Research Article Discrete and Dual Tree Wavelet Features for Real-Time Speech/Music Discrimination

Size: px
Start display at page:

Download "Research Article Discrete and Dual Tree Wavelet Features for Real-Time Speech/Music Discrimination"

Transcription

1 Intrnational cholarly Rsarch Ntwork IRN ignal Procssing Volum, Articl ID 6936, pags doi:.54//6936 Rsarch Articl Discrt and Dual Tr Wavlt Faturs for Ral-Tim pch/music Discrimination Timur Düznli, and Nalan Özkurt, 3 Graduat chool of Natural and Applid cincs, Dokuz Eylul Univrsity, 356 Buca, İzmir, Turky Dpartmnt of Elctronics and Tlcommunications Enginring, Izmir Univrsity of Economics, 3533 Balçova, İzmir, Turky 3 Dpartmnt of Elctrical and Elctronics Enginring, Yaşar Univrsity, 35 Bornova, İzmir, Turky Corrspondnc should b addrssd to Nalan Özkurt, nalan.ozkurt@du.du.tr Rcivd 5 January ; Accptd March Acadmic Editor: P. C. Yun Copyright T. Düznli and N. Özkurt. This is an opn accss articl distributd undr th Crativ Commons Attribution Licns, which prmits unrstrictd us, distribution, and rproduction in any mdium, providd th original work is proprly citd. Th prformanc of wavlt transform-basd faturs for th spch/music discrimination task has bn invstigatd. In ordr to xtract wavlt domain faturs, discrt and complx orthogonal wavlt transforms hav bn usd. Th prformanc of th proposd fatur st has bn compard with a fatur st constructd from th most common tim, frquncy and cpstral domain faturs such as numbr of zro crossings, spctral cntroid, spctral flux, and Ml cpstral cofficints. Th artificial nural ntworks hav bn usd as classification tool. Th principal componnt analysis has bn applid to liminat th corrlatd faturs bfor th classification stag. For discrt wavlt transform, considring th numbr of vanishing momnts and orthogonality, th bst prformanc is obtaind with Daubchis8 wavlt among th othr mmbrs of th Daubchis family. Th dual tr wavlt transform has also dmonstratd a succssful prformanc both in trms of accuracy and tim consumption. Finally, a ral-tim discrimination systm has bn implmntd using th Daubhcis8 wavlt which has th bst accuracy.. Introduction Th discrimination of music and spch has bn an important task in multimdia signal procssing with th incrasing rol of th multimdia sourcs in our lif. Th spch/music discrimination MD) systms can b usd in th dvlopmnt of th fficint coding algorithms for audio dcodrs []. Thus, if th spch can b sparatd, it can b codd with a spch codr which nds lss bandwidth rlativ to th audio codr. Also, spch/music discriminator is important in automatic spch rcognition whn th rcordings includ music such as radio broadcasts []. Th contnt-basd multimdia rtrival [3] and automatic channl slctor dsign for radios ar othr mrging applications with a growing intrst for spch/music discriminators. Thr ar svral faturs which ar usd to classify music and spch such as numbr of zro crossings [4], spctral cntroid, and Ml frquncy cpstral cofficints [5, 6]. Th ntropy and dynamism faturs hav bn usd for hiddn Markov modl classificationin[7]. In [8], a systm which looks for th transition btwn music and spch using two charactristics of signals, which ar RM-basd avrag dnsity of zro crossings and avrag frquncy, has bn proposd. In [9], th harmonic faturs ar usd to discriminat spch and music using a hirarchical obliqu dcision tr. An MD systm dsignd for radio broadcasts that has bn proposd in [] uss a thr-stag structur, which dtrmins th spch and music sgmnts that ar sparabl at first glanc with spctral ntropy and rgion growing. Rcntly, a sgmntation mthod has bn proposd in []whichussth proprty that th man and th variancs of th filtr bank changs mor rapidly and rachs highr valu for spch than music. inc it is important to dal with nonstationary signals and to achiv variabl tim and frquncy localization of acoustic data, th wavlt-basd paramtrs bcam an important tool in spch/music discrimination [ 5]. Howvr, thr ar som important choics to mak for rconstruction of th faturs from th wavlt cofficints. In som studis, only on lvl of wavlt dcomposition is

2 IRN ignal Procssing mployd, and th wavlt transform is applid to or 3 ms windows. To captur th nonstationary information from a tim sris, a longr window should b usd. Th windows in ordr of sconds ar usd in []; howvr, this is too long for a ral-tim application. Also, dcomposing signal into svral frquncy bands givs us mor discriminativ faturs. In anothr rcnt work, Didiot t al. mployd nrgy-basd faturs xtractd from th 5 and 7 bands of discrt wavlt componnts [5]. For audio analysis including MD and gnr classification, Tzantakis and Cook mployd man and variancs of bands of wavlt cofficints and th ratio of th man valus for adjacnt bands using Daubchis 4 wavlts in 3 sc windows []. Th accuracy of th mthod is approximatly 9%. Along with svral advantags, th discrt wavlt transform has som disadvantags such as lack of tim invarianc and oscillatory bhavior. In ordr to cop with ths problms, complx wavlt transform has bn proposd [6]. Th dual tr complx wavlt transform, which is a spcific cas of complx wavlt transform, has bn introducd in [7]. Thrfor, th aim of this study is both to considr th fatur xtraction for MD with DWT to furthr improv prformanc for ral-tim applications and to xamin th faturs obtaind from th statistical paramtrs of th dual tr wavlt cofficints. In ordr to compar th prformanc of th proposd fatur sts, th prviously usd tim, frquncy, and discrt wavlt faturs hav bn usd to classify th sam data st. Th databas has bn constructd from th spch sampls takn from TIMIT databas and th music sampls which ar rcordd from th audio CDs and radios with diffrnt gnrs such as classical, jazz, and pop. Th artificial nural ntworks ANNs) hav bn usd for th comparison of th ffctivnss of th fatur xtraction algorithms. Th papr is organizd as follows: a brif introduction of th prvious and proposd fatur xtraction mthods ar xplaind in ction ; th introduction of th data st and classification algorithm with th rsults ar givn in ction 3; th conclusions and futur works ar discussd in ction 4.. Faturs for pch/music Discrimination In this sction, th rlatd thortical background on th faturs usd for spch/music discrimination systms will b givn brifly... Common Faturs. Th tim-domain faturs such as numbr of zro crossings and frquncy-domain faturs such as low nrgy ratio, spctral cntroid, spctral roll-off and spctral flux ar commonly usd for spch/music discrimination. Also, Ml frquncy cpstrum cofficints ar shown to b succssful in spch/music classification and rcognition applications. For comparison, a fatur vctor constructd from ths faturs hav bn usd for classification in th first mthod of this study.... Numbr of Zro Crossings. It is th tim-domain fatur which rprsnts th numbr of zro crossing in a fram. It is a usful fatur in music and spch discrimination, sinc it is a masur of th dominant frquncy in th signal [5, 6]. Th numbr of zro crossings ar calculatd as Z t =.5 N sgnxn)) sgnxn )), ) n= whr xn)isthnth componnt of th fram of lngth N.... Low Enrgy Ratio. Thisfaturgivsthnumbrofth frams of which th ffctiv or root man squar RM) nrgy is lss than th avrag nrgy. Th RM nrgy for ach fram is dtrmind as X RM = K Xk K, ) whr X k is th magnitud of kth frquncy componnt in th fram. inc th nrgy distribution is mor lft-skwd than for music, this masur will b highr for spch [6]...3. pctral Cntroid. This is th masur of th cntr of mass of th frquncy spctrum and calculatd as C = k= Kk= f k X k Kk= X k, 3) whr X k is th magnitud of th componnt in th frquncy band f k [5, 6]...4. pctral Roll-off. This fatur is important in dtrmining th shap of th frquncy spctrum. Th spctral roll-off point R k is th frquncy whr th 95% of th spctral powr lis blow as summarizd in R k Xk =.95 K Xk, 4) k= k= whr X k is th magnitud of th componnt of th kth frquncy. inc th most of th nrgy is in th lowr frquncis for spch signals, R k has lowr valus for spch [5, 6]...5. pctral Flux. It rprsnts th spctral changs btwn adjacnt frams and calculatd as K ) F t = X t, k Xk t 5) k= whr Xk t is th kth frquncy componnt of th tth fram. Thnthavragofthallframsarcalculatd.Thmusic has a highr rat of changs than th spch dos, thus this valu is highr for music [5, 6]...6. Ml Frquncy Cpstrum Cofficints MFCCs). Th Ml frquncy spctrum is th linar cosin transform of

3 IRN ignal Procssing 3 a log powr spctrum on a nonlinar Ml scal of frquncy [8]. Th Ml scal is inspird from th human auditory systm in which th frquncy bands ar not linarly spacd. Thus, th sound is rprsntd bttr. Th calculation of th MFCCs includs th following stps. i) Th discrt Fourir transform DFT) transforms th windowd spch sgmnt into th frquncy domain, and th short-trm powr spctrum P f )is obtaind. ii) Th spctrum P f ) is warpd along its frquncy axis f in hrtz) into th ml-frquncy axis as PM), whr M is th Ml frquncy using ) M f ) = 595 log + f 7. 6) iii) Th rsultd warpd powr spctrum is thn convolvd with th triangular band-pass filtr PM)into θm). Th convolution with th rlativly broad critical-band masking curvs θm) significantly rducs th spctral rsolution of θm) incomparisonwith th original P f ), which allows for th downsampling of θm). θm k ) = M PM M k )ψm), k =,..., K. 7) Thn, K outputs Xk) = lnθm k )), k =,..., K) arobtaind. In th implmntation, θm k ) is th avrag instad of th sum. iv)thmfccsarcomputdas K [ MFCCd) = X k cos d k.5) π K k= )], k =,..., D... Discrt Wavlt Transform. Th multirsolution analysis MRA) provids a tim-frquncy rprsntation wll suitd for nonstationary signals. MRA dcomposs and analyzs th signal at diffrnt frquncis and diffrnt rsolutions in th spac spannd by wavlts and scaling functions. Th continuous wavlt transform of a signal xt) isth projction of th signal on this spac as WTs, r) = s xt)ψ t r s 8) ), 9) whr ψt) isthmothrwavlts and r ar th scal and translation cofficints, rspctivly [9]. For computational issus, discrt wavlt transform DWT) is obtaind. Thr is a rich st of basis functions for DWT and it is possibl to gt a compact rprsntation of signal using this transform. In practical applications, DWT is applid in sampld signal x[n]; n =,..., N as DWT [ n, j] N = x[m]ψ j [m n], ) m= whr ψ j [n] = / j )ψn/ j ). xt) Low-pass filtr L Downsampling a r) L High-pass filtr H H w r) Figur : DWT with two composition lvls [5]. a r) w r) DWT is implmntd using a pyramidal algorithm rlatd to a multirat filtr-bank approach for multirsolution analysis. Mallat has shown that it is possibl to mak frquncy band dcomposition by using succssiv low-pass L) and high-pass H) filtrs in th tim domain as shown in Figur [5]. Aftr ach filtring stag i, th outputs ar downsampld by, and th outputs ar a i r) approximation and w i r) dtail or wavlt cofficints for low- and high-pass filtrs, rspctivly. Approximation cofficints giv local avrags of th signal. On th othr hand, dtail cofficints show th diffrncs btwn local avrags. In this work, Haar wavlt and Daubchis family, which is known as on of th bst familisforspchprocssingapplications,isusdasth mothr wavlt [9, ]..3. Discrt Wavlt Transform Basd Enrgy Faturs. In study of Didiot t al. [5], th nrgy-basd faturs which ar calculatd using wavlt transform hav bn proposd. According to study, th nrgy distribution in ach frquncy band is a vry rlvant acoustic cu and nrgy, calculatd from DWT, can b usd as a spch/music discrimination fatur. In our study, ths nrgy basd paramtrs hav also bn usd in ordr to mak comparison among diffrnt fatur xtraction mthods..3.. Instantanous Enrgy. This is a fatur which givs th nrgy distribution in ach band and givn as fj E = log N j w j r) ), ) N j whr w j r) is th wavlt cofficint at tim position r and frquncy band j and N is th lngth of th analysis window..3.. Tagr Enrgy. Tagr nrgy has bn rcntly applid for spch rcognition and givn as f TE j = log N j N j r= r= w j r) ) w j r ) w j r +) ). ) It is said that th discrt tagr nrgy oprator TEO) allows modulation nrgy tracking and givs a bttr rprsntation of th formant information in th fatur vctor compard to MFCCs in [5]. It is also pointd out that th

4 4 IRN ignal Procssing Tagr nrgy is a nois robust paramtr for spch rcognition, bcaus th ffctofadditiv nois is attnuatd..4. Complx Wavlt Transform. Convntional discrt wavlt transform suffrs from som fundamntal shortcomings dspit its compact rprsntation and fficint computational algorithm. Th first shortcoming of DWT is that a small shift of th signal in tim domain yilds distortion in th wavlt cofficint oscillation pattrn around singularitis. Th scond problm of DWT is th lack of dirctionality for two and highr dimnsion signals. Complx wavlt transform CWT) has bn proposd inspiring by th Fourir transform which dos not suffr from ths typs of problms. CWT is dfind with a complx-valud scaling function and complx-valud wavlt ψ c t) = ψ r t) + iψ i t), 3) whr ψ r t) andψ i t) ar ral and imaginary parts. If ths functions ar 9 out of phas with ach othr, that is thy form a Hilbrt transform pair, thn ψ c t) isananalytic signal and it has a on-sidd spctrum. Projcting th signal onto j ψ c t) j t n), th complx wavlt cofficints ar obtaind as d c j, n ) = dr j, n ) + jdi j, n ). 4) Complx Wavlt Transform can b prformd by two schms. In th first on, a complx wavlt ψ c t) that forms an orthonormal or biorthogonal basis is sarchd. Th scond mthod sks a rdundant rprsntation, and it sarchs ψ r t) andψ i t) that provid orthonormal and biorthogonal bass individually. Th rsulting CWT has x rdundancy in -D and has powr to ovrcom th shortcomings of DWT. In this study, th dual-tr approach for prforming complx wavlt transform which is a natural approach to scond, rdundant typ has bn prfrrd..4.. Dual-Tr Complx Wavlt Transform DT-CWT). Dual-tr complx wavlt transform was first introducd by Kingsbury in 998 []. Th dual tr implmnts an analytic wavlt transform by using two ral discrt wavlt transform with two filtr-bank trs; th first DWT givs th ral, and th scond on givs th imaginary part of th CWT. Analysis and synthsis filtr-banks can b illustratd as in Figur, whrh n) andh n) dnot th low-pass/highpass filtr pair for th uppr filtr-bank which implmnts WT for ral part. In th sam way, g n) andg n) dnot th low-pass/high-pass filtr pair for th lowr filtrbank for imaginary part. In this approach, th ky challng is joint dsign of two filtrbanks to gt complx wavlt and scaling function as clos as possibl to analytic []. Th filtrs usd for ral and imaginary parts of th transform must satisfy th prfct rconstruction condition givn as h n)h n +k) = δk), n 5) h n) = ) n h M n). xt) h n) h n) g n) g n) h n) h n) g n) g n) Figur : Analysis filtr bank for th dual tr CWT []. Twolow-passfiltrsofdualtrh n) andg n) satisfying a vry simpl proprty mak corrsponding wavlts to form an approximat Hilbrt Transform pair: on of thm must b approximatly a half-sampl shift of th othr [] g n) = h n.5) = ψ g t) = H { ψ h t) }. 6) inc h n) andg n) ar dfind only on intgrs, it will b usful to rwrit th half-sampl dlay condition in trms of magnitud and phas functions sparatly in frquncy domain to mak th statmnt rigorous G ) jw ) H = jw G ) jw = H jw.5w ) 7). Thr ar two popular mthods for dsign of filtrs for DT-CWT []. Q-hift olution. According to q-shift solution, g n) must b slctd as g n) = h N n), 8) whr N is th lngth of filtr h n) and is vn. In this cas, th magnitud condition is satisfid but not th phas conditionasshownin9)inthfrquncydomain G ) jw ) H = jw, G ) jw H jw.5w ) 9), Th quartr-shift q-shift) solution has an intrsting proprty that causs to tak its nam: whn you ask that g n) and h n) b rlatd as g n) = h N n) andalso that thy approximatly satisfy G jw ) = H jw.5w), thn it turns out that th frquncy rspons of h n) has approximatly linar phas. This is vrifid by writing g n) = h N n) in trms of Fourir transforms G ) jw = H ) jw jn )w, ) whr th rprsnts complx conjugation. This implis that th phass satisfy G jw ) = H jw ) N )w. )

5 IRN ignal Procssing 5 If th two filtrs satisfy th phas condition approximatly, it can b writtn that H jw ).5w = H jw ) N )w. ) and w hav th quation H jw ).5N )w +.5w. 3) As it can b sn, h n) is an approximatly linar-phas filtr. This mans that h n) is approximatly symmtric around th point n =.5N ).5. This is on quartr away from th natural point of symmtry, and solutions of this kind wr introducd as q-shift dual-tr filtrs for this rason []..4.. Common Factor olution CF). Anothr mthod for filtr dsign stag namd as commonfactorsolutioncf) can b usd to dsign both orthonormal and biorthogonal solutions for th dual tr CWT []. In this approach, th filtrs, h and g ar st as h n) = f n) dn), g n) = f n) dl n), 4) whr dn) is supportd on n L and rprsnts th discrt tim convolution. In trms of Z-transform, w hav H z) = Fz)Dz), ) G z) = Fz)z L D. z 5) For this solution, th magnitud part of half-sampl dlay condition is satisfid; howvr, th phas part is not xactly satisfid as in q-shift solution [] G jw ) = H jw ), G jw ) H jw ).5w. 6) o, th filtrs must b dsignd so that th phas condition is approximatly satisfid. 3. Exprimntal tudy and Rsults 3.. Datast and Prprocssing. Th two diffrnt data sts hav bn utilizd, and th faturs hav bn xtractd sparatly for ths two diffrnt datasts. In th first datast, TIMIT databas has bn usd for spch and svral CD rcordings with various musical gnrs hav bn usd for music databas. To obtain th scond datast, radio broadcasts wr rcordd containing music and spch. Th sampling frquncy was st as 44 Hz in vry stag of study. Howvr, sinc th data takn from TIMIT databas is sampld with 6 Hz, thy hav bn intrpolatd in th prprocssing stag in ordr to st sampling frquncy to 44 Hz. For th common faturs, th sgmntation has bn prformd for a fram of 496 sampls with 5 Tabl : Contnt of datasts. Ovrall databas Train st Tst st pch Music pch Music pch Music Datast Datast sampls ovrlapping which corrsponds to a fram lngth of 95 ms. Our xprimnts showd that th us of shortr window lngths limits th discriminativ charactristics of window. Both datasts usd contain sampls with lngth of.5 sc. Whil th first datast includs 49 music and 46 spch sampls, th scond datast contains 9 music and 64 spch sampls ntirly drivd from radio broadcasts in contrary to th first datast. In th rst of th contxt, th first and scond data sts will b namd as Datast and Datast, rspctivly. For th prformanc valuation, th data sts hav bn dividd into two groups as training and tst sts. A dtaild rprsntation for datast and datast is givn in Tabl. Th four diffrnt fatur xtraction mthods hav bn mployd in this study. Th first mthod has a paramtr vctor which contains tim-frquncy-basd faturs and Ml cpstrum cofficints with lngth of. Th scond and third mthods us DWT-basd faturs. Th scond mthod contains DWT-basd nrgy paramtrs Tagr and instantanous nrgy as dscribd in ction.3.thlngth of fatur vctor for third mthod is. Thnovlmthodsproposdinthisstudyarthlast two fatur xtraction schms. In th third mthod, - lvl DWT dcomposition has bn prformd to covr th analysis frquncy rang in dtail using svral typs of mothr wavlts of Daubhcis family. Th lngth of fatur vctor constructd from th statistical masurs of th cofficints, and ratios btwn th adjacnt subbands is 38. Usag of ratio paramtrs and th slction of th siz of th analysis window ar th important aspct which improvs th prformanc of th classification in this study. Th last mthod is basd on complx wavlt transform CWT), and two diffrnt filtr dsign stratgis including commonfactorsolutionandq shift solution hav bn usd at fatur xtraction stag. CWT has bn prformd for 5- lvl and 7-lvl to avoid furthr incras in th lngth of th fatur vctor which rsults in fatur vctors with lngth of 5and35for5and7bands,rspctivly. Bfor classification stag, th faturs that ar highly corrlatd with th othr faturs hav bn liminatd using principal componnt analysis PCA) to rduc th lngth of fatur vctors. Th principal componnts that contribut lss than.5% to th total variation in th data st hav bn liminatd. Tabl shows th lngth of th fatur vctors bfor and aftr PCA. It has bn obsrvd from Tabl that th DWT-basd nrgy faturs includ discriminativ information. imilarly, approximatly half of prliminary fatur vctors ar corrlatd with ach othr spcially for CWT-basd faturs.

6 6 IRN ignal Procssing Tabl : Lngths of th fatur vctors bfor and aftr PCA. Original lngth Aftr PCA Convntional Common faturs DWT basd Enrgy DWT basd CWT basd DWT Enrgy db8) 5 DWT Enrgy coif) 3 Haar 38 9 db 38 9 db8 38 db5 38 db 38 CF 5 Lvls ) 5 Q hift 5 Lvls ) 5 CF 7 Lvls ) 35 5 Q hift 7 Lvls ) 35 4 Th fdforward artificial nural ntworks with th scald conjugat gradint CG) backpropagation algorithm in MATLAB s nural ntworks toolbox which blongs to th class of th conjugat gradint algorithms hav bn usd for classification. CG algorithm uss stp siz scaling instad of lin-sarch pr larning itration, and this maks it fastr than othr scond-ordr algorithms []. This algorithm prforms wll for ntworks with a larg numbr of wights,whritisasfastasthlvnbrg-marquardtand rsilint backpropagation algorithms; its prformanc dos not dgrad quickly. Also, th conjugat gradint algorithms hav rlativly modst mmory rquirmnts. Th numbr of hiddn nurons has bn prfrrd as 4, and th targt man squar rror has bn dfind as., as a rsult of xtnsiv simulations. All cods and programs in this study hav bn writtn in MATLAB. Th cods for common faturs, DWT-basd statistical and nrgy faturs hav bn writtn by th authors. For DWT-basd analysis, wavlt toolbox of MATLAB has bn usd. For CWT-basd analysis, th cods ar takn from th study of lsnick [] for common factor solution-basd filtr dsign and th programs writtn by two studnts undr suprvision of I. lsnick hav bn usd for Q-shift filtr basd analysis [3]. In th following sction, th gnral classification rsults will b givn for fatur vctors. Th prformanc has bn givn as th accuracy of th classification which can b formulatd as TP+TN Accuracy = TP+FP+TN+FN, 7) whr TP, TN, FP,andFN rprsnt th numbr of spch sampls labld as spch, th numbr of music sampls labld as music, th numbr of music sampls labld as spch and th numbr of spch sampls labld as music, rspctivly. 3.. Gnral Classification Prformanc. Th rsults of th xprimnts ar summarizd as gnral prformanc in Tabl 3. Tabl 3: Gnral classification rsults. Prformanc %) Datast Datast Convntional Common faturs DWT basd Enrgy DWT basd CWT basd DWT nrgy db8) DWT nrgy coif) Haar db db db db CF 5 Lvls ) Q shift 5 Lvls ) CF 7 Lvls ) Q shift 7 Lvls ) Whn Tabl 3 is takn into considration, it can b sn that wavlt-basd paramtrs hav highr classification rsults than traditional mthods. In gnral, all mthods ar succssful in th classification of sampls in Datast, which indicats that th TIMIT spch data and CD rcordings ar sparabl. Howvr, it is not possibl to say sam thing for Datast, sinc th sampls in Datast rflcts a mor ralistic cas, whr sampls ar rcordd from radio broadcast. Th bst prformanc has bn obtaind with db8 wavlt. Th complx wavlt-basd faturs prform bttr than convntional mthods and wavlts with fwr vanishing momnts. Howvr, thy ar not as succssful as th db8. Th similarity of th mothr wavlt with th analyzd wavforms is an important critrion for th wavlt analysis which may b th caus of this prformanc diffrnc. Thrfor, th accuracy for diffrnt databass may diffrdrastically. Th fatur xtraction mthods ar considrd in trms of thir calculation tims, and th avrag computation tims for fatur-xtraction stag for all mthods usd in this study ar givn in Tabl 4. According to Tabl 4, a sorting among th fatur xtraction mthods can b mad as t C >t DWT >t CWT >t DWTE, 8) whr t C, t DWT, t CWT,andt DWTE show th computation tim for th mthods basd on convntional, DWT, CWT, and DWT-basd nrgy faturs. As xpctd, th convntional mthods tak mor tim, sinc thy includ tim domain calculations. Although nrgy-basd faturs ar th fastst, thy hav poor classification prformanc. Th calculation tims for DWT-basd statistical fatur xtraction show diffrncs according to th usd wavlt in th analysis. Wavlt familis including mor vanishing momnts such as db5 and db spnd mor tim for computation comparing to othr wavlt familis, sinc thy hav longr filtrs. It is ncountrd that th db8 familis as th optimum wavlt for DWT-basd analysis sinc it shows highst prformanc in classification of spch and music and it has accptabl calculation tim.

7 IRN ignal Procssing 7 Tabl 4: Avrag computation tims for usd fatur xtraction mthods. pch msn.) Music msn.) Convntional Common faturs Daubchis8-basd DWT basd.6.7 nrgy faturs Enrgy Coiflt-basd nrgy faturs DWT basd CWT basd Haar Daubchis.4.4 Daubchis Daubchis Daubchis Q-shift-basd CWT faturs CF-basd CWT faturs.3.3 CWT-basd mthod is fastr than DWT-basd analysis, and it shows prformanc rsults clos to DWT. In this prspctiv, CWT-basd faturs can b usd for onlin implmntation as wll. It should b notd that th silnt parts of sampls could b dtrmind quickr than th fatur-xtraction mthods during onlin implmntation, sinc only an nrgy thrshold valu is considrd to mak a dcision if th sgmnt is silnc or not Graphical Usr Intrfac GUI) Dsign for pch/music Discrimination. A graphical usr intrfac has bn dsignd as wll in ordr to prform spch music discrimination visually. An onlin lablling modul has bn also mbddd to th intrfac and obsrvation of prformanc for ral-tim classification has bcom possibl with this tool Main Modul. Main modul can b usd to s classification rsults obtaind by mthods. In Figur 3, thgui dsignd for main modul is shown. Using load fil button, th fil to b analyzd is slctd, and th play button plots and plays th signal at th sam tim. inc tim-/frquncybasd faturs ar also usd at th classification stag, it is important to s th gnral structur of spctrogram. For this aim, thr is a button namd as spctrogram of signal in th modul to plot tim/frquncy proprtis. In th DWT-basd faturs part of modul, -lvl dcomposition is prformd using slctd wavlt from pop-up mnu. It is also possibl to s shap of wavlt and wavlt cofficints using show wavlt and plot wavlt cofficints buttons, rspctivly. For CWT-basd fatur, thr is also a popup mnu which you can slct th filtr dsign mthod for analysis. It can b sn th xisting complx wavlt with its ral and imagind parts using plot filtr Cofficints button in CWT-basd fatur xtraction part of th modul. For tim/frquncy basd fatur xtraction, thr is also a button and th valus of paramtrs such as spctral cntroid, spctral rolloff, spctral flux, th numbr of zro crossings, and low nrgy ratio of loadd fil xist in th blanks whn this button is pushd. It is possibl to gt th classification rsults of four-fatur xtraction mthods simultanously using classification rsults button. If onlin lablling modul button is pushd, th onlin lablling modul will appar in a nw window Ral-Tim pch/music Discrimination Modul. This modul has bn dsignd to obsrv spch/music classification prformanc for onlin implmntations. In th givn graphical usr intrfac in Figur 4, a sampl fil is ftchd using opn button and th onlin lablling procss is startd using start button. paus button maks it possibl to stop th procss tmporarily, and using continu button th labling procss can b continud from whr it is stoppd. Th stop button intrrupts th program and nds th labl assignmnt procss. In th modul, th rd lttrs undr th signal graph shows th prassignd labls for data and, M, and ar usd to indicat spch, music, and silnc parts of data, rspctivly. Onlin classification rsults ar shown with blu color undr prassignd labls, as it can b sn from Figur 4. Ths labls ar assignd for sgmnts which hav th lngth of.5 sc. In onlin labl assigning, th faturs ar xtractd using -lvl DWT with db8 wavlt for ach sampl, sinc it has givn th most accurat rsults in xprimnts and a prviously traind artificial nural ntwork is usd to dtrmin th labls. 4. Conclusions and Futur Work Thr has bn a growing intrst in spch/music discrimination systms which is usually usd in svral applications as a prprocssing stag of svral audio systms. Howvr, still improvmnts for MD systms ar rquird to dvlop ffctiv ral-tim systms. Thrfor, in this study, two fatur-xtraction schms basd on discrt and dual-tr wavlt transforms hav bn proposd which ar suitabl for ral-tim applications. Aftr comparing th proposd faturs with th convntional faturs and rcntly proposd wavlt-basd nrgy faturs, an onlin labling modul has bn implmntd with th Daubhcis8 wavlt. Rgarding th xprimnts and rsults givn in th prvious sction, it has bn obsrvd that convntional faturs ar not vry ffctiv in discrimination of spch/music sampls whn thy ar usd alon. Howvr, if thy ar usd togthr, th accuracy tnds to slightly incras. Th wavlt transform mthods xcpt th nrgy-basd ons hav shown highr prformanc for Databas than th rsults for Databas, bcaus th scond databas consists of th rcordings from radio broadcasts which rflcts a mor ralistic cas. Th slction of th analysis window lngth which spcifis th contnt of th nonstationary signal and th spd of implmntation is an important choic for MD. Th slction of a short window ordr of millisconds as in litratur will not giv th ncssary information on timvarying frquncy contnt, sinc th signal can b assumd

8 IRN ignal Procssing th WHRO voicb ayan rkkk alitli5.wav t ψh t) ψh t) + ψg t) ψg t) Complx ψt) Tim Frquncy Hz) 3 t Figur 3: Graphical usr intrfac for main modul I I Figur 4: Graphical usr intrfac for onlin lablling modul.

9 IRN ignal Procssing 9 as stationary in this intrval. On th othr hand, th usag of long window ordr of sconds, which is rportd as succssful, limits th onlin application of th algorithms. Th proposd algorithm is computationally fficint avrag running tim for th proposd mthod is <5 msn), and this allows th us of mthod for ral-tim implmntation. Th classification prformanc of DWT-basd fatur vctor varis dpnding on th mothr wavlt usd in th fatur-xtraction stag. Whn th numbr of vanishing momnts is incrasd, th wavlt bcoms smoothr. Ths smooth wavlts produc larg cofficints for slowly changing signals lik music, whil it producs rlativly small cofficints for spch signals. This can b usd as a discriminativ proprty for MD. Th Haar and db wavlts hav a fw vanishing momnt this may prvnt th good rprsntation of signal in frquncy domain. On th contrary, db5 and db hav much mor filtr cofficints and vanishing momnts, but this incrass th complxity in th fatur spac and also rquirs longr computations. In this way, db8 has mrgd as th most idal wavlt typ. Among th CWT-and DWT-basd faturs, DWT fatur xtractd with Daubchis8 wavlt has dmonstratd th highst classification prformanc, whil th CWT-basd classification has shown rsults as 99.93% for Databas and 98.3% for Databas. Whn all faturs ar concrnd, w s that Daubchis8-basd paramtrs hav suprior discrimination faturs in trms of classification of spch and music. In th study, th contribution of th ratio paramtrs to th discrimination prformanc hav also bn xamind for DWT- and CWT-basd faturs. It has bn obsrvd that ratio paramtrs provid a contribution about.5% to th ovrall prformanc for DWT-basd paramtrs. Howvr, th rsults wr inconclusiv for CWT. In th classification stag, artificial nural ntworks hav bn usd as classification tool. Th numbr of hiddn nurons has bn prfrrd as 4, and th targt man squar rror has bn dfind as., huristically. Conjugat gradint algorithms hav bn slctd as larning algorithm, sinc thy hav advantags according to othr mthods. Also, principal componnt analysis has bn prformd bfor th classification stag to rprsnt signals mor fficintly and to dcras th dimnsion of fatur vctor. Th obsrvd MD prformanc of CWT-basd faturs was lss than th DWT-basd ons. To obtain a bttr prformanc, a fatur st which rflcts th most powrful proprtis of CWT must b constructd. Th filtr structur usd in CWT-basd paramtrization has th possibility of prsnc of unsuitabl charactristics in trms of spch/ music discrimination, and as a rsult, th accuracy is obsrvd as lowr than prformanc of DWT-basd faturs. In this mannr, adaptiv filtr dsign is rquird to gt mor succssful rsults. Th datast can b xpandd to includ mixd spch-music sampls. In this way, a multiclass classification can b prformd instad of binary classification for futur studis. Th proposd fatur xtraction is also suitabl for a hardwar implmntation using digital signal procssors to hav a fastr MD systm. Rfrncs [] O. M. Mubarak, E. Ambikairajah, and J. Epps, Novl faturs for ffctiv spch and music discrimination, in Procdings of th IEEE Intrnational Confrnc on Enginring of Intllignt ystms ICEI 6), ayfa, Islamabad, Pakistan, April 6. [] K. El-Malh, M. Klin, G. Ptrucci, and P. Kabal, pch/ music discrimination for multimdia applications, in Procdings of th IEEE Intrntional Confrnc on Acoustics, pch, and ignal Procssing, pp , Jun. [3]A.C.GdikandB.Bozkurt, Pitch-frquncyhistogrambasd music information rtrival for Turkish music, ignal Procssing, vol. 9, no. 4, pp ,. [4] J. aundrs, Ral-tim discrimination of broadcast spch/ music, in Procdings of th IEEE Intrnational Confrnc on Acoustics, pch, and ignal Procssing ICA 96), pp , May 996. [5] E. chirr and M. lany, Construction and valuation of a robust multifatur spch/music discriminator, in Procdings of th IEEE Intrnational Confrnc on Acoustics, pch, and ignal Procssing ICA 97), pp , April 997. [6] E. M. aad, M. I. El-Adawy, M. E. Abu-El-Wafa, and A. A. Wahba, A multifatur spch/music discrimination systm, in Procdings of th 9th National Radio cinc Confrnc NRC ), pp. 8 3,. [7] J. Ajmra, I. McCowan, and H. Bourlard, pch/music sgmntation using ntropy and dynamism faturs in a HMM classification framwork, pch Communication, vol. 4, no. 3, pp , 3. [8] C. Panagiotakis and G. Tziritas, A spch/music discriminator basd on RM and zro-crossings, IEEE Transactions on Multimdia, vol. 7, no., pp , 5. [9]J.Wang,Q.Wu,H.Dng,andQ.Yan, Ral-timspch/ music classification with a hirarchical obliqu dcision tr, in Procdings of th IEEE Intrnational Confrnc on Acoustics, pch and ignal Procssing ICA 8), pp , April 8. [] A. Pikrakis, T. Giannakopoulos, and. Thodoridis, A spch/music discriminator of radio rcordings basd on dynamic programming and Baysian ntworks, IEEE Transactions on Multimdia, vol., no. 5, Articl ID 45496, pp , 8. [] M. Kos, M. Grašič, and Z. Kačič, Onlin spch/music sgmntation basd on th varianc man of filtr bank nrgy, EURAIP Journal on Advancs in ignal Procssing, vol. 9, Articl ID 6857, pp. 3, 9. [] G. E. G. Tzantakis and P. Cook, Audio analysis using th discrt wavlt transform, in Mathmatics and imulation with Biological, Economical and Musicoacoustical Applications, pp , WE,. [3] M. K.. Khan and W. G. Al-Khatib, Machin-larning basd classification of spch and music, ACM Journal on Multimdia ystms, vol., no., pp , 6. [4]. Ntalampiras and N. Fakotakis, pch /music discrimination basd on discrt wavlt transform, in Procdings of th 5th Hllnic Confrnc on Artificial Intllignc ETN 8), vol. 538 of Lctur Nots in Artificial Intllignc, pp. 5, yros, Grc, Octobr 8. [5]E.Didiot,I.Illina,D.Fohr,andO.Mlla, Awavlt-basd paramtrization for spch/music discrimination, Computr pch and Languag, vol. 4, no., pp ,. [6] N. G. Kingsbury, Th dual-tr complx wavlt transform: a nw tchniqu for shift invarianc and dirctional filtrs,

10 IRN ignal Procssing in Procdings of th IEEE Digital ignal Procssing Workshop, 998. [7] I. W. lsnick, R. G. Baraniuk, and N. G. Kingsbury, Th dual-tr complx wavlt transform, IEEE ignal Procssing Magazin, vol., no. 6, pp. 3 5, 5. [8] F. Zhng, G. Zhang, and Z. ong, Comparison of diffrnt implmntations of MFCC, Journal of Computr cinc and Tchnology, vol. 6, no. 6, pp ,. [9]. Mallat, A Wavlt Tour of ignal Procssing, Acadmic Prss, 999. [] N. Kingsbury, Th dual-tr complx wavlt transform: a nw tchniqu for shift invarianc and dirctional filtrs, in Procdings of th IEEE Digital ignal Procssing Workshop,pp. 4, 998. [] I. W. lsnick, Th dsign of Hilbrt transform pairs of wavlt bass, IEEE ignal Procssing Lttrs, vol.8,no.6,pp. 7 73,. [] C. Charalambous, Conjugat gradint algorithm for fficint training of artificial nural ntworks, IEEE Procdings-G on Circuit Dvics and ystm, vol. 39, no. 3, pp. 3 3, 99. [3]. Cai and K. Li, Matlab Implmntation of Wavlt Transforms,.

11 Intrnational Journal of Rotating Machinry Enginring Journal of Volum 4 Th cintific World Journal Volum 4 Intrnational Journal of Distributd nsor Ntworks Journal of nsors Volum 4 Volum 4 Volum 4 Journal of Control cinc and Enginring Advancs in Civil Enginring Volum 4 Volum 4 ubmit your manuscripts at Journal of Journal of Elctrical and Computr Enginring Robotics Volum 4 Volum 4 VLI Dsign Advancs in OptoElctronics Intrnational Journal of Navigation and Obsrvation Volum 4 Chmical Enginring Volum 4 Volum 4 Activ and Passiv Elctronic Componnts Antnnas and Propagation Arospac Enginring Volum 4 Volum Volum 4 Intrnational Journal of Intrnational Journal of Intrnational Journal of Modlling & imulation in Enginring Volum 4 Volum 4 hock and Vibration Volum 4 Advancs in Acoustics and Vibration Volum 4

ECE Department Univ. of Maryland, College Park

ECE Department Univ. of Maryland, College Park EEE63 Part- Tr-basd Filtr Banks and Multirsolution Analysis ECE Dpartmnt Univ. of Maryland, Collg Park Updatd / by Prof. Min Wu. bb.ng.umd.du d slct EEE63); minwu@ng.umd.du md d M. Wu: EEE63 Advancd Signal

More information

A Sub-Optimal Log-Domain Decoding Algorithm for Non-Binary LDPC Codes

A Sub-Optimal Log-Domain Decoding Algorithm for Non-Binary LDPC Codes Procdings of th 9th WSEAS Intrnational Confrnc on APPLICATIONS of COMPUTER ENGINEERING A Sub-Optimal Log-Domain Dcoding Algorithm for Non-Binary LDPC Cods CHIRAG DADLANI and RANJAN BOSE Dpartmnt of Elctrical

More information

Problem Set #2 Due: Friday April 20, 2018 at 5 PM.

Problem Set #2 Due: Friday April 20, 2018 at 5 PM. 1 EE102B Spring 2018 Signal Procssing and Linar Systms II Goldsmith Problm St #2 Du: Friday April 20, 2018 at 5 PM. 1. Non-idal sampling and rcovry of idal sampls by discrt-tim filtring 30 pts) Considr

More information

Addition of angular momentum

Addition of angular momentum Addition of angular momntum April, 0 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat th

More information

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches. Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M

More information

Lecture 2: Discrete-Time Signals & Systems. Reza Mohammadkhani, Digital Signal Processing, 2015 University of Kurdistan eng.uok.ac.

Lecture 2: Discrete-Time Signals & Systems. Reza Mohammadkhani, Digital Signal Processing, 2015 University of Kurdistan eng.uok.ac. Lctur 2: Discrt-Tim Signals & Systms Rza Mohammadkhani, Digital Signal Procssing, 2015 Univrsity of Kurdistan ng.uok.ac.ir/mohammadkhani 1 Signal Dfinition and Exampls 2 Signal: any physical quantity that

More information

Homotopy perturbation technique

Homotopy perturbation technique Comput. Mthods Appl. Mch. Engrg. 178 (1999) 257±262 www.lsvir.com/locat/cma Homotopy prturbation tchniqu Ji-Huan H 1 Shanghai Univrsity, Shanghai Institut of Applid Mathmatics and Mchanics, Shanghai 272,

More information

Introduction to the Fourier transform. Computer Vision & Digital Image Processing. The Fourier transform (continued) The Fourier transform (continued)

Introduction to the Fourier transform. Computer Vision & Digital Image Processing. The Fourier transform (continued) The Fourier transform (continued) Introduction to th Fourir transform Computr Vision & Digital Imag Procssing Fourir Transform Lt f(x) b a continuous function of a ral variabl x Th Fourir transform of f(x), dnotd by I {f(x)} is givn by:

More information

Learning Spherical Convolution for Fast Features from 360 Imagery

Learning Spherical Convolution for Fast Features from 360 Imagery Larning Sphrical Convolution for Fast Faturs from 36 Imagry Anonymous Author(s) 3 4 5 6 7 8 9 3 4 5 6 7 8 9 3 4 5 6 7 8 9 3 3 3 33 34 35 In this fil w provid additional dtails to supplmnt th main papr

More information

Procdings of IC-IDC0 ( and (, ( ( and (, and (f ( and (, rspctivly. If two input signals ar compltly qual, phas spctra of two signals ar qual. That is

Procdings of IC-IDC0 ( and (, ( ( and (, and (f ( and (, rspctivly. If two input signals ar compltly qual, phas spctra of two signals ar qual. That is Procdings of IC-IDC0 EFFECTS OF STOCHASTIC PHASE SPECTRUM DIFFERECES O PHASE-OLY CORRELATIO FUCTIOS PART I: STATISTICALLY COSTAT PHASE SPECTRUM DIFFERECES FOR FREQUECY IDICES Shunsu Yamai, Jun Odagiri,

More information

A Propagating Wave Packet Group Velocity Dispersion

A Propagating Wave Packet Group Velocity Dispersion Lctur 8 Phys 375 A Propagating Wav Packt Group Vlocity Disprsion Ovrviw and Motivation: In th last lctur w lookd at a localizd solution t) to th 1D fr-particl Schrödingr quation (SE) that corrsponds to

More information

Outline. Why speech processing? Speech signal processing. Advanced Multimedia Signal Processing #5:Speech Signal Processing 2 -Processing-

Outline. Why speech processing? Speech signal processing. Advanced Multimedia Signal Processing #5:Speech Signal Processing 2 -Processing- Outlin Advancd Multimdia Signal Procssing #5:Spch Signal Procssing -Procssing- Intllignt Elctronic Systms Group Dpt. of Elctronic Enginring, UEC Basis of Spch Procssing Nois Rmoval Spctral Subtraction

More information

Title: Vibrational structure of electronic transition

Title: Vibrational structure of electronic transition Titl: Vibrational structur of lctronic transition Pag- Th band spctrum sn in th Ultra-Violt (UV) and visibl (VIS) rgions of th lctromagntic spctrum can not intrprtd as vibrational and rotational spctrum

More information

Chapter 6. The Discrete Fourier Transform and The Fast Fourier Transform

Chapter 6. The Discrete Fourier Transform and The Fast Fourier Transform Pusan ational Univrsity Chaptr 6. Th Discrt Fourir Transform and Th Fast Fourir Transform 6. Introduction Frquncy rsponss of discrt linar tim invariant systms ar rprsntd by Fourir transform or z-transforms.

More information

Full Waveform Inversion Using an Energy-Based Objective Function with Efficient Calculation of the Gradient

Full Waveform Inversion Using an Energy-Based Objective Function with Efficient Calculation of the Gradient Full Wavform Invrsion Using an Enrgy-Basd Objctiv Function with Efficint Calculation of th Gradint Itm yp Confrnc Papr Authors Choi, Yun Sok; Alkhalifah, ariq Ali Citation Choi Y, Alkhalifah (217) Full

More information

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic

More information

CE 530 Molecular Simulation

CE 530 Molecular Simulation CE 53 Molcular Simulation Lctur 8 Fr-nrgy calculations David A. Kofk Dpartmnt of Chmical Enginring SUNY Buffalo kofk@ng.buffalo.du 2 Fr-Enrgy Calculations Uss of fr nrgy Phas quilibria Raction quilibria

More information

The van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012

The van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012 Th van dr Waals intraction D. E. Sopr 2 Univrsity of Orgon 20 pril 202 Th van dr Waals intraction is discussd in Chaptr 5 of J. J. Sakurai, Modrn Quantum Mchanics. Hr I tak a look at it in a littl mor

More information

Search sequence databases 3 10/25/2016

Search sequence databases 3 10/25/2016 Sarch squnc databass 3 10/25/2016 Etrm valu distribution Ø Suppos X is a random variabl with probability dnsity function p(, w sampl a larg numbr S of indpndnt valus of X from this distribution for an

More information

Slide 1. Slide 2. Slide 3 DIGITAL SIGNAL PROCESSING CLASSIFICATION OF SIGNALS

Slide 1. Slide 2. Slide 3 DIGITAL SIGNAL PROCESSING CLASSIFICATION OF SIGNALS Slid DIGITAL SIGAL PROCESSIG UIT I DISCRETE TIME SIGALS AD SYSTEM Slid Rviw of discrt-tim signals & systms Signal:- A signal is dfind as any physical quantity that varis with tim, spac or any othr indpndnt

More information

Numbering Systems Basic Building Blocks Scaling and Round-off Noise. Number Representation. Floating vs. Fixed point. DSP Design.

Numbering Systems Basic Building Blocks Scaling and Round-off Noise. Number Representation. Floating vs. Fixed point. DSP Design. Numbring Systms Basic Building Blocks Scaling and Round-off Nois Numbr Rprsntation Viktor Öwall viktor.owall@it.lth.s Floating vs. Fixd point In floating point a valu is rprsntd by mantissa dtrmining th

More information

Addition of angular momentum

Addition of angular momentum Addition of angular momntum April, 07 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat

More information

Two Products Manufacturer s Production Decisions with Carbon Constraint

Two Products Manufacturer s Production Decisions with Carbon Constraint Managmnt Scinc and Enginring Vol 7 No 3 pp 3-34 DOI:3968/jms9335X374 ISSN 93-34 [Print] ISSN 93-35X [Onlin] wwwcscanadant wwwcscanadaorg Two Products Manufacturr s Production Dcisions with Carbon Constraint

More information

2F1120 Spektrala transformer för Media Solutions to Steiglitz, Chapter 1

2F1120 Spektrala transformer för Media Solutions to Steiglitz, Chapter 1 F110 Spktrala transformr för Mdia Solutions to Stiglitz, Chaptr 1 Prfac This documnt contains solutions to slctd problms from Kn Stiglitz s book: A Digital Signal Procssing Primr publishd by Addison-Wsly.

More information

Exam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator.

Exam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator. Exam N a m : _ S O L U T I O N P U I D : I n s t r u c t i o n s : It is important that you clarly show your work and mark th final answr clarly, closd book, closd nots, no calculator. T i m : h o u r

More information

10. The Discrete-Time Fourier Transform (DTFT)

10. The Discrete-Time Fourier Transform (DTFT) Th Discrt-Tim Fourir Transform (DTFT Dfinition of th discrt-tim Fourir transform Th Fourir rprsntation of signals plays an important rol in both continuous and discrt signal procssing In this sction w

More information

Determination of Vibrational and Electronic Parameters From an Electronic Spectrum of I 2 and a Birge-Sponer Plot

Determination of Vibrational and Electronic Parameters From an Electronic Spectrum of I 2 and a Birge-Sponer Plot 5 J. Phys. Chm G Dtrmination of Vibrational and Elctronic Paramtrs From an Elctronic Spctrum of I 2 and a Birg-Sponr Plot 1 15 2 25 3 35 4 45 Dpartmnt of Chmistry, Gustavus Adolphus Collg. 8 Wst Collg

More information

PHASE-ONLY CORRELATION IN FINGERPRINT DATABASE REGISTRATION AND MATCHING

PHASE-ONLY CORRELATION IN FINGERPRINT DATABASE REGISTRATION AND MATCHING Anall Univrsităţii d Vst din Timişoara Vol. LII, 2008 Sria Fizică PHASE-OLY CORRELATIO I FIGERPRIT DATABASE REGISTRATIO AD ATCHIG Alin C. Tusda, 2 Gianina Gabor Univrsity of Orada, Environmntal Faculty,

More information

Einstein Equations for Tetrad Fields

Einstein Equations for Tetrad Fields Apiron, Vol 13, No, Octobr 006 6 Einstin Equations for Ttrad Filds Ali Rıza ŞAHİN, R T L Istanbul (Turky) Evry mtric tnsor can b xprssd by th innr product of ttrad filds W prov that Einstin quations for

More information

Estimation of apparent fraction defective: A mathematical approach

Estimation of apparent fraction defective: A mathematical approach Availabl onlin at www.plagiarsarchlibrary.com Plagia Rsarch Library Advancs in Applid Scinc Rsarch, 011, (): 84-89 ISSN: 0976-8610 CODEN (USA): AASRFC Estimation of apparnt fraction dfctiv: A mathmatical

More information

Types of Transfer Functions. Types of Transfer Functions. Types of Transfer Functions. Ideal Filters. Ideal Filters

Types of Transfer Functions. Types of Transfer Functions. Types of Transfer Functions. Ideal Filters. Ideal Filters Typs of Transfr Typs of Transfr x[n] X( LTI h[n] H( y[n] Y( y [ n] h[ k] x[ n k] k Y ( H ( X ( Th tim-domain classification of an LTI digital transfr function is basd on th lngth of its impuls rspons h[n]:

More information

3-2-1 ANN Architecture

3-2-1 ANN Architecture ARTIFICIAL NEURAL NETWORKS (ANNs) Profssor Tom Fomby Dpartmnt of Economics Soutrn Mtodist Univrsity Marc 008 Artificial Nural Ntworks (raftr ANNs) can b usd for itr prdiction or classification problms.

More information

Discrete Hilbert Transform. Numeric Algorithms

Discrete Hilbert Transform. Numeric Algorithms Volum 49, umbr 4, 8 485 Discrt Hilbrt Transform. umric Algorithms Ghorgh TODORA, Rodica HOLOEC and Ciprian IAKAB Abstract - Th Hilbrt and Fourir transforms ar tools usd for signal analysis in th tim/frquncy

More information

5.80 Small-Molecule Spectroscopy and Dynamics

5.80 Small-Molecule Spectroscopy and Dynamics MIT OpnCoursWar http://ocw.mit.du 5.80 Small-Molcul Spctroscopy and Dynamics Fall 008 For information about citing ths matrials or our Trms of Us, visit: http://ocw.mit.du/trms. Lctur # 3 Supplmnt Contnts

More information

Observer Bias and Reliability By Xunchi Pu

Observer Bias and Reliability By Xunchi Pu Obsrvr Bias and Rliability By Xunchi Pu Introduction Clarly all masurmnts or obsrvations nd to b mad as accuratly as possibl and invstigators nd to pay carful attntion to chcking th rliability of thir

More information

A Prey-Predator Model with an Alternative Food for the Predator, Harvesting of Both the Species and with A Gestation Period for Interaction

A Prey-Predator Model with an Alternative Food for the Predator, Harvesting of Both the Species and with A Gestation Period for Interaction Int. J. Opn Problms Compt. Math., Vol., o., Jun 008 A Pry-Prdator Modl with an Altrnativ Food for th Prdator, Harvsting of Both th Spcis and with A Gstation Priod for Intraction K. L. arayan and. CH. P.

More information

Topology Optimization of Suction Muffler for Noise Attenuation

Topology Optimization of Suction Muffler for Noise Attenuation Purdu Univrsity Purdu -Pubs Intrnational Comprssor Enginring Confrnc School of Mchanical Enginring 2012 Topology Optimization of Suction Mufflr for Nois Attnuation Jin Woo L jinwool@ajou.ac.kr Dong Wook

More information

4.2 Design of Sections for Flexure

4.2 Design of Sections for Flexure 4. Dsign of Sctions for Flxur This sction covrs th following topics Prliminary Dsign Final Dsign for Typ 1 Mmbrs Spcial Cas Calculation of Momnt Dmand For simply supportd prstrssd bams, th maximum momnt

More information

SEMG Signal Processing and Analysis Using Wavelet Transform and Higher Order Statistics to Characterize Muscle Force

SEMG Signal Processing and Analysis Using Wavelet Transform and Higher Order Statistics to Characterize Muscle Force SEMG Signal Procssing and Analysis Using Wavlt Transform and Highr Ordr Statistics to Charactriz Muscl Forc M. S. HUSSAIN, M. B. I. REAZ, M. I. IBRAHIMY Dpartmnt of Elctrical and Computr Enginring Intrnational

More information

Fourier Transforms and the Wave Equation. Key Mathematics: More Fourier transform theory, especially as applied to solving the wave equation.

Fourier Transforms and the Wave Equation. Key Mathematics: More Fourier transform theory, especially as applied to solving the wave equation. Lur 7 Fourir Transforms and th Wav Euation Ovrviw and Motivation: W first discuss a fw faturs of th Fourir transform (FT), and thn w solv th initial-valu problm for th wav uation using th Fourir transform

More information

Middle East Technical University Department of Mechanical Engineering ME 413 Introduction to Finite Element Analysis

Middle East Technical University Department of Mechanical Engineering ME 413 Introduction to Finite Element Analysis Middl East Tchnical Univrsity Dpartmnt of Mchanical Enginring ME 43 Introduction to Finit Elmnt Analysis Chaptr 3 Computr Implmntation of D FEM Ths nots ar prpard by Dr. Cünyt Srt http://www.m.mtu.du.tr/popl/cunyt

More information

A Low-Cost and High Performance Solution to Frequency Estimation for GSM/EDGE

A Low-Cost and High Performance Solution to Frequency Estimation for GSM/EDGE A Low-Cost and High Prformanc Solution to Frquncy Estimation for GSM/EDGE Wizhong Chn Lo Dhnr fwc@frscal.com ld@frscal.com 5-996- 5-996-75 77 Wst Parmr Ln 77 Wst Parmr Ln Austin, TX7879 Austin, TX7879

More information

Pipe flow friction, small vs. big pipes

Pipe flow friction, small vs. big pipes Friction actor (t/0 t o pip) Friction small vs larg pips J. Chaurtt May 016 It is an intrsting act that riction is highr in small pips than largr pips or th sam vlocity o low and th sam lngth. Friction

More information

Higher order derivatives

Higher order derivatives Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of

More information

Principles of Humidity Dalton s law

Principles of Humidity Dalton s law Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid

More information

EE140 Introduction to Communication Systems Lecture 2

EE140 Introduction to Communication Systems Lecture 2 EE40 Introduction to Communication Systms Lctur 2 Instructor: Prof. Xiliang Luo ShanghaiTch Univrsity, Spring 208 Architctur of a Digital Communication Systm Transmittr Sourc A/D convrtr Sourc ncodr Channl

More information

MA 262, Spring 2018, Final exam Version 01 (Green)

MA 262, Spring 2018, Final exam Version 01 (Green) MA 262, Spring 218, Final xam Vrsion 1 (Grn) INSTRUCTIONS 1. Switch off your phon upon ntring th xam room. 2. Do not opn th xam booklt until you ar instructd to do so. 3. Bfor you opn th booklt, fill in

More information

Random Access Techniques: ALOHA (cont.)

Random Access Techniques: ALOHA (cont.) Random Accss Tchniqus: ALOHA (cont.) 1 Exampl [ Aloha avoiding collision ] A pur ALOHA ntwork transmits a 200-bit fram on a shard channl Of 200 kbps at tim. What is th rquirmnt to mak this fram collision

More information

2.3 Matrix Formulation

2.3 Matrix Formulation 23 Matrix Formulation 43 A mor complicatd xampl ariss for a nonlinar systm of diffrntial quations Considr th following xampl Exampl 23 x y + x( x 2 y 2 y x + y( x 2 y 2 (233 Transforming to polar coordinats,

More information

Transitional Probability Model for a Serial Phases in Production

Transitional Probability Model for a Serial Phases in Production Jurnal Karya Asli Lorkan Ahli Matmatik Vol. 3 No. 2 (2010) pag 49-54. Jurnal Karya Asli Lorkan Ahli Matmatik Transitional Probability Modl for a Srial Phass in Production Adam Baharum School of Mathmatical

More information

Symmetric centrosymmetric matrix vector multiplication

Symmetric centrosymmetric matrix vector multiplication Linar Algbra and its Applications 320 (2000) 193 198 www.lsvir.com/locat/laa Symmtric cntrosymmtric matrix vctor multiplication A. Mlman 1 Dpartmnt of Mathmatics, Univrsity of San Francisco, San Francisco,

More information

MCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17)

MCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17) MCB37: Physical Biology of th Cll Spring 207 Homwork 6: Ligand binding and th MWC modl of allostry (Du 3/23/7) Hrnan G. Garcia March 2, 207 Simpl rprssion In class, w drivd a mathmatical modl of how simpl

More information

Extraction of Doping Density Distributions from C-V Curves

Extraction of Doping Density Distributions from C-V Curves Extraction of Doping Dnsity Distributions from C-V Curvs Hartmut F.-W. Sadrozinski SCIPP, Univ. California Santa Cruz, Santa Cruz, CA 9564 USA 1. Connction btwn C, N, V Start with Poisson quation d V =

More information

Rotor Stationary Control Analysis Based on Coupling KdV Equation Finite Steady Analysis Liu Dalong1,a, Xu Lijuan2,a

Rotor Stationary Control Analysis Based on Coupling KdV Equation Finite Steady Analysis Liu Dalong1,a, Xu Lijuan2,a 204 Intrnational Confrnc on Computr Scinc and Elctronic Tchnology (ICCSET 204) Rotor Stationary Control Analysis Basd on Coupling KdV Equation Finit Stady Analysis Liu Dalong,a, Xu Lijuan2,a Dpartmnt of

More information

COMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, April 04, 2005, 8:35 AM) PART I: CHAPTER TWO COMB MATH.

COMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, April 04, 2005, 8:35 AM) PART I: CHAPTER TWO COMB MATH. C:\Dallas\0_Courss\03A_OpSci_67\0 Cgh_Book\0_athmaticalPrliminaris\0_0 Combath.doc of 8 COPUTER GENERATED HOLOGRAS Optical Scincs 67 W.J. Dallas (onday, April 04, 005, 8:35 A) PART I: CHAPTER TWO COB ATH

More information

Coupled Pendulums. Two normal modes.

Coupled Pendulums. Two normal modes. Tim Dpndnt Two Stat Problm Coupld Pndulums Wak spring Two normal mods. No friction. No air rsistanc. Prfct Spring Start Swinging Som tim latr - swings with full amplitud. stationary M +n L M +m Elctron

More information

Capturing. Fig. 1: Transform. transform. of two time. series. series of the. Fig. 2:

Capturing. Fig. 1: Transform. transform. of two time. series. series of the. Fig. 2: Appndix: Nots on signal procssing Capturing th Spctrum: Transform analysis: Th discrt Fourir transform A digital spch signal such as th on shown in Fig. 1 is a squnc of numbrs. Fig. 1: Transform analysis

More information

Types of Transfer Functions. Types of Transfer Functions. Ideal Filters. Ideal Filters. Ideal Filters

Types of Transfer Functions. Types of Transfer Functions. Ideal Filters. Ideal Filters. Ideal Filters Typs of Transfr Typs of Transfr Th tim-domain classification of an LTI digital transfr function squnc is basd on th lngth of its impuls rspons: - Finit impuls rspons (FIR) transfr function - Infinit impuls

More information

2008 AP Calculus BC Multiple Choice Exam

2008 AP Calculus BC Multiple Choice Exam 008 AP Multipl Choic Eam Nam 008 AP Calculus BC Multipl Choic Eam Sction No Calculator Activ AP Calculus 008 BC Multipl Choic. At tim t 0, a particl moving in th -plan is th acclration vctor of th particl

More information

Bifurcation Theory. , a stationary point, depends on the value of α. At certain values

Bifurcation Theory. , a stationary point, depends on the value of α. At certain values Dnamic Macroconomic Thor Prof. Thomas Lux Bifurcation Thor Bifurcation: qualitativ chang in th natur of th solution occurs if a paramtr passs through a critical point bifurcation or branch valu. Local

More information

Different Focus Points Images Fusion Based on Steerable Filters

Different Focus Points Images Fusion Based on Steerable Filters Diffrnt Focus Points Imags Fusion Basd on Strabl Filtrs Lin zhng School of Elctronics & information nginring Xi an Jiaotong Univrsity Xi an,shaanxi,china LiinZhng@sina.com Chongzhao an School of Elctronics

More information

Koch Fractal Boundary Single feed Circularly Polarized Microstrip Antenna

Koch Fractal Boundary Single feed Circularly Polarized Microstrip Antenna 1 Journal of Microwavs, Optolctronics and Elctromagntic Applications, Vol. 6, No. 2, Dcmbr 2007 406 Koch Fractal Boundary Singl fd Circularly Polarizd Microstrip Antnna P. Nagswara Rao and N. V. S.N Sarma

More information

Image Filtering: Noise Removal, Sharpening, Deblurring. Yao Wang Polytechnic University, Brooklyn, NY11201

Image Filtering: Noise Removal, Sharpening, Deblurring. Yao Wang Polytechnic University, Brooklyn, NY11201 Imag Filtring: Nois Rmoval, Sharpning, Dblurring Yao Wang Polytchnic Univrsity, Brooklyn, NY http://wb.poly.du/~yao Outlin Nois rmoval by avraging iltr Nois rmoval by mdian iltr Sharpning Edg nhancmnt

More information

Why is a E&M nature of light not sufficient to explain experiments?

Why is a E&M nature of light not sufficient to explain experiments? 1 Th wird world of photons Why is a E&M natur of light not sufficint to xplain xprimnts? Do photons xist? Som quantum proprtis of photons 2 Black body radiation Stfan s law: Enrgy/ ara/ tim = Win s displacmnt

More information

Dynamic Modelling of Hoisting Steel Wire Rope. Da-zhi CAO, Wen-zheng DU, Bao-zhu MA *

Dynamic Modelling of Hoisting Steel Wire Rope. Da-zhi CAO, Wen-zheng DU, Bao-zhu MA * 17 nd Intrnational Confrnc on Mchanical Control and Automation (ICMCA 17) ISBN: 978-1-6595-46-8 Dynamic Modlling of Hoisting Stl Wir Rop Da-zhi CAO, Wn-zhng DU, Bao-zhu MA * and Su-bing LIU Xi an High

More information

Recursive Estimation of Dynamic Time-Varying Demand Models

Recursive Estimation of Dynamic Time-Varying Demand Models Intrnational Confrnc on Computr Systms and chnologis - CompSysch 06 Rcursiv Estimation of Dynamic im-varying Dmand Modls Alxandr Efrmov Abstract: h papr prsnts an implmntation of a st of rcursiv algorithms

More information

Quasi-Classical States of the Simple Harmonic Oscillator

Quasi-Classical States of the Simple Harmonic Oscillator Quasi-Classical Stats of th Simpl Harmonic Oscillator (Draft Vrsion) Introduction: Why Look for Eignstats of th Annihilation Oprator? Excpt for th ground stat, th corrspondnc btwn th quantum nrgy ignstats

More information

Spectral Synthesis in the Heisenberg Group

Spectral Synthesis in the Heisenberg Group Intrnational Journal of Mathmatical Analysis Vol. 13, 19, no. 1, 1-5 HIKARI Ltd, www.m-hikari.com https://doi.org/1.1988/ijma.19.81179 Spctral Synthsis in th Hisnbrg Group Yitzhak Wit Dpartmnt of Mathmatics,

More information

What are those βs anyway? Understanding Design Matrix & Odds ratios

What are those βs anyway? Understanding Design Matrix & Odds ratios Ral paramtr stimat WILD 750 - Wildlif Population Analysis of 6 What ar thos βs anyway? Undrsting Dsign Matrix & Odds ratios Rfrncs Hosmr D.W.. Lmshow. 000. Applid logistic rgrssion. John Wily & ons Inc.

More information

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding...

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding... Chmical Physics II Mor Stat. Thrmo Kintics Protin Folding... http://www.nmc.ctc.com/imags/projct/proj15thumb.jpg http://nuclarwaponarchiv.org/usa/tsts/ukgrabl2.jpg http://www.photolib.noaa.gov/corps/imags/big/corp1417.jpg

More information

Answer Homework 5 PHA5127 Fall 1999 Jeff Stark

Answer Homework 5 PHA5127 Fall 1999 Jeff Stark Answr omwork 5 PA527 Fall 999 Jff Stark A patint is bing tratd with Drug X in a clinical stting. Upon admiion, an IV bolus dos of 000mg was givn which yildd an initial concntration of 5.56 µg/ml. A fw

More information

EXST Regression Techniques Page 1

EXST Regression Techniques Page 1 EXST704 - Rgrssion Tchniqus Pag 1 Masurmnt rrors in X W hav assumd that all variation is in Y. Masurmnt rror in this variabl will not ffct th rsults, as long as thy ar uncorrlatd and unbiasd, sinc thy

More information

3 Finite Element Parametric Geometry

3 Finite Element Parametric Geometry 3 Finit Elmnt Paramtric Gomtry 3. Introduction Th intgral of a matrix is th matrix containing th intgral of ach and vry on of its original componnts. Practical finit lmnt analysis rquirs intgrating matrics,

More information

Evaluating Reliability Systems by Using Weibull & New Weibull Extension Distributions Mushtak A.K. Shiker

Evaluating Reliability Systems by Using Weibull & New Weibull Extension Distributions Mushtak A.K. Shiker Evaluating Rliability Systms by Using Wibull & Nw Wibull Extnsion Distributions Mushtak A.K. Shikr مشتاق عبذ الغني شخير Univrsity of Babylon, Collg of Education (Ibn Hayan), Dpt. of Mathmatics Abstract

More information

INFLUENCE OF GROUND SUBSIDENCE IN THE DAMAGE TO MEXICO CITY S PRIMARY WATER SYSTEM DUE TO THE 1985 EARTHQUAKE

INFLUENCE OF GROUND SUBSIDENCE IN THE DAMAGE TO MEXICO CITY S PRIMARY WATER SYSTEM DUE TO THE 1985 EARTHQUAKE 13 th World Confrnc on Earthquak Enginring Vancouvr, B.C., Canada August 1-6, 2004 Papr No. 2165 INFLUENCE OF GROUND SUBSIDENCE IN THE DAMAGE TO MEXICO CITY S PRIMARY WATER SYSTEM DUE TO THE 1985 EARTHQUAKE

More information

The graph of y = x (or y = ) consists of two branches, As x 0, y + ; as x 0, y +. x = 0 is the

The graph of y = x (or y = ) consists of two branches, As x 0, y + ; as x 0, y +. x = 0 is the Copyright itutcom 005 Fr download & print from wwwitutcom Do not rproduc by othr mans Functions and graphs Powr functions Th graph of n y, for n Q (st of rational numbrs) y is a straight lin through th

More information

Association (Part II)

Association (Part II) Association (Part II) nanopoulos@ismll.d Outlin Improving Apriori (FP Growth, ECLAT) Qustioning confidnc masur Qustioning support masur 2 1 FP growth Algorithm Us a comprssd rprsntation of th dtb databas

More information

A High-speed Method for Liver Segmentation on Abdominal CT Image

A High-speed Method for Liver Segmentation on Abdominal CT Image A High-spd Mthod for Livr Sgmntation on Abdominal CT Imag Wnhan Wang School of Elctronic and Information Enginring Liaoning Tchnical Univrsity Huludao, China yuoiobst@gmail.com Xih Gao Northastrn Univrsity

More information

LINEAR DELAY DIFFERENTIAL EQUATION WITH A POSITIVE AND A NEGATIVE TERM

LINEAR DELAY DIFFERENTIAL EQUATION WITH A POSITIVE AND A NEGATIVE TERM Elctronic Journal of Diffrntial Equations, Vol. 2003(2003), No. 92, pp. 1 6. ISSN: 1072-6691. URL: http://jd.math.swt.du or http://jd.math.unt.du ftp jd.math.swt.du (login: ftp) LINEAR DELAY DIFFERENTIAL

More information

Data Assimilation 1. Alan O Neill National Centre for Earth Observation UK

Data Assimilation 1. Alan O Neill National Centre for Earth Observation UK Data Assimilation 1 Alan O Nill National Cntr for Earth Obsrvation UK Plan Motivation & basic idas Univariat (scalar) data assimilation Multivariat (vctor) data assimilation 3d-Variational Mthod (& optimal

More information

Hospital Readmission Reduction Strategies Using a Penalty-Incentive Model

Hospital Readmission Reduction Strategies Using a Penalty-Incentive Model Procdings of th 2016 Industrial and Systms Enginring Rsarch Confrnc H. Yang, Z. Kong, and MD Sardr, ds. Hospital Radmission Rduction Stratgis Using a Pnalty-Incntiv Modl Michll M. Alvarado Txas A&M Univrsity

More information

Construction of asymmetric orthogonal arrays of strength three via a replacement method

Construction of asymmetric orthogonal arrays of strength three via a replacement method isid/ms/26/2 Fbruary, 26 http://www.isid.ac.in/ statmath/indx.php?modul=prprint Construction of asymmtric orthogonal arrays of strngth thr via a rplacmnt mthod Tian-fang Zhang, Qiaoling Dng and Alok Dy

More information

ECE602 Exam 1 April 5, You must show ALL of your work for full credit.

ECE602 Exam 1 April 5, You must show ALL of your work for full credit. ECE62 Exam April 5, 27 Nam: Solution Scor: / This xam is closd-book. You must show ALL of your work for full crdit. Plas rad th qustions carfully. Plas chck your answrs carfully. Calculators may NOT b

More information

There is an arbitrary overall complex phase that could be added to A, but since this makes no difference we set it to zero and choose A real.

There is an arbitrary overall complex phase that could be added to A, but since this makes no difference we set it to zero and choose A real. Midtrm #, Physics 37A, Spring 07. Writ your rsponss blow or on xtra pags. Show your work, and tak car to xplain what you ar doing; partial crdit will b givn for incomplt answrs that dmonstrat som concptual

More information

(Upside-Down o Direct Rotation) β - Numbers

(Upside-Down o Direct Rotation) β - Numbers Amrican Journal of Mathmatics and Statistics 014, 4(): 58-64 DOI: 10593/jajms0140400 (Upsid-Down o Dirct Rotation) β - Numbrs Ammar Sddiq Mahmood 1, Shukriyah Sabir Ali,* 1 Dpartmnt of Mathmatics, Collg

More information

Volterra Kernel Estimation for Nonlinear Communication Channels Using Deterministic Sequences

Volterra Kernel Estimation for Nonlinear Communication Channels Using Deterministic Sequences 1 Voltrra Krnl Estimation for Nonlinar Communication Channls Using Dtrministic Squncs Endr M. Ekşioğlu and Ahmt H. Kayran Dpartmnt of Elctrical and Elctronics Enginring, Istanbul Tchnical Univrsity, Istanbul,

More information

Robust surface-consistent residual statics and phase correction part 2

Robust surface-consistent residual statics and phase correction part 2 Robust surfac-consistnt rsidual statics and phas corrction part 2 Ptr Cary*, Nirupama Nagarajappa Arcis Sismic Solutions, A TGS Company, Calgary, Albrta, Canada. Summary In land AVO procssing, nar-surfac

More information

Communication Technologies

Communication Technologies Communication Tchnologis. Principls of Digital Transmission. Structur of Data Transmission.2 Spctrum of a Data Signal 2. Digital Modulation 2. Linar Modulation Mthods 2.2 Nonlinar Modulations (CPM-Signals)

More information

Computing and Communications -- Network Coding

Computing and Communications -- Network Coding 89 90 98 00 Computing and Communications -- Ntwork Coding Dr. Zhiyong Chn Institut of Wirlss Communications Tchnology Shanghai Jiao Tong Univrsity China Lctur 5- Nov. 05 0 Classical Information Thory Sourc

More information

Application of Vague Soft Sets in students evaluation

Application of Vague Soft Sets in students evaluation Availabl onlin at www.plagiarsarchlibrary.com Advancs in Applid Scinc Rsarch, 0, (6):48-43 ISSN: 0976-860 CODEN (USA): AASRFC Application of Vagu Soft Sts in studnts valuation B. Chtia*and P. K. Das Dpartmnt

More information

Sliding Mode Flow Rate Observer Design

Sliding Mode Flow Rate Observer Design Sliding Mod Flow Rat Obsrvr Dsign Song Liu and Bin Yao School of Mchanical Enginring, Purdu Univrsity, Wst Lafaytt, IN797, USA liu(byao)@purdudu Abstract Dynamic flow rat information is ndd in a lot of

More information

Impact of the Sampling Period on the Design of Digital PID Controllers

Impact of the Sampling Period on the Design of Digital PID Controllers Impact of th Sampling Priod on th Dsign of Digital PID Controllrs Dimitris Tsamatsoulis Halyps Building Matrials S.A. 17 th klm Nat. Road Athns Korinth, Aspropyrgos, Grc d.tsamatsoulis@halyps.gr Abstract

More information

ECE 407 Computer Aided Design for Electronic Systems. Instructor: Maria K. Michael. Overview. CAD tools for multi-level logic synthesis:

ECE 407 Computer Aided Design for Electronic Systems. Instructor: Maria K. Michael. Overview. CAD tools for multi-level logic synthesis: 407 Computr Aidd Dsign for Elctronic Systms Multi-lvl Logic Synthsis Instructor: Maria K. Michal 1 Ovrviw Major Synthsis Phass Logic Synthsis: 2-lvl Multi-lvl FSM CAD tools for multi-lvl logic synthsis:

More information

u x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula

u x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula 7. Intgration by Parts Each drivativ formula givs ris to a corrsponding intgral formula, as w v sn many tims. Th drivativ product rul yilds a vry usful intgration tchniqu calld intgration by parts. Starting

More information

First derivative analysis

First derivative analysis Robrto s Nots on Dirntial Calculus Chaptr 8: Graphical analysis Sction First drivativ analysis What you nd to know alrady: How to us drivativs to idntiy th critical valus o a unction and its trm points

More information

Quaternion Fourier Transform for Colour Images

Quaternion Fourier Transform for Colour Images Vikas R. Duby / (IJCSIT) Intrnational Journal of Computr Scinc and Information Tchnologis, Vol. 5 (3), 4, 44-446 Quatrnion Fourir Transform for Colour Imags Vikas R. Duby Elctronics, Mumbai Univrsity VJTI,

More information

Brief Introduction to Statistical Mechanics

Brief Introduction to Statistical Mechanics Brif Introduction to Statistical Mchanics. Purpos: Ths nots ar intndd to provid a vry quick introduction to Statistical Mchanics. Th fild is of cours far mor vast than could b containd in ths fw pags.

More information

Improving Color Image Segmentation by Spatial-Color Pixel Clustering

Improving Color Image Segmentation by Spatial-Color Pixel Clustering Improving Color Imag Sgmntation by Spatial-Color Pixl Clustring Hnryk Palus and Mariusz Frackiwicz Silsian Univrsity of Tchnology, ul. kadmicka 16, Gliwic, Poland BSTCT Imag sgmntation is on of th most

More information

Linear-Phase FIR Transfer Functions. Functions. Functions. Functions. Functions. Functions. Let

Linear-Phase FIR Transfer Functions. Functions. Functions. Functions. Functions. Functions. Let It is impossibl to dsign an IIR transfr function with an xact linar-phas It is always possibl to dsign an FIR transfr function with an xact linar-phas rspons W now dvlop th forms of th linarphas FIR transfr

More information

The Matrix Exponential

The Matrix Exponential Th Matrix Exponntial (with xrciss) by D. Klain Vrsion 207.0.05 Corrctions and commnts ar wlcom. Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix A A k I + A + k!

More information