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EE 3350

MATLAB INTRODUCTION

Instructor: Dr. Duncan MacFarlane

Teaching Assistant: Yuan Hu

2

WHAT IS MATLAB?

• MATLAB is a numerical computing environment

developed by MathWorks. • MATLAB allows matrix manipulations, plotting of functions and data, and implementation of

algorithms. • MatLab program and script files always have filenames ending with ".m".

• The programming language is exceptionally

straightforward since almost every data object is assumed to be an array. 3

MATLAB WINDOWS

• We can type the commands in the command window. • As for programming, .m file script is preferred.

File ã New ã Script

GETTING HELP Ñ

Online help is available from the Matlab prompt (a double arrow) ggenerally (listing all available commands): >> help [a long list of help topics follows] specific commands >> help fft [a help message on the fft function follows].

DATA REPRESENTATIONS IN MATLAB Ñ

VVariables: Variables are defined as the assignment operator =Ž . The syntax of variable assignment is variable name = a value (or an expression)

Example:

DATA REPRESENTATIONS IN MATLAB Ñ

VVectors/Matrices :

MATLAB can create and manipulate arrays of 1 ( vectors) , 2 (matrices), or more dimensions. row vectors: a = [1, 2, 3, 4] is a 1X4 matrix column vectors: b = [5; 6; 7; 8; 9] is a 5X1 matrix

Example:

ARITHMETIC OPERATIONS Ñ

Five basic arithmetic operators

ARITHMETIC OPERATIONS

Three operators working on an element-by element basis.

The results of the three examples are the same as

those of * / ^. But what will happen when it comes to the vector operations?

VECTOR OPERATIONS

Consider the vectors: The following operations indicate the resulting vectors:

VECTOR OPERATIONS

EExamples

(1)Compute the dot product: (2) Compute an element-by-element multiplication of two vectors:

RELATIONAL & LOGICAL OPERATORS

Relational Operators Logical Operators

CONTROL FLOW

iif statements for loops while loops .m files have the following control flow constructs: Each of the constructs needs to terminate with an end statement.

CONTROL FLOW

iif conditional execution of certain parts of a code

Matlab code:

Results: Example:

CONTROL FLOW

ffor repeat certain commands in a predetermined way

Matlab code:

Results: Example

CONTROL FLOW

wwhile: repeats a sequence of commands as long as some condition is met.

Matlab code:

Results: Example:

MATHEMATICAL FUNCTIONS IN MATLAB Ñ

MATLAB offers many predefined mathematical functions for technical computing, e.g.

CColon operator (:)

Suppose we want to enter a vector x consisting of points (0,0.1,0.2,0.3,...,5).We can use the command

FFT FUNCTION IN MATLAB Ñ

fft function uses the Fast Fourier transform algorithm to compute Discrete Fourier transform.

SSyntax

Y

Y=fft(x)

Y=fft(x,n) Ñ

Definition

The functions Y=fft(x) and y=ifft(X) implement the transform and inverse transform pair given for vectors of length N by:

Is an Nth root of unity

FFT FUNCTION IN MATLAB

DDescription

Y =fft(x) returns the DFT of vector x, computed

with a fast Fourier transform algorithm. Y=fft(x,n) returns the n-point DFT. If the length of x is less than n, x is padded with trailing zeros to length n. If the length of x is greater than n, the sequence x is truncated.

BASIC PLOTTING IN MATLAB Ñ

MATLAB has an excellent set of graphic tools. Plotting a given data set or the results of computation is possible with very few commands .

The MATLAB command to plot a graph is p

plot(x,y), e.g. MATLAB enables you to add axis labels and titles, e.g.

BASIC PLOTTING IN MATLAB

BASIC PLOTTING IN MATLAB

EExample 1: Sine Wave

Matlab code:

BASIC PLOTTING IN MATLAB

EExample 1: Sine Wave

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -1 -0.8-0.6-0.4-0.2 0

0.20.40.60.8

1

Sine Wave Signal

Time (s)

Amplitude

Plot: signal in time domain

BASIC PLOTTING IN MATLAB

EExample 1: Sine Wave

Plot: signal in frequency domain

-80 -60 -40 -20 0 20 40
60
80
0

1020304050607080

Spectrum of a Sine Wave

Frequency (Hz)

Amplitude

BASIC PLOTTING IN MATLAB

EExample 2:Multiplication of two Cosine Waves

f1 = 20; f2=10

Matlab code:

BASIC PLOTTING IN MATLAB

EExample 2:Multiplication of two Cosine Waves

f1 = 20; f2=10

Plot: signal in time domain

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -1 -0.8-0.6-0.4-0.2 0

0.20.40.60.8

1

Multiplication of two coine Wave Signals

Time (s)

Amplitude

BASIC PLOTTING IN MATLAB

EExample 2:Multiplication of two Cosine Waves

f1 = 20; f2=10

Plot: signal in frequency domain

-100 -80 -60 -40 -20 0 20 40
60
80
100
0

102030405060

Spectrum of a Sine Wave

Frequency (Hz)

Amplitude

BASIC PLOTTING IN MATLAB

EExample 2:Multiplication of two Cosine Waves

What happens when f1=f2?

BASIC PLOTTING IN MATLAB

EExample 2:Multiplication of two Cosine Waves

f1 = 10; f2=10

Plot: signal in time domain

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.10.20.30.40.50.60.70.80.9

1

Multiplication of two coine Wave Signals

Time (s)

Amplitude

BASIC PLOTTING IN MATLAB

EExample 2:Multiplication of two Cosine Waves

f1 = 10; f2=10

Plot: signal in frequency domain

-100 -80 -60 -40 -20 0 20 40
60
80
100
0

20406080

100120

Spectrum of a Sine Wave

Frequency (Hz)

Amplitude

It has 3 spectrum components instead of 4. Why?

BASIC PLOTTING IN MATLAB

EExample 2:Multiplication of two Cosine Waves

f1 = 10; f2=10

Plot: signal in frequency domain

It has 3 spectrum components instead of 4. Why?

Hints:

12 12 12 cos(2 ( ) ) cos(2 ( ) )cos(2 ) cos(2 )2fft fftft ft ppppquotesdbs_dbs21.pdfusesText_27

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