SGN Audio and Speech Processing. Linear Prediction
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1 SGN-46 Audo d Seech Poceg Le Pedcto Slde fo th lectue e bed o thoe ceted by Kt Mhoe fo TUT coue Puheeättely meetelmät Sg 3. Othe ouce: K. Koe: Puheeättely meetelmät, lectue mtel, TUT, htt://
2 Fom the evou lectue: Seech oducto vowel Voced glottl exctto Vocl tct eoe Poduced eech oud
3 3 Fom the evou lectue: Kelly-Lochbum equto Model the vocl tct ug mle ufom tube ecto:
4 4 Fom the evou lectue: Lttce-tuctued ll-ole flte The lttce-tuctued flte eultg fom the Kelly-Lochbum equto ll-ole flte, meg tht t tfe fucto H z g A z clude oly ole zeo of the deomto Az
5 Le model c be ctegozed oe of the followg eech oceg, ut x efe to glott exctto d outut y to meued eech: Autoegeve movg vege model ARMA Coeod to geec le ecuve flte Movg vege model MA Coeod to FIR flte Autoegeve model AR Coeod to ll-ole flte g g cott Le ytem model 5 q x b y y ˆ q x b y ˆ y gx y ˆ z A z B z H ARMA z B z H MA z A g z H AR
6 6 AR model good choce fo modelg the vocl tct Tyclly the AR model ued eech oceg, becue The bove-decbed lttce-tuctued model fo the vocl tct coeod to ll-ole flte à AR model. I othe wod, the vocl tct wth cet umto theoetclly ll-ole flte The ut gl x ot ow glottl exctto. AR model tme c be comuted effcetly. Le edctve ly ug the Levo-Dub lgothm A hghe-ode AR model c to ome extet eeet lo the moe geec ARMA model
7 7 Fom AR model to le edcto Le edcto ly llow u to etmte the AR model mete fom ut gl > Le edcto good method fo etmtg the mete of the vocl tct > Le edcto oe of the mot mott tool eech oceg - Acoym: LP le edcto, LP-ly, LPC le edctve codg - Fom the eech oceg vewot, the mot mott oety of LP t blty to model the vocl tct
8 8 Le edcto ly LP ly fd the flte coeffcet,,,, tht bet edct the gl mle ccodg to the AR model dcdg x tem: y gx y à yˆ y The coeffcet of the edctve flte e choe o tht the qued edcto eo mmzed the ly wdow: g m y yˆ Kee md tht eech oceed hot fme d LP ly doe ox. evey -3 m tly ovelg fme
9 9 xmle: Mgtude ectum d LP ectum of vowel Wdowed hoe // Mgtude ectum d LP ectum Wdow legth ecod: 48/6Hz 3m
10 Sce we model eech gl hee, let ue to deote the meued eech gl, ted of y bove. ŝ deote the edcted vlue, d e - ŝ the edcto eo. Ug edcto coeffcet,,..., legth of the edcto flte the eegy of the edcto eo e By defg, the eo eegy c be wtte coveetly tmtg mete,,..., ˆ
11 We w t to fd mete,, tht mmze. A ecey codto fo the otmlty of coeffcet tht the tl devtve of fucto wth eect to zeo. Ptl devtve of wth eect to vble,,..., tmtg mete,,..., # $ % & '
12 Let eeet the bove devtve of the eo fucto ug the utocoelto: whee Autocoelto fucto,,
13 Let get bc to the eult of the devto Devtve of the eo wth eect to coeffcet,,...,: The zeo of the devtve of the edcto eo eegy e obted : quto: ubttute thee: me mtx-vecto fom: Autocoelto equto 3! 3 3 3!! "! #!!! " " "
14 Addg the equto o the to ow of the bove mtx equto, we get: whee the coeffcet mtx R ü ymmetc, becue ü Toeltz dgol-cott mtx Tht eetl whe loog fo effcet olvg lgothm 4 3!! "! #!!! " " " R Autocoelto equto
15 Let ove tht, wth otml coeffcet, The oof obted by exdg the que d egg tem???? 5 ˆ ˆ
16 d futhe: So we got tht??? 6 ˆ
17 7 Levo-Dub ecuve lgothm Pedcto coeffcet,,..., could be olved dectly fom the bove-deved equto ug fo exmle the mtx vee R -. Howeve tht comuttolly exeve. A effcet lgothm fo olvg Toeltz-tye mtx equto Levo-Dub ecuve lgothm The de to olve the mtx equto R y bloc by ceg the ze of mtx R d the legth of vecto x d by comutg ew oluto bed o the evou oe.
18 8 Levo-Dub ecuo : [ ][ ] [ ]
19 : : Levo-Dub ecuo 9 [ ][ ] [ ]
20 Levo-Dub ecuo : : [ ][ ] [ ]
![Levo-Dub ecuo : : [ ][](/docs-images/89/99396071/images/21-0.jpg "] [ ] q q q q q 3,4,")
21 Levo-Dub ecuo : : [ ][ ] [ ] q q q q q 3,4, etc.
22 Note bout the Levo-Dub lgothm The vble of the Levo-Dub lgothm e the eflecto coeffcet of the coeodg coutc tube model! The eegy of the eo decee whe moe coeffcet e dded to the edcto flte: oof: q q becue both d e lwy otve, thu q q
23 3 Choog the model ode Thee uully oe fomt e Hz Model ode c be etmted the mlg te Hz Fo exmle: mlg te 8Hz model ode 8 mlg te 6Hz model ode 6 Howeve to comete fo model ccuce, uully lghtly hghe model ode elected Fo exmle: mlg te 8Hz model ode o mlg te 6Hz model ode 8 o
24 4 Choog the model ode xmle: Let te hot egmet of hoe /y/ mlg te6hz d wdow t ug mooth wdow fucto Phoe y-ääe/y/ Wdowed uotu y-ääe hoe /y/ Next, let olve the edcto coeffcet fo model of vyg ode d vetgte the fequecy eoe of the obted LP flte -.6
25 5 Choog the model ode Ate 6 Ate 4 Ode 6 Ode Ate 8 Ate 56 4 Ode 8 Ode At mlg te 6Hz, good choce fo model ode would be 8. Wht he f too hgh o low model ode choe?
26 6 Pe-emh of hgh fequece A c be ee the bove fgue, eech ectum h much le eegy t hgh fequece th t low fequece. Tht my hve the coequece tht LP ly wll ot fd y of the hghe fomt. To dde the ue, uully e-emh flte ued tht fltte the ectl tlt befoe the LP ly: H e em z b z whee uully:.95 < b <.99 S S e Mgtude db LP ly Fequecy
27 7 Pe-emh of hgh fequece: exmle Ogl ectum Pe-emhzed ectum
28 8 Whee LP ly ued? Seech codg: eble the ete codg of exctto d vocl tct mete Seech ecogto: ovde fomto bout the eech ectum d theefoe bout the hoeme detty Seech ythe: llow ete cotol of the exctto d vocl tct mete I MATLAB, LP ly c be doe wth the commd lc
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