WINTER TRAINING
Project Project Report STUDY OF COMMUNICATION COMMUNICATION SYSTEM OF ONGC Submitted by RAJATSUBHRA KAR WINTER TRAINEE
Under the guidance of: Mr. Sukesh Debbarma
Chie E!"i!eer E#T ONGC Tr Trip$r% ip$r% A&&et
Dep%rt'e!t o E(ectro!ic& # Co''$!ic%tio! E!"i!eeri!" N%tio!%( I!&tit$te o Tech!o(o")* A"%rt%(% Trip$r%+,--./0
RAJATSUBH RAJATSUBHRA RA KAR
WINTER TRAINING
Ac1!o2(e3"e'e!t I would like to express my deep sense o !r"titude "nd sin#ere t$"nks to my pro%e#t !uide &r' Anir("nB$"tt"#$er%ee or $is #ontinuous support "nd en#o en#our ur"! "!em emen entt t$r t$rou!$ ou!$ou outt t$is t$is peri period od'' His His meti meti#u #ulou lous s "ppr "ppro" o"#$ #$ in de"lin! wit$ #omplex pro(lem "nd #riti#"l #omments "t e"#$ st"!e $elped me to m"ke t$is pro%e#t " re"l su##ess' Espe#i"lly sir)s !uid"n#e "t e"#$ step m"de me eel "s i t$is period w"s %ust " #"ke w"lk' He w"s re"lly in*ol*ed wit$ t$is pro%e#t "nd !"*e $is input "t "ll rele*"nt situ"tions' He "llowed me to inno*"ti*e wit$ my ide"s "s $e ne*er tried to impose $is ide"s on me or#i(ly' I would "lso like to #on*ey my $e"rtelt t$"nks or o+erin o+erin! ! me t$is t$is oppor opportun tunity ity to undert undert"k "ke e t$is t$is pro%e pro%e#t' #t' Wit$o Wit$out ut $im it would not $"*e (een possi(le or me to undert"ke t$is pro%e#t' I would like to (estow " sin#ere round o !r"titude to $im' T$e $e"rty support o t$e institute, N"tion"l institute o Te#$nolo!yTe#$nolo!y- A!"rt"l" is $i!$ly soli#ited' T$e (lessin!s o my lo*in! p"rents rem"ined wit$ me t$rou!$out t$rou!$out t$is period' T$eir #ontinuous en#our"!ement m"de me eel #omort"(le e*ery time I r"n into " (it o dis"rr"y' I s$"ll #"rry t$e "+e#tion "nd (lessin!s o &r' &r' An Anir ir(" ("nB nB$" $"tt tt"# "#$" $"r% r%ee ee t$r t$rou!$ ou!$ou outt my lie lie'' He $"s $"s re"ll e"lly y (een (een "n epitome o $"rd work- dedi#"tion "nd moti*"tion' His in*ol*ement $"s re"lly s$own me t$e w"y to su##eed'T$e list is re"lly unendin! "nd t$ere "re m"ny ot$ers w$o $elped me t$rou!$ e"#$ "nd e*ery w"lk o t$is pro%e#t "nd en"(led me to #omplete it in " soot$in! "nd #omortin! w"y' T$is period $"s re"lly (een .uite entert"inin! "nd en%oy"(le' /"st (ut not le"st I would like to t$"nk t$e Almi!$ty or "lw"ys s$owerin! $is (lessin!s on me w$i#$ en"(led me to #omplete t$is pro%e#t' p ro%e#t'
RAJATSUBH RAJATSUBHRA RA KAR
WINTER TRAINING
ABSTRACT
Audi os i gnal pr oc es s i ngi sanengi neer i ngfi el dt hatf oc us esont hec omput at i onal met hodsf ori nt ent i onal l yal t er i ngs ounds ,met hodst hatar eus edi nmanymu mus i c al appl i c at i ons . Her ei sano v er v i e w wh er ee v er y o nec anpl a ywi t ha ud i os i g na l swh i l ego i ngd ee p i nt os ev er al s i gnal pr oc es si ngt opi c s.Wef oc usont hes pec t r al pr oc es si ng t ec hni quesofr el ev anc ef ort hedes cr i pt i onandt r ans f or mat i onofs ounds ,dev el opi ng t hebas i ct heor et i c al andpr ac t i c al k nowl edgewi t hwhi c ht oanal y ze,s ynt hes i z e, t r ans f or m anddes cr i beaudi os i gnal si nt hec ont ex tofmus i cappl i c at i ons . Th ec o ur s ei sba s edo no pe ns o f t wa r ea ndc o nt e nt .Th ed emo ns t r a t i o nsan d pr ogr ammi ngex e r c i s esar ed on eus i ngMat l ab ,whi c hi sapr o pe r t yofmat hwor k san d t her ef er enc esandmat er i al sf ort hec our s ec omef r om openonl i ner epos i t or i esand s omedi gi t al s i gnal pr oc es s i ngbook s .
RAJATSUBH RAJATSUBHRA RA KAR
WINTER TRAINING
CONTENTS
Goal Objective Signals
o Introduction o Audio Signals o Signal Processing o Noise o Additive White Gaussian Noise o igital !iltering o "utter#orth !ilter o Wiener !ilter o Audio Signal noise removal using Wiener !ilter o Simulation $esult %onclusion and !uture Wor&s $eference
RAJATSUBHRA KAR
WINTER TRAINING
Go%( 'he goal of this thesis is to study the nature of audio signals( Analy)ing the audio signal in fre*uency domain( Study its distinct characteristics and study its behavior under the a++lication of different digital filters(
O4jecti5e ,ere our objective is to add an Additive White Gaussian Noise to an audio signal and then reconstruct the signal using Wiener !ilter(
Si"!%(& A &i"!%( as referred to in communication systems- signal +rocessing- and electrical engineering .is a function that conveys information about the behavior or attributes of some +henomenon.( In the +hysical #orld- any *uantity e/hibiting variation in time or variation in s+ace 0such as an image1 is +otentially a signal that might +rovide information on the status of a +hysical system- or convey a message bet#een observers- among other +ossibilities( 'he IEEE Transactions on Signal Processing states that the term .signal. includes audio- video- s+eech- imagecommunication- geo+hysical- sonar- radar- medical and musical signals( Other e/am+les of signals are the out+ut of a thermocou+le- #hich conveys tem+erature information- and the out+ut of a +, meter #hich conveys acidity information( 'y+ically- signals are often +rovided by a sensor- and often the original form of a signal is converted to another form of energy using a transducer( !or e/am+le- a micro+hone converts an acoustic signal to a voltage #aveform- and a s+ea&er does the reverse(
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Analog and digital signals '#o main ty+es of signals encountered in +ractice are analog and digital ( 'he figure sho#s a digital signal that results from a++ro/imating an analog signal by its values at +articular time instants( igital signals are discrete and quantized - #hile analog signals +ossess neither +ro+erty( igital signals often arise via sam+ling of analog signals- for e/am+le- a continually fluctuating voltage on a line that can be digiti)ed by an analog2to2 digital converter circuit- #herein the circuit #ill read the voltage level on the linesay- every 34 microseconds and em+loying a fi/ed number of bits( 'he resulting stream of numbers is stored as digital data on a discrete2time and *uanti)ed2 am+litude signal( %om+uters and other digital devices are restricted to discrete time(
Time discretization One of the fundamental distinctions bet#een different ty+es of signals is bet#een continuous and discrete time( In the mathematical abstraction- the domain of a continuous2time 0%'1 signal is the set of real numbers 0or some interval thereof1- #hereas the domain of a discrete2time 0'1 signal is the set of integers 0or some interval1( What these integers re+resent de+ends on the nature of the signal5 most often it is time(
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2is#rete3time si!n"l #re"ted rom " #ontinuous si!n"l (y s"mplin!
2i!it"l si!n"l resultin! rom "pproxim"tion to "n "n"lo! si!n"lw$i#$ is " #ontinuous un#tion o time If for a signal- the *uantities are defined only on a discrete set of times- #e call it a discrete2time signal( A sim+le source for a discrete time signal is the sam+ling of a continuous signal- a++ro/imating the signal by a se*uence of its values at +articular time instants( A discrete2time real 0or com+le/1 signal can be seen as a function from 0a subset of1 the set of integers 0the inde/ labeling time instants1 to the set of real 0or com+le/1 numbers 0the function values at those instants1( A continuous2time real 0or com+le/1 signal is any real2valued 0or com+le/2 valued1 function #hich is defined at every time t in an interval- most commonly an infinite interval(
Amplitude quantization If a signal is to be re+resented as a se*uence of numbers- it is im+ossible to maintain arbitrarily high +recision 2 each number in the se*uence must have a finite number of digits( As a result- the values of such a signal are restricted to belong to a finite set5 in other #ords- it is *uanti)ed( 6uanti)ation is the +rocess of converting a continuous analog audio signal to a digital signal #ith discrete numerical values(
Examples of signals Signals in nature can be converted to electronic signals by various sensors( Some e/am+les are:
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Motion, T$e motion o "n o(%e#t #"n (e #onsidered to (e " si!n"l- "nd #"n (e monitored (y *"rious sensors to pro*ide ele#tri#"l si!n"ls' 5or ex"mple- r"d"r #"n pro*ide "n ele#trom"!neti# si!n"l or ollowin! "ir#r"t motion' A motion si!n"l is one3dimension"l 6time7- "nd t$e r"n!e is !ener"lly t$ree3dimension"l' 8osition is t$us " 43*e#tor si!n"l9 position "nd orient"tion o " ri!id (ody is " :3*e#tor si!n"l' ;rient"tion si!n"ls #"n (e !ener"ted usin! " !yros#ope' Sound, Sin#e " sound is " *i(r"tion o " medium 6su#$ "s "ir7- " sound si!n"l "sso#i"tes " pressure *"lue to e*ery *"lue o time "nd t$ree sp"#e #oordin"tes' A sound si!n"l is #on*erted to "n ele#tri#"l si!n"l (y " mi#rop$one!ener"tin! " *olt"!e si!n"l "s "n "n"lo! o t$e sound si!n"lm"kin! t$e sound si!n"l "*"il"(le or urt$er si!n"l pro#essin!' Sound si!n"ls #"n (e s"mpled "t " dis#rete set o time points9 or ex"mple- #omp"#t dis#s 6<2s7 #ont"in dis#rete si!n"ls representin! sound- re#orded "t ==-0>> s"mples per se#ond9 e"#$ s"mple #ont"ins d"t" or " let "nd ri!$t #$"nnel- w$i#$ m"y (e #onsidered to (e " 13*e#tor si!n"l 6sin#e <2s "re re#orded in stereo7' T$e <2 en#odin! is #on*erted to "n ele#tri#"l si!n"l (y re"din! t$e inorm"tion wit$ " l"ser- #on*ertin! t$e sound si!n"l to "n opti#"l si!n"l' Images, A pi#ture or im"!e #onsists o " (ri!$tness or #olor si!n"l- " un#tion o " two3dimension"l lo#"tion' T$e o(%e#t?s "ppe"r"n#e is presented "s "n emitted or re@e#ted ele#trom"!neti# w"*e- one orm o ele#troni# si!n"l' It #"n (e #on*erted to *olt"!e or #urrent w"*eorms usin! de*i#es su#$ "s t$e #$"r!e3#oupled de*i#e' A 12 im"!e #"n $"*e " #ontinuous sp"ti"l dom"in- "s in " tr"dition"l p$oto!r"p$ or p"intin!9 or t$e im"!e #"n (e dis#retied in sp"#e- "s in " r"ster s#"nned di!it"l im"!e'
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Biolo!i#"l membrane potentials, T$e *"lue o t$e si!n"l is "n ele#tri# potenti"l 6C*olt"!eC7' T$e dom"in is more diD#ult to est"(lis$' Some #ells or or!"nelles $"*e t$e s"me mem(r"ne potenti"l t$rou!$out9 neurons !ener"lly $"*e di+erent potenti"ls "t di+erent points' T$ese si!n"ls $"*e *ery low ener!ies- (ut "re enou!$ to m"ke ner*ous systems work9 t$ey #"n (e me"sured in "!!re!"te (y t$e te#$ni.ues o ele#trop$ysiolo!y'
A$3io Si"!%(& An %$3io &i"!%( is a re+resentation of sound- ty+ically as an electrical voltage( Audio signals have fre*uencies in the audio fre*uency range of roughly 74 to 74-444 ,) 0the limits of human hearing 1( Audio signals may be synthesi)ed directly- or may originate at a transducer such as a micro+hone- musical instrument +ic&u+- +honogra+h cartridge- or ta+e head( 8ouds+ea&ers or head+hones convert an electrical audio signal into sound( igital re+resentations of audio signals e/ist in a variety of formats( An %$3io ch%!!e( or %$3io tr%c1 is an audio signal communications channel in a storage device- used in o+erations such as multi2trac& recording and sound reinforcement(
Digital equivalent As much of the older analog audio e*ui+ment has been emulated in digital formusually through the develo+ment of audio +lug2ins for digital audio #or&station 0AW1 soft#are- the +ath of digital information through the AW 0i(e( from an audio trac& through a +lug2in and out a hard#are out+ut1 is also called an audio signal or signal flow( A digital audio signal being sent through #ire can use several formats including o+tical 0AA'- 'I!1- coa/ial 0S9PI!1- 8$ 0A;S9;"U1and ;thernet(
WINTER TRAINING
A$3io Si"!%( Proce&&i!" A$3io &i"!%( proce&&i!"- sometimes referred to as %$3io proce&&i!"- is the intentional alteration of auditory signals- or sound- often through an %$3io eect or effects unit( As audio signals may be electronically re+resented in either digital or analog format- signal +rocessing may occur in either domain( Analog +rocessors o+erate directly on the electrical signal- #hile digital +rocessors o+erate mathematically on the digital re+resentation of that signal(
Audio un+rocessed by reverb and delay is meta+horically referred to as .dry.#hile +rocessed audio is referred to as .#et.( •
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echo 3 to simul"te t$e e+e#t o re*er(er"tion in " l"r!e $"ll or #"*ern- one or se*er"l del"yed si!n"ls "re "dded to t$e ori!in"l si!n"l' To (e per#ei*ed "s e#$o- t$e del"y $"s to (e o order 4 millise#onds or "(o*e' S$ort o "#tu"lly pl"yin! " sound in t$e desired en*ironment- t$e e+e#t o e#$o #"n (e implemented usin! eit$er di!it"l or "n"lo! met$ods' An"lo! e#$o e+e#ts "re implemented usin! t"pe del"ys "ndFor sprin! re*er(s' W$en l"r!e num(ers o del"yed si!n"ls "re mixed o*er se*er"l se#onds- t$e resultin! sound $"s t$e e+e#t o (ein! presented in " l"r!e room- "nd it is more #ommonly #"lled re*er(er"tion or re*er( or s$ort' fanger 3 to #re"te "n unusu"l sound- " del"yed si!n"l is "dded to t$e ori!in"l si!n"l wit$ " #ontinuously *"ri"(le del"y 6usu"lly sm"ller t$"n 0> ms7' T$is e+e#t is now done ele#troni#"lly usin! 2S8- (ut ori!in"lly t$e e+e#t w"s #re"ted (y pl"yin! t$e s"me re#ordin! on two syn#$ronied t"pe pl"yers- "nd t$en mixin! t$e si!n"ls to!et$er' As lon! "s t$e m"#$ines were syn#$ronied- t$e mix would sound more3or3less norm"l- (ut i t$e oper"tor pl"#ed $is n!er on t$e @"n!e o one o t$e pl"yers 6$en#e C@"n!erC7- t$"t m"#$ine would slow down "nd its si!n"l would "ll out3o3 p$"se wit$ its p"rtner- produ#in! " p$"sin! e+e#t' ;n#e t$e oper"tor took $is n!er o+- t$e pl"yer would speed up until its t"#$ometer w"s ("#k in p$"se wit$ t$e m"ster- "nd "s t$is $"ppened- t$e p$"sin! e+e#t would "ppe"r to slide up
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t$e re.uen#y spe#trum' T$is p$"sin! up3"nd3down t$e re!ister #"n (e perormed r$yt$mi#"lly' •
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phaser 3 "not$er w"y o #re"tin! "n unusu"l sound9 t$e si!n"l is split- " portion is ltered wit$ "n "ll3p"ss lter to produ#e " p$"se3s$it- "nd t$en t$e unltered "nd ltered si!n"ls "re mixed' T$e p$"ser e+e#t w"s ori!in"lly " simpler implement"tion o t$e @"n!er e+e#t sin#e del"ys were diD#ult to implement wit$ "n"lo! e.uipment' 8$"sers "re oten used to !i*e " Csynt$esiedC or ele#troni# e+e#t to n"tur"l sounds- su#$ "s $um"n spee#$' T$e *oi#e o <3 48; rom St"r W"rs w"s #re"ted (y t"kin! t$e "#tor?s *oi#e "nd tre"tin! it wit$ " p$"ser' chorus 3 " del"yed si!n"l is "dded to t$e ori!in"l si!n"l wit$ " #onst"nt del"y' T$e del"y $"s to (e s$ort in order not to (e per#ei*ed "s e#$o- (ut "(o*e ms to (e "udi(le' I t$e del"y is too s$ort- it will destru#ti*ely interere wit$ t$e un3del"yed si!n"l "nd #re"te " @"n!in! e+e#t' ;ten- t$e del"yed si!n"ls will (e sli!$tly pit#$ s$ited to more re"listi#"lly #on*ey t$e e+e#t o multiple *oi#es' equalization 3 di+erent re.uen#y ("nds "re "ttenu"ted or (oosted to produ#e desired spe#tr"l #$"r"#teristi#s' &oder"te use o e.u"li"tion 6oten "((re*i"ted "s CEC7 #"n (e used to Cne3tuneC t$e tone .u"lity o " re#ordin!9 extreme use o e.u"li"tion- su#$ "s $e"*ily #uttin! " #ert"in re.uen#y #"n #re"te more unusu"l e+e#ts' ltering 3 E.u"li"tion is " orm o lterin!' In t$e !ener"l sense- re.uen#y r"n!es #"n (e emp$"sied or "ttenu"ted usin! low3p"ss- $i!$3p"ss- ("nd3p"ss or ("nd3stop lters' B"nd3p"ss lterin! o *oi#e #"n simul"te t$e e+e#t o " telep$one (e#"use telep$ones use ("nd3p"ss lters' overdrive e+e#ts su#$ "s t$e use o " u (ox #"n (e used to produ#e distorted sounds- su#$ "s or imit"tin! ro(oti# *oi#es or to simul"te distorted r"diotelep$one tr"D# 6e'!'t$e r"dio #$"tter (etween st"r!$ter pilots in t$e s#ien#e #tion lm Star Wars7' T$e most ("si# o*erdri*e e+e#t in*ol*es clipping t$e si!n"l w$en its "(solute *"lue ex#eeds " #ert"in t$res$old'
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pitch shit 3 t$is e+e#t s$its " si!n"l up or down in pit#$' 5or ex"mple- " si!n"l m"y (e s$ited "n o#t"*e up or down' T$is is usu"lly "pplied to t$e entire si!n"l- "nd not to e"#$ note sep"r"tely' Blendin! t$e ori!in"l si!n"l wit$ s$ited dupli#"te6s7 #"n #re"te $"rmonies rom one *oi#e' Anot$er "ppli#"tion o pit#$ s$itin! is pit#$ #orre#tion' Here " musi#"l si!n"l is tuned to t$e #orre#t pit#$ usin! di!it"l si!n"l pro#essin! te#$ni.ues' T$is e+e#t is u(i.uitous in k"r"oke m"#$ines "nd is oten used to "ssist pop sin!ers w$o sin! out o tune' It is "lso used intention"lly or "est$eti# e+e#t in su#$ pop son!s "s <$er?s Believe "nd &"donn"?s Die nother Da! ' time stretching 3 t$e #omplement o pit#$ s$it- t$"t is- t$e pro#ess o #$"n!in! t$e speed o "n "udio si!n"l wit$out "+e#tin! its pit#$' resonators 3 emp$"sie $"rmoni# re.uen#y #ontent on spe#ied re.uen#ies' T$ese m"y (e #re"ted rom p"r"metri# Es or rom del"y3("sed #om(3lters' robotic voice e"ects "re used to m"ke "n "#tor?s *oi#e sound like " synt$esied $um"n *oi#e' s!nthesizer 3 !ener"te "rti#i"lly "lmost "ny sound (y eit$er imit"tin! n"tur"l sounds or #re"tin! #ompletely new sounds' modulation 3 to #$"n!e t$e re.uen#y or "mplitude o " #"rrier si!n"l in rel"tion to " predened si!n"l' Rin! modul"tion- "lso known "s "mplitude modul"tion- is "n e+e#t m"de "mous (y 2o#tor W$o?s2"leks "nd #ommonly used t$rou!$out s#i3' compression 3 t$e redu#tion o t$e dyn"mi# r"n!e o " sound to "*oid unintention"l @u#tu"tion in t$e dyn"mi#s' /e*el #ompression is not to (e #onused wit$ "udio d"t" #ompression- w$ere t$e "mount o d"t" is redu#ed wit$out "+e#tin! t$e "mplitude o t$e sound it represents' #D audio e"ects 3 pl"#e sounds outside t$e stereo ("sis reverse echo 3 " swellin! e+e#t #re"ted (y re*ersin! "n "udio si!n"l "nd re#ordin! e#$o "ndFor del"y w$ile t$e si!n"l runs in re*erse' W$en pl"yed ("#k orw"rd t$e l"st
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e#$os "re $e"rd (eore t$e e+e#ted sound #re"tin! " rus$ like swell pre#edin! "nd durin! pl"y("#k' Jimmy 8"!e o /ed eppelin used t$is e+e#t in t$e (rid!e o CW$ole /ott" /o*eC' •
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active noise control3 " met$od or redu#in! unw"nted sound $ave eld s!nthesis 3 " sp"ti"l "udio renderin! te#$ni.ue or t$e #re"tion o *irtu"l "#ousti# en*ironments
Noi&e In electronics- !oi&e is a random fluctuation in an electrical signal- a characteristic of all electronic circuits(Noise generated by electronic devices varies greatly- as it can be +roduced by several different effects( 'hermal noise is unavoidable at non2 )ero tem+erature 0see fluctuation2dissi+ation theorem 1- #hile other ty+es de+end mostly on device ty+e 0such as shot noise- #hich needs stee+ +otential barrier1 or manufacturing *uality and semiconductor defects- such as conductance fluctuations- including <9f noise( In communication systems- noise is an error or undesired random disturbance of a useful information signal in a communication channel( 'he noise is a summation of un#anted or disturbing energy from natural and sometimes man2made sources( Noise is- ho#ever- ty+ically distinguished from interference- 0e(g( cross2tal& deliberate jamming or other un#anted electromagnetic interference from s+ecific transmitters1- for e/am+le in the signal2to2noise ratio 0SN$1- signal2to2interference ratio 0SI$1 and signal2to2noise +lus interference ratio 0SNI$1 measures( Noise is also ty+ically distinguished from distortion- #hich is an un#anted systematic alteration of the signal #aveform by the communication e*ui+ment- for e/am+le in the signal2to2noise and distortion ratio 0SINA1( In a carrier2modulated +assband analog communication system- a certain carrier2to2noise ratio 0%N$1 at the radio receiver in+ut #ould result in a certain signal2to2noise ratio in the detected message signal( In a digital communications system- a certain E b9 N 4 0normali)ed signal2to2noise ratio1 #ould result in a certain bit error rate 0";$1( While noise is generally un#anted- it can serve a useful +ur+ose in some a++lications- such as random number generation or dithering(
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Analog dis+lay of random fluctuations in voltage: e(g(- +in& noise(
ADDITI6E WHITE GAUSSIAN NOISE A33iti5e 2hite G%$&&i%! !oi&e 0AWGN1 is a basic noise model used in Information theory to mimic the effect of many random +rocesses that occur in nature( 'he modifiers denote s+ecific characteristics: •
Additive (e#"use
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White reers
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Gaussian (e#"use
it is "dded to "ny noise t$"t mi!$t (e intrinsi# to t$e inorm"tion system' to t$e ide" t$"t it $"s uniorm power "#ross t$e re.uen#y ("nd or t$e inorm"tion system' It is "n "n"lo!y to t$e #olor w$ite w$i#$ $"s uniorm emissions "t "ll re.uen#ies in t$e *isi(le spe#trum' it $"s " norm"l distri(ution in t$e time dom"in wit$ "n "*er"!e time dom"in *"lue o ero'
Wideband noise comes from many natural sources- such as the thermal vibrations of atoms in conductors 0referred to as thermal noise or =ohnson2Ny*uist noise1- shot noise- blac& body radiation from the earth and other #arm objects- and from celestial sources such as the Sun( 'he central limit theorem of +robability theory indicates that the summation of many random +rocesses #ill tend to have distribution called Gaussian or Normal( AWGN is often used as a channel model in #hich the only im+airment to communication is a linear addition of #ideband or #hite noise #ith a constant s+ectral density 0e/+ressed as #atts +er hert) of band#idth1 and a Gaussian distribution of am+litude( 'he model does not account for fading- fre*uency selectivity- interference- nonlinearity or dis+ersion( ,o#everit +roduces sim+le and tractable mathematical models #hich are useful for gaining insight into the underlying behavior of a system before these other +henomena are considered( 0>
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'he AWGN channel is a good model for many satellite and dee+ s+ace communication lin&s( It is not a good model for most terrestrial lin&s because of multi+ath- terrain bloc&ing- interference- etc( ,o#ever- for terrestrial +ath modeling- AWGN is commonly used to simulate bac&ground noise of the channel under study- in addition to multi+ath- terrain bloc&ing- interference- ground clutter and self2interference that modern radio systems encounter in terrestrial o+eration(
Di"it%( Fi(teri!"
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In signal +rocessing- a 3i"it%( i(ter is a system that +erforms mathematical o+erations on a sam+led- discrete2time signal to reduce or enhance certain as+ects of that signal( 'his is in contrast to the other major ty+e of electronic filter the analog filter - #hich is an electronic circuit o+erating on continuous2time analog signals( A digital filter system usually consists of an analog2to2digital converter to sam+le the in+ut signal- follo#ed by a micro+rocessor and some +eri+heral com+onents such as memory to store data and filter coefficients etc( !inally a digital2to2analog converter to com+lete the out+ut stage( Program Instructions 0soft#are1 running on the micro+rocessor im+lement the digital filter by +erforming the necessary mathematical o+erations on the numbers received from the A%( In some high +erformance a++lications- an !PGA or ASI% is used instead of a general +ur+ose micro+rocessor- or a s+eciali)ed SP #ith s+ecific +aralleled architecture for e/+editing o+erations such as filtering( igital filters may be more e/+ensive than an e*uivalent analog filter due to their increased com+le/ity- but they ma&e +ractical many designs that are im+ractical or im+ossible as analog filters( When used in the conte/t of real2time analog systemsdigital filters sometimes have +roblematic latency 0the difference in time bet#een the in+ut and the res+onse1 due to the associated analog2to2digital and digital2to2 analog conversions and anti2aliasing filters- or due to other delays in their im+lementation( igital filters are common+lace and an essential element of everyday electronics such as radios- cell+hones- and A> receivers( A digital filter is characteri)ed by its transfer function- or e*uivalentlyits difference e*uation( ?athematical analysis of the transfer function can describe ho# it #ill res+ond to any in+ut( As such- designing a filter consists of develo+ing 01
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s+ecifications a++ro+riate to the +roblem 0for e/am+le- a second2order lo# +ass filter #ith a s+ecific cut2off fre*uency1- and then +roducing a transfer function #hich meets the s+ecifications( 'he transfer function for a linear- time2invariant- digital filter can be e/+ressed as a transfer function in the Z2domain5 if it is causal- then it has the form:
Where- the order of the filter is the greater of N or M (
B$tter2orth Fi(ter
T$e re.uen#y response plot rom Butterwort$?s 04> p"per' 'he B$tter2orth i(ter is a ty+e of signal +rocessing filter designed to have as flat a fre*uency res+onse as +ossible in the +assband( It is also referred to as a '%7i'%(() (%t '%"!it$3e i(ter ( It #as first described in <@4 by the 04
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"ritish engineer and +hysicist Ste+hen "utter#orth in his +a+er entitled .On the 'heory of !ilter Am+lifiers.
M%t(%4 co3e o $&i!" B$tter2orth i(ter i! 4%!3p%&& 'o3e
Fs=16384; Order=2; Sampling_freq=16384; [B,A]=!""er#Order,[$%&,$%'](; freq)#B,A,*$$$,Sampling_freq(; [Fl!"e,Fs]=+aread#-Fl!"e.i/0ing"one%+a-(; =fil"er#B,A,Fl!"e(; so!nds#,Fs( =ff"#,4$'6(; =%5on#(74$'6; f_al=3e474$'65#$2$48(; plo"#f_al,#12$4'((
Original Singal (amplitude vs frequency)
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Fi(ter 8B$tter2orth B%!3p%&&9
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Fi(tere3 Si"!%(8A'p(it$3e 5& Fre:$e!c)9
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NOISE REMO6A; Noi&e re3$ctio! is the +rocess of removing noise from a signal(
All recording devices- both analog or digital- have traits #hich ma&e them susce+tible to noise( Noise can be random or #hite noise #ith no coherence- or coherent noise introduced by the deviceBs mechanism or +rocessing algorithms( In electronic recording devices- a major form of noise is hiss caused by random electrons that- heavily influenced by heat- stray from their designated +ath( 'hese stray electrons influence the voltage of the out+ut signal and thus create detectable noise(
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In the case of +hotogra+hic film and magnetic ta+e- noise 0both visible and audible1 is introduced due to the grain structure of the medium( In +hotogra+hic film- the si)e of the grains in the film determines the filmBs sensitivity- more sensitive film having larger si)ed grains( In magnetic ta+e- the larger the grains of the magnetic +articles 0usually ferric o/ide or magnetite1- the more +rone the medium is to noise( 'o com+ensate for this- larger areas of film or magnetic ta+e may be used to lo#er the noise to an acce+table level( In selecting a noise reduction algorithm- one must #eigh several factors: •
•
•
the available com+uter +o#er and time available: a digital camera must a++ly noise reduction in a fraction of a second using a tiny onboard %PU#hile a des&to+ com+uter has much more +o#er and time #hether sacrificing some real detail is acce+table if it allo#s more noise to be removed 0ho# aggressively to decide #hether variations in the image are noise or not1 the characteristics of the noise and the detail in the image- to better ma&e those decisions
Wie!er Fi(ter In signal +rocessing- the Wie!er i(ter is a filter used to +roduce an estimate of a desired or target random +rocess by linear time2invariant 08'I1 filtering of an observed noisy +rocess- assuming &no#n stationary signal and noise s+ectraand additive noise( 'he Wiener filter minimi)es the mean s*uare error bet#een the estimated random +rocess and the desired +rocess(
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'he goal of the Wiener filter is to com+ute a statistical estimate of an un&no#n signal using a related signal as an in+ut and filtering that &no#n signal to +roduce the estimate as an out+ut( !or e/am+le- the &no#n signal might consist of an un&no#n signal of interest that has been corru+ted by additive noise( 'he Wiener filter can be used to filter out the noise from the corru+ted signal to +rovide an estimate of the underlying signal of interest( 'he Wiener filter is based on a statistical a++roach- and a more statistical account of the theory is given in the minimum mean2s*uare error 0??S;1 article( 'y+ical deterministic filters are designed for a desired fre*uency res+onse( ,o#ever- the design of the Wiener filter ta&es a different a++roach( One is assumed to have &no#ledge of the s+ectral +ro+erties of the original signal and the noise- and one see&s the linear time2invariant filter #hose out+ut #ould come as close to the original signal as +ossible( Wiener filters are characteri)ed by the follo#ing: C
0' Assumption, si!n"l "nd 6"dditi*e7 noise "re st"tion"ry line"r sto#$"sti# pro#esses wit$ known spe#tr"l #$"r"#teristi#s or known "uto#orrel"tion "nd #ross3 #orrel"tion 1' Re.uirement, t$e lter must (e p$ysi#"lly re"li"(leF#"us"l 6t$is re.uirement #"n (e dropped- resultin! in " non3#"us"l solution7 4' 8erorm"n#e #riterion, minimum me"n3s.u"re error 6&&SE7 'his filter is fre*uently used in the +rocess of deconvolution5 for this a++licationsee Wiener deconvolution(
IMP;EMENTATION OF WIENER FI;TER 'he inverse filtering is a restoration techni*ue for deconvolution- i(e(- #hen the image is blurred by a &no#n lo#+ass filter- it is +ossible to recover the image by inverse filtering or generali)ed inverse filtering( ,o#ever- inverse filtering is very sensitive to additive noise( 'he a++roach of reducing one 0
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degradation at a time allo#s us to develo+ a restoration algorithm for each ty+e of degradation and sim+ly combine them( 'he Wiener filtering e/ecutes an o+timal tradeoff bet#een inverse filtering and noise smoothing( It removes the additive noise and inverts the blurring simultaneously( 'he Wiener filtering is o+timal in terms of the mean s*uare error( In other #ords- it minimi)es the overall mean s*uare error in the +rocess of inverse filtering and noise smoothing( 'he Wiener filtering is a linear estimation of the original image( 'he a++roach is based on a stochastic frame#or&( 'he orthogonality +rinci+le im+lies that the Wiener filter in !ourier domain can be e/+ressed as follo#s:
w$ere "re respe#ti*ely power spe#tr" o t$e ori!in"l im"!e "nd t$e "dditi*e noise- "nd H60-17 is t$e (lurrin! lter' It is e"sy to see t$"t t$e Wiener lter $"s two sep"r"te p"rt- "n in*erse lterin! p"rt "nd " noise smoot$in! p"rt' It not only perorms t$e de#on*olution (y in*erse lterin! 6$i!$p"ss lterin!7 (ut "lso remo*es t$e noise wit$ " #ompression oper"tion 6lowp"ss lterin!7' Implementation
To implement t$e Wiener lter in pr"#ti#e we $"*e to estim"te t$e power spe#tr" o t$e ori!in"l im"!e "nd t$e "dditi*e noise' 5or w$ite "dditi*e noise t$e power spe#trum is e.u"l to t$e *"ri"n#e o t$e noise' To estim"te t$e power spe#trum o t$e ori!in"l im"!e m"ny met$ods #"n (e used' A dire#t estim"te is t$e periodo!r"m estim"te o t$e power spe#trum #omputed rom t$e o(ser*"tion,
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w$ere Y(k,l) is t$e 25T o t$e o(ser*"tion' T$e "d*"nt"!e o t$e estim"te is t$"t it #"n (e implemented *ery e"sily wit$out worryin! "(out t$e sin!ul"rity o t$e in*erse lterin!' Anot$er estim"te w$i#$ le"ds to " #"s#"de implement"tion o t$e in*erse lterin! "nd t$e noise smoot$in! is
w$i#$ is " str"i!$torw"rd result o t$e "#t, T$e power spe#trum Syy#"n (e estim"ted dire#tly rom t$e o(ser*"tion usin! t$e periodo!r"m estim"te' T$is estim"te results in " #"s#"de implement"tion o in*erse lterin! "nd noise smoot$in!,
T$e dis"d*"nt"!e o t$is implement"tion is t$"t w$en t$e in*erse lter is sin!ul"r- we $"*e to use t$e !ener"lied in*erse lterin!' 8eople "lso su!!est t$e power spe#trum o t$e ori!in"l im"!e #"n (e estim"ted ("sed on " model su#$ "s t$e model'
iener !ilter function creation in "AT#A$ f!n"ion e/ = +ienerFil"er#,:,sigma,gamma,alp:a( = si)e#,1(;
27>2; sf = f%5#as#f(?$(@17gamma5#as#f(==$(; if = 1%7sf; 10
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if = if%5#as#f(5gamma?1(@gamma5as#sf(%5if%5#as#sf(5gamma=1 (; f = f%5#f?sigma>2(@sigma>25#f=sigma>2(; f = if%5#fCsigma>2(%7#fC#1Calp:a(5sigma>2(; eDf = f%5
A33itio! o AWGN to %! %$3io i(e %!3 reco!&tr$ctio! $&i!" Wie!er Fi(teri!"< loseall; learall; Fs=4$'6; [A,Fs]=+aread#-Ag!ner%+a-(; 0=A#ro!nd#1725endend((; S0=1; EdB =a+gn#0,S0,-meas!red-(; fig!re#1(, plo"#(, :old, plo"#0, -r-(, /lael#-freq!en-( lael#-ampli"!de-(
legend#-A snr=11dB-,-Glean Signal-(; =4$'6; : =ones#4,4(764; sigma = *$$; gamma = 1; alp:a = *; e+/=+ienerFil"er#,:,sigma,gamma,alp:a(; 11
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so!nds#e+/,Fs( H=ff"#,4$'6(; =as#H(%>2; dBs=1$5log1$#(; .a=ma/#dBs( E.eas!ring ma/ima of ois Signal I=ff"#e+/,4$'6(; )=as#I(%>2; dBS=1$5log1$#)(; .aa=ma/#dBS( E.eas!ring ma/ima of reons"r!"ed signal fig!re#2(,plo"#e+/,-r-(, /lael#-freq!en-( lael#-ampli"!de-( legend#-0eons"r!"ed Signal-(;
Si'$(%tio! Re&$(t&<
NOISE SIGNA8 SN$F
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Reco!&tr$cte3 Si"!%(<
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Co!c($&io! %!3 F$t$re Wor1&< On the basis of this #or& one can +rogress this techni*ue to ma&e other useful contribution in signal noise removal using the basic filtering techni*ues( igital filtering of audio signals can be done to ma&e audio signals as much free from noise as +ossible &ee+ing in mind that the *uality of the audio signal must be &e+t as +ure as +ossible(
Reere!ce&< 1
