft) for f = 2
Data visualisation – plotting graphs
Example on mesh and surf – 3 dimensional plot
Supposed we want to visualize a function
Z = 10e(–0.4a) sin (2ft) for f = 2
when a and t are varied from 0.1 to 7 and 0.1 to 2, respectively
>>> [t,a] = meshgrid(0.1:.01:2, 0.1:0.5:7);
>>> f=2;
>>> Z = 10.*exp(-a.*0.4).*sin(2*pi.*t.*f);
>>> surf(Z);
>>> figure(2);
>>> mesh(Z);

60. Built in functions (commands)
Data visualisation – plotting graphs
Example on mesh and surf – 3 dimensional plot

61. Built in functions (commands)
eg3_srf.m
Data visualisation – plotting graphs
Example on mesh and surf – 3 dimensional plot
[x,y] = meshgrid(-3:.1:3,-3:.1:3);
z = 3*(1-x).^2.*exp(-(x.^2) - (y+1).^2) ...
- 10*(x/5 - x.^3 - y.^5).*exp(-x.^2-y.^2) ...
- 1/3*exp(-(x+1).^2 - y.^2);
surf(z);

62. Built in functions (commands)
Data visualisation – plotting graphs
Example on mesh and surf – 3 dimensional plot

63. plot, stairs, bar (…), stem, Loglog, Semilogx, Semilogy,
polar, fplot, ezplot, ezplot,
subplot

64. Flow Control • MATLAB has five flow control constructs: – for loops
– if statements
–switch statements
–while loops
– break statements

65. Logical Conditions • == , < , > , (not equal)~= ,(not)~
• find(‘condition’) - Returns indexes of A’s
elements that satisfies the condition.
>> A = [1 2; 3 4], I = find(A<4)
A =
1 2
3 4
I = 1 2 3

66. for % Example: • FOR Repeat statements a specific number of times.
• The general form of a FOR statement is:
FOR variable = expr, statement, ..., END
% Example:
N=5
for I = 1:N
for J = 1:N
A(I,J) = 1/(I+J-1);
end

67. IF • IF statement condition. The general form of the IF statement is
IF expression
statements
ELSEIF expression
ELSE
END

68. Example for I=1:4 for J=1:4 if I == J A(I,J) = 2 elseif abs(I-J) == 1
end A

69. switch • SWITCH - Switch among several cases based on expression.
• The general form of the SWITCH statement is:
SWITCH switch_expr
CASE case_expr,
statement, ..., statement
CASE {case_expr1, case_expr2, case_expr3,...}
...
OTHERWISE,
END

70. Example a=input('enter value for a') x=2; y=5; switch a case 1 u=x+y
end

71. while • WHILE Repeat statements an indefinite number of times.
• The general form of a WHILE statement is:
WHILE expression
statements
END

72. Example

73. M-files : Script and function files
When problems become complicated and require re–evaluation, entering command at MATLAB prompt is not practical
Solution : use M-files
Script
Function
Collections of commands
Executed in sequence when called
Saved with extension “.m”
User defined commands
Normally has input & output
Saved with extension “.m”

74. At Matlab prompt type in edit to invoke M-file editor
M-files : script and function files (script)
eg1_plt.m
At Matlab prompt type in edit to invoke M-file editor
Save this file as test1.m

75. To run the M-file, type in the name of the file at the prompt e. g
To run the M-file, type in the name of the file at the prompt e.g >>> test1
It will be executed provided that the saved file is in the known path
Type in matlabpath to check the list of directories listed in the path
Use path editor to add the path: File  Set path …

76. Write an m–file to plot I and versus frequency for R =10, C = 100 uF,
Example – RLC circuit + V –
R = 10 C L
Write an m–file to plot I and versus frequency for
R =10,
C = 100 uF,
L = 0.01 H.

77. Example – RLC circuit C=1e-4 L=0.01 R=10 V=220*sqrt(2) for W=1:50000
XC=1/(W*C);
XL=W*L;
Z=sqrt(R^2+(XL-XC)^2);
I(W)=V/Z;
end
W=1:5000
plot(W,I(W))
grid
title('Current with Frequency')
ylabel('Current(Amp)')
xlabel('Frequency(Hz)')

78. Example – RLC circuit

79. M-files : script and function files (function)
Function is a ‘black box’ that communicates with workspace through input and output variables.
INPUT
FUNCTION
OUTPUT
– Commands
– Functions
– Intermediate variables

80. M-files : script and function files (function)
Every function must begin with a header:
function output=function_name(inputs)
Output variable
Must match the file name
input variable

81. Function File Stat.m
%This function calculate the Mean and Root Mean Square
function [mean,RMS] = stat(x)
n = length(x);
mean = sum(x)/n;
RMS = sqrt(sum(x.*x)/n);
Script File calc.m
x=[1:20]
[mean,RMS] = stat(x)
mean
RMS
>> help stat
This function calculate the Mean and Root Mean Square

82. Ex IM Control 1- AC Voltage Control 2-V/F control speed_torque.m
function a=speed_torque(r1,l1,r2,l2,f,p,v)
w=2*pi*f
ns=120*f/p
for k=1:100
s=1-k/100
nr=ns*(1-s)
i=((v)/(sqrt((r1+r2/s)^2+(w*l1+w*l2)^2)))
T=((3*i*i*r2/s)/(2*pi*ns/60))
plot(nr,T,'b+:')
hold on
end

83. IM_Control.m p=4 l1=0.0001565 l2=0.0001777 r1=0.029 r2=.059 f=60 v=100
speed_torque(r1,l1,r2,l2,f,p,v)
v=200
v=300
f=30
v=150
f=20

84. Example contains read and write
i=sqrt(-1)
R=input('Enter R: ');
C=input('Enter C: ');
L=input('Enter L: ');
w=input('Enter w: ');
R2=R*R
X=(w*L-1/(w*C))
z=(R+X*i)
Mag = abs(z)
Phase = angle(z)
fprintf('\n The magnitude of the impedance at %.1f rad/s is %.3f ohm\n', w,Mag);
fprintf('\n The angle of the impedance at %.1f rad/s is %.3f degrees\n\n', w, Phase);

85. Classical Control In Matlab

86. Classical Control Classical Control Transfer Function Step Response
Root Locus
Bode Diagram
Nyquist Plot

87. Transfer Function >> G=tf([1],[1 2 5]) Transfer function: 1
s^2 + 2 s + 5

88. Step Response >> G=tf([1],[1 2 5]) Transfer function: 1
s^2 + 2 s + 5
>> step(G)

89. Root Locus Diagram >> G=tf([1 1],[1 2 5]) Transfer function:
s^2 + 2 s + 5
>> rlocus(G)

90. Bode Plot >> G=tf([1 1],[1 2 5]) Transfer function: s + 1
s^2 + 2 s + 5
>> bode(G)
>> grid

91. Nyquist Plot >> G= tf([2 5 1],[1 2 3]) Transfer function:
2 s^2 + 5 s + 1
s^2 + 2 s + 3
>> nyquist(G)
>> grid

92. PID Controller G_num=[5] G_den=[1 2 5] G=tf(G_num,G_den) H=[-1]
kp=4; ki=50; kd=1
pid_num=[kd kp Ki]
pid_den=[1 0];
[num,den]=cloop(conv(G_num,pid_num),conv(G_den,pid_den),H);
closed_Loop=tf(num,den)
step(G,'r')
hold on
step(closed_Loop,'b')
legend('Open Loop','Closed Loop')
grid on

93. Symbolic Calculus Linear Algebra Simplification – Equation Solutions
Symbolic mathematics deals with equations before you plug in the numbers.
Calculus
integration, differentiation, Taylor series expansion, …
Linear Algebra
inverses, determinants, eigenvalues, …
Simplification –
algebraic and trigonometric expressions
Equation Solutions
algebraic and differential equations
Transforms
Fourier, Laplace, Z  transforms and inverse transforms, …

94. Equation Solutions syms a b c x eq=a*x^2+b*x+c [x]=solve(eq) x =
-(b + (b^2 - 4*a*c)^(1/2))/(2*a)
-(b - (b^2 - 4*a*c)^(1/2))/(2*a)
subs(eq,2)
ans =
4*a + 2*b + c

95. Differentiation & Integration
clear
syms m x b th n y
y = m*x + b
diff(y, x)
diff(y, b)
clear
syms m x b th n y
y = m*x + b
int(y, x)
int(y, b)

96. Linear Algebra syms a l r w a=[w*l r;-r w*l] inv(a)
[ (l*w)/(l^2*w^2 + r^2), -r/(l^2*w^2 + r^2)]
[ r/(l^2*w^2 + r^2), (l*w)/(l^2*w^2 + r^2)]

97. Transformation syms x y v n t z w s %Laplace Transform
x=laplace(3*t^3)
%Z Transform
y=ztrans(2^n)
%Fourrier Transform
v=fourier(exp(-5*abs(t)))
% Inverse Laplace Transform
x=ilaplace(18/s^4)
%Inverse Z Transform
y=iztrans(z/(z - 2))
%Inverse Fourrier Transform
v=ifourier(1/w)

98. Matlab with Hardware
Serial Port
Parallel Port
Sound Card
Camera

99. Serial Port Example: % To construct a serial port object:
s1 = serial('COM1', 'BaudRate', 1200);
% To connect the serial port object to the serial port:
fopen(s1)
% To query the device.
fprintf(s1, ‘Moh');
data= fscanf(s1);
% To disconnect the serial port object from the serial port.
fclose(s1);

100. Parallel Port
% Create a Digital I/O Object with the digitalio function
dio=digitalio('parallel',‘lpt1');
%Add lines to a Digital I/O Object
% add the hardware lines 0 until 7 from port 0 to the
addline(dio,0:7,0,'out');
%Send data to the lines
for i=1:20
putvalue(dio.line(1),1); % send data ‘1’ to line 1
pause(1)
putvalue(dio.line(1),0); % send data ‘1’ to line 1
end

101. Parallel Port
% Create a Digital I/O Object with the digitalio function
dio=digitalio('parallel',‘lpt1'); % LPT 3 Port 0,1,2
%Add lines to a Digital I/O Object
% add the hardware lines 0 until 7 from port 0 to the
addline(dio,0:7,0,'out');
%Send data to the lines
for i=1:20
putvalue(dio.line(1:8),[ ]);
pause(1)
putvalue(dio.line(1:8),[ ]);
end

102. Sound Card Example: Record and play back 5 seconds of 16-bit audio
sampled at kHz
Fs = 11025;
y = wavrecord(5*Fs, Fs, 1);
wavplay(y, Fs);
Example: Read and play
sampled at kHz
Fs = 11025;
y = wavread(‘d:\moh\sound.wav');
wavplay(y, Fs);

103. Camera and Image % Initiate the camera
vid = videoinput('winvideo', 1);
set(vid, 'ReturnedColorSpace', 'RGB');
img = getsnapshot(vid);
imshow(img)
imwrite(img,'d:\1\ball24.jpg');
photo=img;
photo=imread('d:\1\ball7.jpg');
figure
image(photo)

104. Image processing in matlab
To read and display images
im = imread(“filename.fmt”)
im is r x c if gray scale
im is r x c x 3 if color image (RGB)
imshow(im) % displays image
imwrite(im, “filename.fmt”) % writes image
Size of image
[r c] = size(im)
Examples during Matlab demo

105. DSP
Common Signal
FFT

106. FFT clear all; for i=1:10000 t=0.01*(i-1) x(i) = 5*sin(3*2*pi*t); end
plot(x(i))
axis([ ])
grid
figure
y = fft(x,10000);
my = abs(y)/10000;
plot(my);
axis([ ])

107. Non-periodic Signals Step Impulse Ramp Nonperiodic Signals
>> t = linspace(0,1,11);
Step
>> y = ones(11,1);
Impulse
>> y = [1;zeros(10,1)];
Ramp
>> y = 2*t;
Useful MATLAB functions
step, impulse, gensig
Non-periodic Signals
>> t = linspace(0,1,11)
Step
>> y = ones(11,1);
Impulse
>> y = [1;zeros(10,1)];
Ramp
>> y = 2*t;
Try
Step function:
>> fs = 10;
>> ts = ...
[0:1/fs:5, :1/fs:10];
>> x = [zeros(1,51), ...
ones(1,51)];
>> stairs(ts,x)
Impulse function
with width w:
>> w = 0.1;
[-1:1/fs:-w, ,w:1/fs:1];
>> x = [zeros(1,10), ...
1,zeros(1,10)];
>> plot(ts,x)
Delta function impulse:
>> ts = 0:0.5:5;
>> x = [1, zeros(1, length(ts)-1)];
>> stem(ts,x)
>> axis([ ])
Step
Impulse
Ramp

108. Sine Waves Parameters Amplitude A Frequency f Phase shift φ
Sine wave parameters
Amplitude A
Frequency f
Phase shift φ
Vertical offset B
The general form of a sine wave is
Example: Generate a sine wave given the following specifications:
A = 5
f = 2 Hz
φ = π/8
>> t = linspace(0,1,1001);
>> A = 5; % Amplitude
>> f = 2; % Frequency in Hertz
>> p = pi/8; % Phase in radians
>> sinewave = A*sin(2*pi*f*t + p);
>> plot(t,sinewave)
Sine Waves
Parameters
Amplitude A
Frequency f
Phase shift φ
Vertical offset B
General form
Try
>> edit sine_wave
>> sine_wave
>> edit sinfun
>> [A,T] = ...
sinfun(1,2,3,4)
Exercise
High and Low (p. AIII-3)

109. Square Waves Duty cycle is 50% (default) Frequency is 4 Hz
Square wave generation is like sine wave generation, but you
specify a duty cycle, which is the percent of time over one
period that the amplitude is 1.
Example:
Duty cycle is 50% (default)
Frequency is 4 Hz
>> t = linspace(0,1,1001);
>> sqw1 = square(2*pi*4*t);
>> plot(t,sqw1)
>> axis([ – ])
Duty cycle is 75%
>> sqw2 = square(2*pi*4*t,75);
>> plot(t,sqw2)
Square Waves
>> sqw1 = square(2*pi*4*t);
Duty cycle is 50% (default)
Frequency is 4 Hz
Try
>> t = ...
linspace(0,1,1001);
>> sqw1 = ...
square(2*pi*4*t);
>> plot(t,sqw1)
>> axis(...
[ – ])
>> sqw2 = ...
square(2*pi*4*t,75);
>> plot(t,sqw2)
>> sqw2 = square(2*pi*4*t,75);
Duty cycle is 75%
Frequency is 4 Hz

110. Sawtooth Waves Peak at end of cycle (default) Frequency is 3 Hz
Sawtooth waves are like square waves except that instead of specifying a duty cycle you specify the location of the peak.
Example:
Peak at end of cycle (default)
Frequency is 3 Hz
>> t = linspace(0,1,1001);
>> saw1 = sawtooth(2*pi*3*t);
>> plot(t,saw1)
Peak halfway through cycle
>> saw2 = sawtooth(2*pi*3*t,1/2);
>> plot(t,saw2)
Sawtooth Waves
>> saw1 = sawtooth(2*pi*3*t);
Peak at end of cycle (default)
Frequency is 3 Hz
Try
>> t = ...
linspace(0,1,1001);
>> saw1 = ...
sawtooth(2*pi*3*t);
>> plot(t,saw1)
>> saw2 = ...
sawtooth(...
2*pi*3*t,1/2);
>> plot(t,saw2)
>> saw2 = sawtooth(2*pi*3*t,1/2);
Peak halfway through cycle
Frequency is 3 Hz

111. FFT clear all; for i=1:10000 t=0.01*(i-1) x(i) = 5*sin(3*2*pi*t); end
plot(x(i))
axis([ ])
grid
figure
y = fft(x,10000);
my = abs(y)/10000;
plot(my);
axis([ ])