introduction to matlab ppt

Introduction to MATLAB
MATLAB in Science, Engineering, and
Mathematics Instruction
John Sebeson
DeVry University
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
What is MATLAB?

MATLAB stands for MATrix LABoratory.

MATLAB is a high-performance language for
technical computing.

Math and computation

Algorithm development (optimized for DSP)

Data acquisition

Modeling, simulation, and prototyping

Data analysis, exploration, and visualization

Scientific and engineering graphics

Application development, including graphical
user interface building
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
Why Learn and Use MATLAB?


Heavily used in EET/CET courses with DSP
content (CET311, EET350, EET453)

Extensive built-in commands for scientific
and engineering mathematics

Easy way to generate class demonstrations
and test examples

Simple and intuitive programming for more
complex problems

Standard and widely-used computational
environment with many features,
extensions, and links to other software.
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
MATLAB in DSP Product
Development
Develop and
Test Algorithms
in MATLAB
SIMULINK
Simulation
Code
Composer
DSP
Processor
Platform

MATLAB + PC = DSP Processor!! (just less efficient)
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
Why Learn MATLAB (and DSP)?

Digital Signal Processing (DSP) is the
dominant technology today, and into the
future, for small-signal electronic systems
(i.e., just about everything)

MATLAB has become one of the standard
design environments for DSP engineering

Our students need to be literate and skilled
in this environment: knowledgeable in both
DSP and MATLAB
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
How Can I Learn MATLAB?

Keep a copy of this presentation for
reference (available on my Web
Page)

Get MATLAB loaded on your PC

Read the “Getting Started” Users
Guide at the MathWorks web site

Study some of the built-in help files

and demos

Dive right in and use it!
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
This Presentation

The MATLAB System

The basics of MATLAB computation

The basics of MATLAB graphing

The basics of MATLAB programming

Various course examples

Mathematics

Electronics

Physics

Signal Processing(*)
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
The MATLAB System

Development Environment.


MATLAB desktop

Editor and debugger for MATLAB programs (“m-files”)

Browsers for help, built-in and on-line documentation

Extensive demos

The MATLAB Mathematical Function Library.

Elementary functions, like sum, sine, cosine, and complex arithmetic

More sophisticated functions like matrix inverse, matrix eigenvalues, Bessel
functions, and fast Fourier transforms.

“Toolboxes” for special application areas such as Signal Processing

The MATLAB Language.

“Programming in the small" to rapidly create quick and dirty throw-away
programs, or

“Programming in the large" to create large and complex application programs.

Graphics.

2D and 3D plots

Editing and annotation features


The MATLAB Application Program Interface (API).

A library that allows you to write C and Fortran programs that interact with
MATLAB.
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
MATLAB Development Environment
(Workspace)
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
MATLAB “Help” Utilities

MATLAB is so rich that ‘help’ is essential

Command name and syntax

Command input/output parameters

Usage examples

Help command

help command_name

help [partial_name] tab

Help documents

Demos
January 18, 2005 J. M. Sebeson - DeVry Uni

versity © 2005
MATLAB Function Library
(A Subset)
matlab\general - General purpose commands.
matlab\ops - Operators and special characters.
matlab\lang - Programming language constructs.
matlab\elmat - Elementary matrices and matrix manipulation.
matlab\elfun - Elementary math functions.
matlab\specfun - Specialized math functions.
matlab\matfun - Matrix functions - numerical linear algebra.
matlab\datafun - Data analysis and Fourier transforms.
matlab\polyfun - Interpolation and polynomials.
matlab\funfun - Function functions and ODE solvers.
matlab\sparfun - Sparse matrices.
matlab\scribe - Annotation and Plot Editing.
matlab\graph2d - Two dimensional graphs.
matlab\graph3d - Three dimensional graphs.
matlab\specgraph - Specialized graphs.
matlab\graphics - Handle Graphics.
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
Some Elementary Functions
Exponential.
exp - Exponential.
expm1 - Compute exp(x)-1 accurately.
log - Natural logarithm.
log1p - Compute log(1+x) accurately.
log10 - Common (base 10) logarithm.
log2 - Base 2 logarithm and dissect floating point number.
pow2 - Base 2 power and scale floating point number.

realpow - Power that will error out on complex result.
reallog - Natural logarithm of real number.
realsqrt - Square root of number greater than or equal to zero.
sqrt - Square root.
nthroot - Real n-th root of real numbers.
nextpow2 - Next higher power of 2.
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
Some Specialized Functions
Number theoretic functions.
factor - Prime factors.
isprime - True for prime numbers.
primes - Generate list of prime numbers.
gcd - Greatest common divisor.
lcm - Least common multiple.
rat - Rational approximation.
rats - Rational output.
perms - All possible permutations.
nchoosek - All combinations of N elements taken K at a time.
factorial - Factorial function.
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
The MATLAB Language
(M-file example)
function one_period(amp,freq,phase)
% ONE_PERIOD(AMP,FREQ,PHASE)
% This function plots one period of a sine wave with a given amplitude,
% frequency (in Hz), and phase ( in degrees).
T=1000/freq; % Compute the period in ms
t=0:T/100:T; % Define a 100 point ms time vector 1 period long

y=amp*sin(2*pi*t/T+phase*pi/180); % One period of the sine function
plot(t,y) % Plot the result and format the axes and title
xlabel('milliseconds')
ylabel('amplitude')
title(['One Period of a ',num2str(freq),' Hz Sinewave with
',num2str(phase), ' Degree phase'])
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
MATLAB Graphics:
2D Functions (Physics Example)
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
MATLAB Graphics:
2D Functions (Physics Example)
0 1 2 3 4 5 6 7 8 9 10
0
500
1000
1500
2000
2500
3000
3500
wavelength microns
kilowatts/sq.meter-micron
Planck Radiation Law
3000 K
2700 K
2500 K
January 18, 2005 J. M. Sebeson - DeVry Uni

versity © 2005
MATLAB Graphics:
3D Functions (DSP Example)
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
Basic MATLAB Computation:
Representation of Numbers and Variables

MATLAB operates on n row by m column
matrices:

A n x m quantity is an array

A 1 x m or a n x 1 quantity is a vector
[8 1 6]

A 1 x 1 quantity is a scalar
[8]
[8 1 6
3 5 7
4 9 2]
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
Basic MATLAB Computation:
Basic Operations

Array manipulation (Magic Square
example)

Sum, diag, transpose, colon operator,

indexing

Array, vector, and scalar operators

Matrix and vector addition and
multiplication

Element-by-element operations

Variable statements and definitions
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
MATLAB Plotting and Graphics

Rich set of commands for 2D and 3D
plotting of functions

Command formatting and editing

GUI formatting and editing

Image display capabilities

Animation capabilities

Simple “copy and paste” for
publishing generated figures
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
MATLAB Plotting

Basic Commands

plot – x,y line plots

stem – n,y discrete plots (standard
representation of digital signals)

bar – vertical bar plots

plot3 – 3D x,y,z line plots

mesh, surf, etc. – 3D surface plots

show_img – display matrix as an image

hold – hold current figure for multiple line plots

subplot – put multiple plots in one figure frame

Etc, etc. - See MATLAB help documentation
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
Basic Plotting - Examples

Plot of sin(x) function

Stem of sin(x) function

Bar of sin(x) function


Several sine functions with “hold”

Several sine functions with “subplot”

2D plot of sinc(x)

3D plot of sinc(x) [“plot_sinc” m-file]

GUI editing

View by rotation

Animation [“brownian_demo” m-file]
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
Basic MATLAB Programming

Scripts

String of MATLAB commands

Stored as m-file (*.m)

Use variables from command line

Variables have names consistent with script variable names

Used for “quick and dirty” programs

Example: “dydx_script”


Functions

String of MATLAB commands

Stored as m-file (*.m)

Use variables as function parameters

No restriction on parameter names

Can return variable results

Used for general purpose programs

Example: “yy=dydx(x,y)
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
Structure of m-file Functions:
Examples

“one_period”

Use of “num2str” for variable formatting

“sumofsines”

Use of parameter-controlled data input
loops


“fft_plot”

Use of MATLAB functions as subroutines

Use of “nargin” test and branch
January 18, 2005 J. M. Sebeson - DeVry Uni
versity © 2005
Mathematics Example:
Polynomial Algebra (Convolution Operator)

Polynomial products and factoring:
82026218)445)(23(
2345232
+++++=+++++ xxxxxxxxxx
>> p1=[1,3,2];
>> p2=[1,5,4,4];
>> pc=conv(p1,p2)
pc =
1 8 21 26 20 8
>> deconv(pc,p2)
ans =
1 3 2
>> deconv(pc,p1)
ans =
1 5 4 4