Signals and Systems
Laboratory 2013
•
Teacher: Marek Ossowski
[email protected]
Phone: 42 6312515, 501 673231
Room 14, C3, Al.Politechniki 11
Laboratory: Room 105, C3
Department of Nonlinear Circuits and Systems,
Institute of Electrical Engineering Systems (I12)
Signals and Systems
Laboratory
•
•
Teacher home page:
http://matel/p.lodz.pl/wee/i12zet/mosso/mos
so_index.html
•
Files for today:
– Front page
– Experiment 0
– Experiment 1
Signals and Systems
Laboratory
•
Introduction
What is Matlab? A WORKSHOP.
•
Experiment 0
–Elementary Matlab functions and
operations
– Basic Signals Manipulations
– Systems identifications
Signals and SystemsLaboratory
•
•
•
•
•
•
Experiment 1. Discrete and analog
convolution
Experiment 2. Properties of Discrete
Fourier Transform.
Experiment 3. Spectral analysis of periodic
signals. Fourier series.
Experiment 4. Fourier transform.
Experiment 5. Analysis of dynamic LTI
systems using state equations and Laplace
transform concept.
Experiment 6. Z-transform. Digital filters.
MATLAB
Short
Overview
Before getting started…
•
Acknowledgement:
– This material was almost entirely created from information
compiled from various internet sources
• It is available for download from SBEL website in PPT format for other
to be able to save, edit, and distribute as they see fit
• Please let me know of any mistakes you find
– email me at [email protected], where mylastname is: negrut
• Purpose of the document:
– You will not be able to say at the end of workshop that you know
MATLAB but rather that you have been exposed to MATLAB (I
don’t know MATLAB myself, I’m just using it…:-)
– It is expected of you to use MATLAB’s “help” function a lot, as well
as search the web for examples that come close to what you need
• You learn how to use MATLAB by using it, that’s why the start is
maybe slow and at times frustrating
Contents
1. First part of workshop




What is Matlab?
MATLAB Components
MATLAB Desktop
Matrices


Numerical Arrays
String Arrays
 Importing and Exporting Data
 Elementary math with MATLAB
Contents
Continued
2. Second part of workshop
 M-file Programming
 Functions vs. Scripts
 Variable Type/Scope
 Debugging MATLAB functions
 Flow control in MATLAB
 Other Tidbits
 Function minimization
 Root finding
 Solving ODE’s
 Graphics Fundamentals
 Data Types
most likely won’t have time for it
What is MATLAB?
• Integrated software environment
– Computation
– Visualization
– Easy-to-use environment
• High-level language
–
–
–
–
–
–
Data types
Functions
Control flow statements
Input/output
Graphics
Object-oriented programming capabilities
MATLAB Parts
•
•
•
•
•
High Level Development Environment
Programming Language
Graphics
Toolboxes
Application Program Interface
Toolboxes
• Collections of functions to solve problems from
several application fields.
–
–
–
–
–
–
–
–
DSP (Digital Signal Processing) Toolbox
Image Toolbox
Wavelet Toolbox
Neural Network Toolbox
Fuzzy Logic Toolbox
Control Toolbox
Multibody Simulation Toolbox
And many others…
MATLAB 7x Desktop Tools
•
•
•
•
•
•
Command Window
Command History
Help Browser
Workspace Browser
Editor/Debugger
To select what you
want to see, go under
“Desktop” tab
MATLAB 7x DESKTOP
Editor/Debugger
HELP BROWSER
Figure
Window
Wokspace
Browser
Command
History
Interpreter
Command Window
MATLAB 5.3 – main window= interpreter
MATLAB – editor (new file)
MATLAB – editor (opening a file)
MATLAB – figure editor
MATLAB – path browser
HELP - help, lookfor
Calculations at the Command Line
»MATLAB
-5/(4.8+5.32)^2
as a calculator
ans =
-0.0488
» (3+4i)*(3-4i)
ans =
25
» cos(pi/2)
ans =
6.1230e-017
» exp(acos(0.3))
ans =
3.5470
Assigning Variables
» a = 2;
» b = 5;
» a^b
ans =
32
» x = 5/2*pi;
» y = sin(x)
Semicolon
suppresses
screen output
Results
assigned to
“ans” if name
not specified
y =
1
» z = asin(y)
z =
() parentheses for
function inputs
1.5708
A Note about Workspace:
Numbers stored in double-precision floating point format
General Functions
•
•
•
•
•
•
•
•
whos: List current variables and their size
clear: Clear variables and functions from memory
cd: Change current working directory
dir: List files in directory
pwd: Tells you the current directory you work in
echo: Echo commands in M-files
format: Set output format (long, short, etc.)
diary(filename): Saves all the commands you type
in in a file in the current directory called filename
Getting help
• help command
(>>help)
• lookfor command
(>>lookfor)
• Help Browser
(>>doc)
• helpwin command
(>>helpwin)
• Search Engine
• Printable Documents
– “Matlabroot\help\pdf_doc\”
• Link to The MathWorks
Handling
Matrices in
Matlab
Matrices
•
•
•
•
•
•
•
Entering and Generating Matrices
Subscripts
Scalar Expansion
Concatenation
Deleting Rows and Columns
Array Extraction
Matrix and Array Multiplication
Entering Numeric Arrays
» a=[1 2;3 4]
Use square
brackets [ ]
a =
NOTE:
1) Row separator
semicolon (;)
2) Column separator
space OR comma (,)
1
2
3
4
» b=[-2.8, sqrt(-7), (3+5+6)*3/4]
b =
-2.8000
0 + 2.6458i
10.5000
» b(2,5) = 23
b =
-2.8000
0 + 2.6458i
10.5000
0
0
0
0
0
0
23.0000
• Any MATLAB expression can be entered as a matrix
element (internally, it is regarded as such)
• In MATLAB, the arrays are always rectangular
The Matrix in MATLAB
Columns
(n)
2
3
4
1
A=
5
4
1
10
6
1
11
6
16
2
21
8
2
1.2
7
9
12
4
17
25
22
7.2 3
5
8
7
13
1
18
11 23
4
0
4
0.5 9
4
14
5
19
56 24
5
23
5
13
15
0
20
10
1
2
Rows (m) 3
83
10
25
A (2,4)
A (17)
Rectangular Matrix:
Scalar: 1-by-1 array
Vector: m-by-1 array
1-by-n array
Matrix: m-by-n array
Entering Numeric Arrays
Scalar expansion
Creating sequences:
colon operator (:)
» w=[1 2;3 4] + 5
w =
6
7
8
9
» x = 1:5
x =
1
2
» y = 2:-0.5:0
Utility functions for
creating matrices.
y =
2.0000
1.5000
» z = rand(2,4)
3
4
5
1.0000
0.5000
0.8913
0.7621
0.4565
0.0185
z =
0.9501
0.2311
0.6068
0.4860
0
Examples (Entering Numeric
Arrays)
• Enter the matrix:
1 2 3
A  2 3 4
3 4 5
• enter the row vector:
• Enter the column
vector :
B  6 7 8 9
6 
7 
C 
8 
 
9 
Numerical Array Concatenation
Use [ ] to combine
existing arrays as
matrix “elements”
» a=[1 2;3 4]
1
2
3
4
» cat_a=[a, 2*a; 3*a,
cat_a =
1
2
2
3
4
6
Column separator:
3
6
4
9
12
12
space / comma (,)
5
10
6
15
20
18
Row separator:
semicolon (;)
Use square
brackets [ ]
a =
4*a; 5*a, 6*a]
4
8
8
16
12
24
4*a
Note:
The resulting matrix must be rectangular
Deleting Rows and Columns
» A=[1 5 9;4 3 2.5; 0.1 10 3i+1]
A =
1.0000
5.0000
9.0000
4.0000
3.0000
2.5000
0.1000
10.0000
1.0000+3.0000i
» A(:,2)=[]
A =
1.0000
9.0000
4.0000
2.5000
0.1000
1.0000 + 3.0000i
» A(2,2)=[]
???
Indexed empty matrix assignment is not allowed.
Array Subscripting / Indexing
1
A=
A(3,1)
A(3)
2
4
1
2
2
8
3
7.2 3
5
8
7 13
1
18
11 23
4
0
4
0.5 9
4 14
5
19
56 24
5
23
5
83 10 1315
0
20
10 25
1
1.2 7
11
6
16
9 12
4
17
5
4
10
6
3
1
2
21
25 22
A(1:5,5) A(1:end,end)
A(:,5)
A(:,end)
A(21:25) A(21:end)’
A(4:5,2:3)
A([9 14;10 15])
Matrix Multiplication
» a = [1 2 3 4; 5 6 7 8];
[2x4]
» b = ones(4,3);
[4x3]
» c = a*b
[2x4]*[4x3]
[2x3]
c =
10
26
10
26
10
26
a(2nd row).b(3rd column)
Array Multiplication
» a = [1 2 3 4; 5 6 7 8];
» b = [1:4; 1:4];
» c = a.*b
c =
1
5
4
12
9
21
16
32
c(2,4) = a(2,4)*b(2,4)
Matrix Manipulation Functions
•
•
•
•
•
•
•
•
•
zeros: Create an array of all zeros
ones: Create an array of all ones
eye: Identity Matrix
rand: Uniformly distributed random numbers
diag: Diagonal matrices and diagonal of a matrix
size: Return array dimensions
fliplr: Flip matrices left-right
flipud: Flip matrices up and down
repmat: Replicate and tile a matrix
Matrix Manipulation Functions
•
•
•
•
•
•
•
•
•
•
transpose (’): Transpose matrix
rot90: rotate matrix 90
tril: Lower triangular part of a matrix
triu: Upper triangular part of a matrix
cross: Vector cross product
dot: Vector dot product
det: Matrix determinant
inv: Matrix inverse
eig: Evaluate eigenvalues and eigenvectors
rank: Rank of matrix
Exercise 1 (5 minutes)
Define a matrix A of dimension 2 by 4 whose (i,j) entry is
A(i,j)=i+j
Extract two 2 by 2 matrices A1 and A2 out of the matrix A.
A1 contains the first two columns of A, A2 contains the last
two columns of A
Compute the matrix B to be the sum of A1 and A2
Compute the eigenvalues and eigenvectors of B
Solve the linear system Bx=b, where b has all the entries
equal to 1
Compute the determinant of B
Compute the inverse of B
Compute the condition number of B
NOTE: Use only MATLAB native functions for all operations
Character String
Manipulation
Character Arrays (Strings)
•
Created using single quote delimiter (')
» str
= 'Hi there,'
str =
Hi there,
» str2 = 'Isn''t MATLAB great?'
str2 =
Isn't MATLAB great?
•
Each character is a separate matrix element
(16 bits of memory per character)
str =
•
H
i
t
h
e
r
e
,
1x9 vector
Indexing same as for numeric arrays
String Array
Concatenation
Using [ ] operator:
» str ='Hi there,';
Each row must be
same length
» str1='Everyone!';
Row separator:
semicolon (;)
Column separator:
space / comma (,)
1x9 vectors
» new_str=[str, ' ', str1]
new_str =
Hi there, Everyone!
vectors
1x19 vector
» str2 = 'Isn''t MATLAB great?';
» new_str2=[new_str; str2]
new_str2 =
Hi there, Everyone!
Isn't MATLAB great?
2x19 matrix
For strings of different length:
• STRVCAT
• char
» new_str3 = strvcat(str, str2)
new_str3 =
2x19 matrix
Hi there,
(zero padded)
Isn't MATLAB great?
Working with String Arrays
• String Comparisons
– strcmp: compare whole strings
– strncmp: compare first ‘N’ characters
– findstr: finds substring within a larger string
• Converting between numeric & string arrays:
– num2str: convert from numeric to string array
– str2num: convert from string to numeric array
Elementary Math
Elementary Math
• Logical Operators
• Math Functions
• Polynomial and Interpolation
Logical Operations
»
»
Mass = [-2 10 NaN 30 -11 Inf 31];
each_pos = Mass>=0
> greater than
each_pos =
0
1
0
1
0
1
< less than
» all_pos = all(Mass>=0)
>= Greater or equal all_pos =
0
<= less or equal
» all_pos = any(Mass>=0)
~ not
all_pos =
1
& and
» pos_fin = (Mass>=0)&(isfinite(Mass))
pos_fin =
|
or
0
1
0
1
0
0
= = equal to
isfinite(), etc. . . .
all(), any()
find
Note:
• 1 = TRUE
• 0 = FALSE
1
1
Elementary Math Function
•
abs, sign: Absolute value and Signum
Function
• sin, cos, asin, acos…: Triangular functions
• exp, log, log10: Exponential, Natural and
Common (base 10) logarithm
• ceil, floor: Round toward infinities
• fix: Round toward zero
Elementary Math Function
•
•
•
•
•
round: Round to the nearest integer
gcd: Greatest common devisor
lcm: Least common multiple
sqrt: Square root function
real, imag: Real and Image part of
complex
• rem: Remainder after division
Elementary Math Function
•
•
max, min: Maximum and Minimum of arrays
mean, median: Average and Median of arrays
• std, var: Standard deviation and variance
• sort: Sort elements in ascending order
• sum, prod: Summation & Product of Elements
• trapz: Trapezoidal numerical integration
• cumsum, cumprod: Cumulative sum, product
• diff, gradient: Differences and Numerical
Gradient
Polynomials and Interpolation
• Polynomials
–
–
–
–
–
–
Representing
Roots
Evaluation
Derivatives
Curve Fitting
Partial Fraction Expansion
• Interpolation
– One-Dimensional (interp1)
– Two-Dimensional (interp2)
(>> roots)
(>> polyval)
(>> polyder)
(>> polyfit)
(>>residue)
Example
polysam=[1 0 0 8];
roots(polysam)
ans =
-2.0000
1.0000 + 1.7321i
1.0000 - 1.7321i
polyval(polysam,[0 1 2.5 4 6.5])
ans =
8.0000
9.0000
23.6250
72.0000
polyder(polysam)
ans =
3
0
0
[r p k]=residue(polysam,[1 2 1])
r = 3
7
p = -1
-1
k = 1
-2
282.6250
Example
x
y
p
p
= [0: 0.1: 2.5];
= erf(x);
= polyfit(x,y,6)
=
0.0084 -0.0983
0.4217
-0.7435
interp1(x,y,[0.45 0.95 2.2 3.0])
ans =
0.4744
0.8198
0.9981
0.1471
NaN
1.1064
0.0004
Exercise 2 (5 minutes)
• Let x be an array of values from 0 to 2, equally
spaced by 0.01
– Compute the array of exponentials corresponding to
the values stored in x
– Find the polynomial p of degree 5 that is the best least
square approximation to y on the given interval [0,2]
– Evaluate the polynomial p at the values of x, and
compute the error z with respect to the array y
– Interpolate the (x,z) data to approximate the value of
the error in interpolation at the point .9995
Programming
and
Application
Development
Topics discussed…
• The concept of m-file in MATLAB
• Script versus function files
• The concept of workspace
• Variables in MATLAB
– Type of a variable
– Scope of a variable
• Flow control in MATLAB
• The Editor/Debugger
Before getting lost in details…
• Obtaining User Input
– “input” - Prompting the user for input
>> apls = input( ‘How many apples? ‘ )
– “keyboard” - Pausing During Execution (when in Mfile)
• Shell Escape Functions (! Operator)
• Optimizing MATLAB Code
– Vectorizing loops
– Preallocating Arrays
Function M-file
function r = ourrank(X,tol)
% rank of a matrix
s = svd(X);
if (nargin == 1)
tol = max(size(X)) * s(1)* eps;
end
r = sum(s > tol);
Multiple Input Arguments
use ( )
»r=ourrank(rand(5),.1);
function [mean,stdev] = ourstat(x)
[m,n] = size(x);
Multiple Output
if m == 1
Arguments, use [ ]
m = n;
»[m std]=ourstat(1:9); end
mean = sum(x)/m;
stdev = sqrt(sum(x.^2)/m – mean.^2);
Basic Parts of a Function M-File
Output Arguments
Online Help
Function Name
Input Arguments
function y = mean (x)
% MEAN Average or mean value.
% For vectors, MEAN(x) returns the mean value.
% For matrices, MEAN(x) is a row vector
% containing the mean value of each column.
[m,n] = size(x);
Function Code
if m == 1
m = n;
end
y = sum(x)/m;
Script and Function Files
• Script Files
• Work as though you typed commands into
MATLAB prompt
• Variable are stored in MATLAB workspace
• Function Files
• Let you make your own MATLAB Functions
• All variables within a function are local
• All information must be passed to functions as
parameters
• Subfunctions are supported
The concept of Workspace
• At any time in a MATLAB session, the code has a workspace
associated with it
• The workspace is like a sandbox in which you find yourself at a
certain point of executing MATLAB
• Base Workspace: the workspace in which you live when you
execute commands from prompt
• Remarks:
• Each MATLAB function has its own workspace (its own
sandbox)
• A function invoked from a calling function has its own and
separate workspace (sandbox)
• A script does not lead to a new workspace (unlike a function),
but lives in the workspace from which it was invoked
Variable Types in MATLAB
• Local Variables
• In general, a variable in MATLAB has local scope, that is, it’s only
available in its workspace
• The variable disappears when the workspace ceases to exist
• Recall that a script does not define a new workspace – be careful,
otherwise you can step on variables defined at the level where the
script is invoked
• Since a function defines its own workspace, a variable defined in a
function is local to that function
• Variables defined outside the function should be passed to function as
arguments. Furthermore, the arguments are passed by value
• Every variable defined in the subroutine, if to be used outside the
body of the function should be returned back to the calling
workspace
Variable Types in MATLAB
• Global Variables
• These are variables that are available in multiple workspaces
• They have to be explicitly declared as being global
• Not going to expand on this, since using global variables are a bad
programming practice
• Note on returning values from a function
• Since all variables are local and input arguments are passed by value,
when returning from a function a variable that is modified in the
function will not appear as modified in the calling workspace unless
the variable is either global, or declared a return variable for that
function
Flow Control Statements
if Statement
if ((attendance >= 0.90) & (grade_average >= 60))
pass = 1;
end;
while Loops
eps = 1;
while (1+eps) > 1
eps = eps/2;
end
eps = eps*2
Flow Control Statements
a = zeros(k,k)
% Preallocate matrix
for m = 1:k
for n = 1:k
for Loop:
a(m,n) = 1/(m+n -1);
end
end
method = 'Bilinear';
switch lower(method)
case {'linear','bilinear'}
switch
Statement:
disp('Method is linear')
case 'cubic'
disp('Method is cubic')
otherwise
disp('Unknown method.')
end
Method is linear
Editing and Debugging M-Files
• The Editor/Debugger
• Debugging M-Files
– Types of Errors (Syntax Error and Runtime Error)
– Using keyboard and “ ; ” statement
– Setting Breakpoints
– Stepping Through
 Continue, Go Until Cursor, Step, Step In, Step Out
– Examining Values
 Selecting the Workspace
 Viewing Datatips in the Editor/Debugger
 Evaluating a Selection
Debugging
Select
Workspace
Set AutoBreakpoints
tips
Importing and Exporting Data
• Using the Import Wizard
• Using Save and Load command
save
save
save
save
fname
fname x y z
fname -ascii
fname -mat
load
load
load
load
fname
fname x y z
fname -ascii
fname -mat
Input/Output for Text File
•Read formatted data, reusing the
format string N times.
»[A1…An]=textread(filename,format,N)
•Import and Exporting Numeric Data
with General ASCII delimited files
» M = dlmread(filename,delimiter,range)
Input/Output for Binary File
•
•
•
•
•
»
»
»
»
»
»
fopen: Open a file for input/output
fclose: Close one or more open files
fread: Read binary data from file
fwrite: Write binary data to a file
fseek: Set file position indicator
fid= fopen('mydata.bin' , 'wb');
fwrite (fid,eye(5) , 'int32');
fclose (fid);
fid= fopen('mydata.bin' , 'rb');
M= fread(fid, [5 5], 'int32')
fclose (fid);
Exercise 3: A debug session
(10 minutes)
• Use the function demoBisect provided on the
next slide to run a debug session
– Save the MATLAB function to a file called
demoBisect.m in the current directory
– Call once the demoBisect.m from the MATLAB
prompt to see how it works
>>help demoBisect
>>demoBisect(0, 5, 30)
– Place some breakpoints and run a debug session
• Step through the code, and check the values of variables
• Use the MATLAB prompt to echo variables
• Use dbstep, dbcont, dbquit commands
function xm = demoBisect(xleft,xright,n)
% demoBisect Use bisection to find the root of x - x^(1/3) - 2
%
% Synopsis: x = demoBisect(xleft,xright)
%
x = demoBisect(xleft,xright,n)
%
% Input:
xleft,xright = left and right brackets of the root
%
n = (optional) number of iterations; default: n = 15
%
% Output: x = estimate of the root
if nargin<3, n=15; end
a = xleft;
b = xright;
fa = a - a^(1/3) - 2;
fb = b - b^(1/3) - 2;
fprintf(' k
a
%
%
%
Default number of iterations
Copy original bracket to local variables
Initial values of f(a) and f(b)
xmid
b
f(xmid)\n');
for k=1:n
xm = a + 0.5*(b-a);
% Minimize roundoff in computing the midpoint
fm = xm - xm^(1/3) - 2; % f(x) at midpoint
fprintf('%3d %12.8f %12.8f %12.8f %12.3e\n',k,a,xm,b,fm);
if sign(fm)==sign(fa)
% Root lies in interval [xm,b], replace a
a = xm;
fa = fm;
else
% Root lies in interval [a,xm], replace b
b = xm;
fb = fm;
end
end
Other Tidbits
Nonlinear Numerical Functions
• inline function »
f = inline('3*sin(2*x.^2)','x')
f =
Inline function:
f(x) = 3*sin(2*x.^2)
» f(2)
ans =
2.9681
Use char function
to convert inline
object to string
• Numerical Integration using quad
»
»
»
»
Q
F
Q
Q
=
=
=
=
quad('1./(x.^3-2*x-5)',0,2);
inline('1./(x.^3-2*x-5)');
quad(F,0,2);
quad('myfun',0,2)
Note:
quad function use adaptive
Simpson quadrature
function y = myfun(x)
y = 1./(x.^3-2*x-5);
Nonlinear Numerical Functions
• fzero finds a zero of a single variable function
[x,fval]= fzero(fun,x0,options)
– fun is inline function or m-function
• fminbnd minimize a single variable function on a
fixed interval. x1<x<x2
[x,fval]= fminbnd(fun,x1,x2,options)
• fminsearch minimize a several variable function
[x,fval]= fminsearch(fun,x0,options)
• Use optimset to determine options parameter.
options = optimset('param1',value1,...)
Ordinary Differential Equations
(Initial Value Problem)
• An explicit ODE with initial value:
• Using ode45 for non-stiff functions and ode23t
for stiff functions.
[t,y] = solver(odefun,tspan,y0,options)
function dydt = odefun(t,y)
[initialtime
Initialvlue
finaltime]
• Use odeset to define options parameter
ODE Example:
function dydt=myfunc(t,y)
dydt=zeros(2,1);
dydt(1)=y(2);
dydt(2)=(1-y(1)^2)*y(2)-y(1);
»
[t,y]=ode45('myfunc',[0 20],[2;0])
3
Note:
Help on odeset to set options
for more accuracy and other
useful utilities like drawing
results during solving.
2
1
0
-1
-2
-3
0
2
4
6
8
10
12
14
16
18
20
Example 4: Using ODE45
(5 minutes)
• Use the example on the previous page to
solve the slightly different IVP on the
interval [0,20] seconds:
y1  (1  0.9 y12 ) y1  y1  0
y1 (0)  2
y1 (0)  0
Graphics
Fundamentals
Graphics and Plotting in MATLAB
• Basic Plotting
– plot, title, xlabel, grid, legend, hold, axis
• Editing Plots
– Property Editor
• Mesh and Surface Plots
– meshgrid, mesh, surf, colorbar, patch, hidden
• Handle Graphics
2-D Plotting
Syntax:
color
line
marker
plot(x1, y1, 'clm1', x2, y2, 'clm2', ...)
Example:
x=[0:0.1:2*pi];
y=sin(x);
z=cos(x);
plot(x,y,x,z,'linewidth',2)
title('Sample Plot','fontsize',14);
xlabel('X values','fontsize',14);
ylabel('Y values','fontsize',14);
legend('Y data','Z data')
grid on
Sample Plot
Title
Ylabel
Grid
Legend
Xlabel
Displaying Multiple Plots
• Nomenclature:
– Figure window – the window in which MATLAB displays plots
– Plot – a region of a window in which a curve (or surface) is
displayed
• Three typical ways to display multiple curves in MATLAB
(other combinations are possible…)
– One figure contains one plot that contains multiple curves
• Requires the use of the command “hold” (see MATLAB help)
– One figure contains multiple plots, each plot containing one curve
• Requires the use of the command “subplot”
– Multiple figures, each containing one or more plots, each
containing one or more curves
• Requires the use of the command “figure” and possibly “subplot”
Subplots
Syntax:
subplot(rows,cols,index)
»subplot(2,2,1);
» …
»subplot(2,2,2)
» ...
»subplot(2,2,3)
» ...
»subplot(2,2,4)
» ...
The “figure” Command
• Use if you want to have several figures open for
plotting
• The command by itself creates a new figure
window and returns its handle
>> figure
• If you have 20 figures open and want to make
figure 9 the default one (this is where the next
plot command will display a curve) use
>> figure(9)
>> plot(…)
• Use the command close(9) if you want to close
figure 9 in case you don’t need it anymore
Surface Plot Example
x = 0:0.1:2;
y = 0:0.1:2;
[xx, yy] = meshgrid(x,y);
zz=sin(xx.^2+yy.^2);
surf(xx,yy,zz)
xlabel('X axes')
ylabel('Y axes')
3-D Surface Plotting
contourf-colorbar-plot3-waterfall-contour3-mesh-surf
Specialized Plotting Routines
bar-bar3h-hist-area-pie3-rose
Handle Graphics
• Graphics in MATLAB consist of
objects:
– root, figure, axes, image, line, patch,
rectangle, surface, text, light
• Creating Objects
• Setting Object Properties Upon
Creation
• Obtaining an Object’s Handles
• Knowing Object Properties
• Modifying Object Properties
– Using Command Line
– Using Property Editor
Graphics Objects
Root
object
Figure
object
UIMenu
objects
Surface
object
Line
objects
Text
objects
Axes object
UIControl
objects
Obtaining an Object’s Handle
1. Upon Creation
h_line = plot(x_data, y_data, ...)
2. Utility Functions
What is the current object?
• Last object created
OR
• Last object clicked
0 - root object handle
gcf - current figure handle
gca
- current axis handle
gco
- current object handle
3. FINDOBJ
h_obj = findobj(h_parent, 'Property', 'Value', ...)
Default = 0 (root object)
Modifying Object Properties
• Obtaining a list of current properties:
get(h_object)
• Obtaining a list of settable properties:
set(h_object)
• Modifying an object’s properties
 Using Command Line
set(h_object,'PropertyName','New_Value',...)
 Using Property Editor
Graphical User Interface
•
•
•
•
•
What is GUI?
What is figure and *.fig file?
Using guide command
GUI controls
GUI menus
static text
Axes
Checkbox
Frames
Slider
Edit text
Radio Buttons
Push Buttons
Guide Editor
Property Inspector
Result Figure
Data Types
Data Types
• Numeric Arrays
• Multidimensional Arrays
• Structures and Cell Arrays
Multidimensional Arrays
The first references array dimension
1, the row.
»
The second references dimension 2, »
the column.
The third references dimension 3,
The page.
0
16
1
15
9
2
4
3
1
4
1
1
0
0
20 30 130
0 100 80
11
1
1
70 60 120
3
4
14 15
1
6 10
0
10
0
20
Page 1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
Page N
A = pascal(4);
A(:,:,2) = magic(4)
A(:,:,1) =
1
1
1
1
2
3
1
3
6
1
4
10
A(:,:,2) =
16
2
3
5
11
10
9
7
6
4
14
15
» A(:,:,9) =
diag(ones(1,4));
1
4
10
20
13
8
12
1
Structures
• Arrays with named data containers called fields.
»
»
»
patient.name='John Doe';
patient.billing = 127.00;
patient.test= [79 75 73;
180 178 177.5;
220 210 205];
• Also, Build structure arrays using the struct function.
• Array of structures
» patient(2).name='Katty Thomson';
» Patient(2).billing = 100.00;
» Patient(2).test= [69 25 33; 120 128 177.5; 220
210 205];
Cell Arrays
• Array for which the elements are cells and can hold
other MATLAB arrays of different types.
»
A(1,1)
0 5 8;
7 2 9]};
» A(1,2)
» A(2,1)
» A(2,2)
= {[1 4 3;
= {'Anne Smith'};
= {3+7i};
= {-pi:pi/10:pi};
• Using braces {} to point to elements of cell array
• Using celldisp function to display cell array
Conclusion
 Matlab is a language of technical computing.
 Matlab, a high performance software, a highlevel language
 Matlab supports GUI, API, and …
 Matlab Toolboxes best fits different applications
 Matlab …
Getting more help
• Contact http://www.mathworks.com/support
• You can find more help and FAQ about
mathworks products on this page.
• Contact comp.soft-sys.matlab Newsgroup
• Use google to find more information (like the
content of this presentation, in the first place)
Example 1a
Example 1b
Example 1c