Master in Optical Fiber Communications and Photonic Technologies Foundations of Digital Transmission...

Master in Optical Fiber Communications and Photonic Technologies

Foundations of Digital Transmission - Fall quarter

Introduction to Matlab

Copyright 2001 OCG 2

What Is MATLAB?

MATLAB is an interactive program for scientific and engineering numeric calculation.

It integrates computation, visualization, and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.

Typical uses include:Math and computationAlgorithm developmentModeling, simulation, and prototypingScientific and engineering graphics


Command Window

Command Window is used to enter variables and run functions and M-files.

Navigation within MATLAB is done using regular UNIX commandscd (change directory)pwd (show the path) ls (list contents of directory)whos (list of the variable stored in the memory)

In latest version, most of this is also available using a graphical interface


Command Window

Getting help from the command window

help <function_name> (show the help document for a given function)

By the way you can use this help only if you know the name of the function to be used. If you do not know it, just use the windows help, which is much more easy and complete. Here you can find also several examples.

P.S.If you want to have an help for your own functions, you can write it

at the beginning of the function as :

% your own help. After this statement, the matlab file will start.


Variables

MATLAB does not require any type declarations!

Real scalar: >> x=1Complex scalar: >> x=1+2iRow vector: >> x=[1 2 3]Column vector: >> x=[1; 2; 3]2x2 Matrix: >> x=[1 2; 3 4]

You can define global variables by putting in front the variable the statement global.


Complex numbers

Some useful operations on complex numbers:

Complex scalar >> x = 3+4jReal part of x >> real(x) ->3 Imaginary part of x >> imag(x) ->4Magnitude of x >> abs(x) ->5Angle of x >> angle(x) ->0.9273Complex conjugate of x >> conj(x) ->3 - 4i


Generating vectors

>> x=[a:step:b]Generate a vector that takes on the values a to b in

increments of step

>> x=linspace(a,b,n)generates a row vector x of n points linearly

spaced between a and b

>> x=logspace(a,b,20)generates a logarithmically spaced vector x of n

points between 10^a and 10^b.


Generating matrices

Matrix building functions:>> A=zeros(m,n) returns an m-by-n matrix of zeros

>> A=ones(m,n) returns an m-by-n matrix of 1s

>> A=eye(m,n) returns an m-by-n matrix with 1's on the diagonal

and 0's elsewhere


Generating random matrices

>> A=rand(m,n) returns an m-by-n matrix of random numbers whose

elements are uniformly distributed in the interval (0,1)

>> A=randn(m,n) returns an m-by-n matrix of random numbers whose

elements are normally distributed with mean 0 and variance 1

>> A=randint(m,n,range) generates an m-by-n integer matrix. The entries are

uniformly distributed and independently chosen from the range:

[0, range-1] if range is a positive integer[range+1, 0] if range is a negative integer


Accessing matrix elements

Elements of a matrix are accessed by specifying the row and column

>> A=[1 2 3; 4 5 6; 7 8 9];>> x=A(1,3)

Returns the element in the first row and third column

>> y=A(2,:)Returns the entire second row [4 5 6]“:” means “take all the entries in the column”

>> B=A(1:2,1:3)Returns a submatrix of A consisting of rows 1 and 2

and all three columns [1 2 3; 4 5 6]


Arithmetic matrix operation

The basic arithmetic operations on matrices are:

+ addition - subtraction* multiplication / division^ power ’ conjugate transpose

This operation are to be meant in the “matrix sense”

MATRIX-wise operation


element-by-element operations

MATLAB provides element-by-element operations by prepending a ‘.’ before the operator

.* multiplication ./ division .^ power .’ transpose (unconjugated)

BE CAREFUL when operating on matrix: the meaning of the two operations .* and * are completely different

element-wise operation


Relational operations

MATLAB defines the following relational operations:

< less than<= less than or equal to> greater than>= greater than or equal to== equal to~= not equal to


Logical operations

MATLAB defines the following logical operations:

& and | or~ not


Math functions

The following functions operate element-wise, also when applied to a matrix:

sin cos tan asin acos atan sinh cosh tanh exp log(natural log) log10 abs sqrt sign


M-files

MATLAB is an interpretive language M-files are text files containing MATLAB scripts Scripts are sequences of commands typed by an

editor The instructions are executed by typing the file

name in the command window at the MATLAB prompt

All the variables used in the m-file are placed in MATLAB’s workspace that contains all the variables defined in the MATLAB session


M-files Debug

In Matlab you can debug your m-file, like in other programming languages

To do it, you need to open your matlab file from the window command.

Afterwards, you can operate exactly like for other languages and you can use usual command as:

step instep outbreak pointetc. etc


Flow control

If statements

if expression statementselse statements end

Example

If n<0a=a-1;

elsea=a+1;

end


Flow control

ForRepeats a group of statements a fixed,

predetermined number of times.

a=0;for n = 1:10

a=a+1;end


Function in Matlab

To simplify your matlab file structure, you can use functions. An example of how to use Matlab functions is the following:

Main Matlab Program

SegEqRx = SegEqNew + 1*SegRx(DimC*TTaps+1:LRx-DimC*TTaps);clear SegEqNew; clear SegEqOld;[SAMPLE_CENTRAL, BIT_DETECTED] =

=syncronizer(SegEqRx,PNSEQ_VECTOR,NS_BIT,NBIT_PNSEQ);…

Function declaration:function [ SAMPLE_CENTRAL, BIT_DETECTED]=syncro(SIGNAL,PNSEQ_VECTOR,NS_BIT,NBIT_PNSEQ);Main of the function


Creating a plot

>> plot(x,y) produces a graph of y versus x, where x and y are

two vectors

x=linspace(0,2*pi,100);plot(x,sin(x));

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

x

Sin

e of

x


Line styles and colors

It is possible to specify color, line styles, and markers when you plot your data using the plot command

plot(x,y,'color_style_marker') color_style_marker is a string containing from one

to four characters constructed from a color, a line style, and a marker type:Color strings: 'c', 'm', 'y', 'r', 'g', 'b', 'w', and 'k'.

These correspond to cyan, magenta, yellow, red, green, blue, white, and black

Linestyle strings are '-' for solid, '--' for dashed, ':' for dotted, '-.' for dash-dot, and 'none' for no line

The marker types are '+', 'o', '*' and 'x'


Axis lables and titles

xlabel('string') labels the x-axis of the current axes

ylabel('string') labels the y-axis of the current axes

Title(‘string’)add a title to a graph at the MATLAB command

prompt or from an M-file


The figure function

MATLAB directs graphics output to a figure window Graphics functions automatically create new figure

windows if none currently exist>>figurecreates a new window and makes it the current

figure

>>figure(h)make an existing figure current by passing its handle

(the number indicated in the window title bar), as an argument to figure

>>clfClear current figure window


Adding plots

Setting hold to on, MATLAB doesn’t remove the existing graph and adds the new data to the current graph

x=linspace(0,2*pi,100);plot(x,sin(x));hold on;plot(x,cos(x));xlabel('x');ylabel('Sine of x');

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

x

Sin

e of

x


Adding plots

With more graphics functionalities:

x=linspace(0,2*pi,100);plot(x,sin(x),’-ob’);hold on; grid on;plot(x,cos(x),’->r’);xlabel('x');ylabel('Sine of x');legend('sin(x)','cos(x)',3)


Basic plotting commands

PlotGraph 2-D data with linear scales for both axes

LoglogGraph with logarithmic scales for both axes

SemilogxGraph with a logarithmic scale for the x-axis and a

linear scale for the y-axis Semilogy

Graph with a logarithmic scale for the y-axis and a linear scale for the x-axis


Specialized plots

bar(x,Y) draws a bar for each element in Y at locations

specified in x, where x is a monotonically increasing vector defining the x-axis intervals for the vertical bars

>> bar((1:1:10),(1:1:10))


Specialized plots

Stemdisplays data as lines (stems) terminated with a

marker symbol at each data value

x=linspace(0,2*pi,10);stem(x,sin(x));


Specialized plots

StairsStairstep plots are useful for drawing time-history

plots of digitally sampled data systems

x=linspace(0,2*pi,20);stairs(x,sin(x));

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