proceso de señales continuas y discretas en matlab

7/17/2019 Proceso de señales continuas y discretas en matlab

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IEEES-1Universidad Autónoma de Occidente, Señales y Sistemas

04 de sept de 201! "ali-"olom#ia!In$orme %o!1

DISCRETE AND CONTINUOUS PROCESSING SIGNALS INMATLAB

PROCESAMIENTO DE SEÑALES CONTINUAS Y DISCRETAS EN MATLAB

%elson &ordon, 'ulia (ercedes1! Sarria &ar)on, *ina "aterine2! Esco#ar "ru), 'uan %icolas+

2101116 1, 2100357 2 , 21114793

[email protected] 1, [email protected] , [email protected] Ingeniería iom!"ica, #aculta" "e Ingeniería, $ni%ersi"a" &ut'noma "e (cci"ente, )ali )olombia1

Ingeniería iom!"ica, #aculta" "e Ingeniería, $ni%ersi"a" &ut'noma "e (cci"ente, )ali )olombia2 Ingeniería *ultime"ia, #aculta" "e Ingeniería, $ni%ersi"a" &ut'noma "e (cci"ente, )ali )olombia3

ABST

RACTis report so.s te application developed in(A*A/, .ic studies te #eavior o$ #asicsins and operations scrollin, scalin andinvestment #ot in varia#les as continuousdiscrete! 3inally te conclusions o#tained a$ter teprocess o$ researc and development o$ tepresented application are presented!

RESUMEN

Este documento muestra la aplicacióndesarrollada en (A*A/, ue estudia elcomportamiento de las señales y operaciones#5sicas despla)amiento, escalamiento einversión, tanto en varia#les discretas comocontinuas! 6or 7ltimo se presentan lasconclusiones o#tenidas tras el proceso deinvestiación y desarrollo de la solicitudpresentada!

INTRODUCTION

&iven te vast amount o$ in$ormation surroundinte ne. .orld, many times, as a matter o$ practicality, tat in$ormation can #e represented #ya matematical lanuae, .ic, $or te person

.it te necessary e8pertise in tis area, is easy tovisuali)e in$ormation! Sinals are a .ay to #rinmuc in$ormation to te and o$ te person .oneeds it! "urrently, in most pro$essional $ields,sinals play a very important role, tere areseveral e8amples tat are enineerin related, $or e8ample, a sinal A" voltae, processin #otvoice and video, te #eavior o$ pysicalpenomena, tousands o$ e8amples .ic .ill not$it more in dept in tis report, #ut are e8amples.ic see9s to :usti$y te development o$ applications to vie. tis 9ind o$ penomena in anoptimal .ay!

o carry out various applications .itin $ocused, as

in tis case, sinal andlin, reuires tools tatyou $ind in te rit to ma9e di$$erent aloritms inorder to et to te end, an application tat is use$ul$or te manaement o$ te common person, andpresent various varia#les and $acilities $or tedeveloper! (A*A/ is a matematical tool tato$$ers an interated development environmentI;E .it its o.n lanuae o$ proramminlanuae (, .ic is very similar to te 'A<Alanuae in .ic you can carry out teimplementation o$ aloritms, creation o$ rapical

User inter$aces and communication .it proramsin oter lanuaes and oter ard.are devices!

OBJECTIVES

is document .as carried out in order to meet te$ollo.in o#:ectives=

• >no. and deepen a#out a tool suc as

(A*A/ trou te development o$ saidapplication, .ic can #e e8ploited .itvarious purposes!

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• &et a 9no.lede #ase in order to deal

.it issues arisin in te near $uture!

Image No.1 (example GUI in MATLAB)http://m2matlabdb.ma.tm.de/do!nload."#p$

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THEORETICAL FRAMEWORK

(A*A/ is a matematical so$t.are tool tato$$ers an interated development environmentI;E .it a lanuae o$ its o.n proramminlanuae called (!

Amon its #asic $eatures are= matri8 manipulation,te representation o$ data and $unctions,

implementation o$ aloritms, creation o$ user inter$aces &UI, .ic .ill #uild te report andcommunication .it oter prorams andlanuaes oter ard.are devices!

Sinal analysis and classi$ication o$ sinalsprocessin! It is #ased on te results o$ te teoryo$ in$ormation, statistics and appliedmatematics !A sinal is a $lo. o$ in$ormationcomin $rom a source, .ic may ave a di$$erentnature= mecanical, optical, manetic, electric,acoustic,!!! In eneral, to #e a#le to #e processed,sinals are trans$ormed into electrical sinals #ytransducers!

3or its analysis, te sinals are usually modeled asmatematical $unctions! e most #asicclassi$ication o$ sinals are produced accordin toteir representation .it respect to te varia#lestey depend on time, space!!!!

,ignal# !ith di#-ete aiable#

Sinals .it discrete varia#les, are #asically$unctions in .ic te independent varia#le canonly ta9e inteer values 0!1, 2!+, itsnomenclature is commonly=

• 0n $or te independent varia#le!

• 0xn3 $or te dependent varia#le!

Image No.2 (4.g. #ignal !ith di#-ete aiable)http://apnte#5de5anali#i#5de5

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,ignal# !ith -ontino# aiable#

Sinals .it continuous varia#les, are #asically$unctions in .ic te independent varia#le canta9e values decimal 0,12+ $or e8ample, itsnomenclature, commonly is tus=

• 0t $or te independent varia#le!

• 0x(t) $or te dependent varia#le!

Image No.8 (4.g. #ignal !ith -ontino# aiable)http://apnte#5de5anali#i#5de5


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&iven tat te application consists o$ severalvaria#les to raps suc as scalin, investmentreardin a8ial sa$t, and modi$ication o$ teamplitude, is .ort vie.in a little a#out tese

canes!

Operati!" # t$e %aria&'e" ()!ti!**" a!++i")rete,-

/elo. are di$$erent operations scalin, scrollinand investment .ic can #e a sinal $or tevaria#le o. continuous discrete!

Ine#tment:

is operation is #asically to cane te sino$ te arument o$ te dependent varia#le!is .ill involve tat $unction to reverse tea8ial sa$t connection!

• Sea 8 t, its inverse is 8 -t!

• Sea 8 ?n@, its inverse is 8 ?-n@!

Image No. (4.g. ineted -ontino# #ignal)http://apnte#5de5anali#i#5de5


,-olling:

&rapically euivalent to move te sinaladvance le$t or rit delay! is is acieved #yaddin to te arument o$ te dependent varia#levalues eiter positive to tem or neative to

delay tem!

e $unction 8 t moves ta9in te $orm

8 t t0!

e $unction 8 ?n@ move to ta9in te

$orm 8 ?n n0@!

Image No. ;. (,ignal -ontine# a o66#et in time).http://apnte#5de5anali#i#5de5


Image No. <. ('i#-ete #ignal !ith an o66#et in time).http://apnte#5de5anali#i#5de5


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S)a'i!.-

A tird trans$ormation is te scalin, to scale asinal tis means tat a sinal 8t is te oriinalsinal, tis sinal occurs 82t .ic is te scalino$ te oriinal sinal, or in oter .ords is t.ice tesinal, also ives tis sinal 8t is tat itBs tereduction o$ te sinal in al$! In tis case $or discrete sinals tere is no steppin in time sincetere are no intermediate intervals in te sinal!

FUNCTIONS

ere are some #asic $unctions in continuous and

discrete sinals suc as unitary impulse and te

step unit, tese t.o $unctions are analyses trou

a proram to see i$ #eavior!

F*!)ti! p*"$ *!it-

/0 ;iscreet=

δ [n]={0,∧n≠0

1,∧n=0

10 "ontinuous=

δ (t )={0,∧t ≠0

1,∧t =0

U!it "tep #*!)ti!-

/0 ;iscreet=

u[n]={0,∧n<01,∧n>0

10 "ontinuous=

u(t )={0,∧t <0

1,∧t >0

ANALYSIS

te inter$ace as di$$erent options .ere te user

can coose te parameters o$ te sinal as is te

amplitude o$ it and te operation to #e per$ormed,

eiter scalin, reverse or displace te sinal is

reuired to #e continuous or discrete, in te same

inter$ace te t.o sinals are andled, as itCs so.n

in te $ollo.in!

/elo. are several e8amples o$ operations carried

out te Inter$a8 .it several sins and sinal

pulses!

e $ollo.in picture so.s o. it is invested,

moves and spreads te continuous sinal .it an

amplitude o$ unit 10, tis is acieved #y scalin

processes, investment and movement a#ove and

te oriinal sinal!

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Image No. >. (%ontino# #ignal !ith #-aling).http://apnte#5de5anali#i#5de5


Image No. ?. (U#e Inte6a-e). authorshi+ on image











e $ollo.in imae so.s te displacement o$ a

discrete sinal!

In te ne8t picture .e see a continuous pulsesinal inverted and te oriinal pulse o$ te sinal!

e ne8t picture .e see a pulse o$ te oriinal

discrete sinal and te sinal .ic is applied

to te operation o$ scalin and o$$set!

And as a last e8ample, .e see a continuous sinal

displaced, so in tis .ay .e could see eac and

every one o$ te possi#le com#inations tat can #e

accomplised .it inter$ace $or eiter a sinal or a

continuous or discrete pulse!

CONCLUSIONS

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Image No. 11. (di#pla-ed di#-ete #ignal.). authorshi+ onimage

Image No. 12. (ineted -ontino# #ignal pl#e.). &uthorshi+ on image

Image No. 18. (ineted di#-ete #ignal pl#e.). &uthorshi+on image

Image No. 1. (-ontino# #ignal di#pla-ed.). &uthorshi+on image





e temes o$ te $irst module o$ te course, seen

in class, .ere tey .ere implemented trou

practice usin te proram (A*A/, .ere it .as

possi#le to understand a little more te sinal

#eavior and #asic operations .it te sameapplied!

/ot o#served as te impulse sinal o.continuous discrete andled te same #eavior, interms o$ its modi$ication in te a8is o$ teindependent varia#le, altou tey are used $or di$$erent purposes!

It is appreciated as te study o$ te sinalsreardin modi$ication o$ te independent varia#leis important and necessary to understand o.today develop many o$ te tecnoloicalinventions and leisure!

e ease o$ processin o$ sinals trou te(A*A/ proram, elped us to see te moredetailed o$ eac o$ te #asic $unctions, #eavior as.ell as per$orm trans$ormations and analy)e teir #eavior o$ o. continuous discrete varia#le!

It .as concluded tat te (A*A/ tool is e$$ectiveand use$ul $or te study and manaement o$ sinals!

BIBLIOGRAPHY

?1@ Señales y Sistemas seunda edición Alan <!Oppeneim, Alan S! Dills9y!

?2@ Introducción a las señales y sistemas, $!'A<IE A"E<E;O Universidad de Alcal5!

?+@ F.ei Fsu - ScaumCs Outline o$ Sinals andSystems G (c&ra. Fill!

?4@ (at*a#ttp=HHnereida!deioc!ull!esHpcullHiiu01HcdromHmatla#HcontenidoHnode2!tml

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proceso de señales continuas y discretas en matlab

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