Assessment of Speech Intelligibility by Formant-Modulation Method

Transcription

1 Journal of Basc and Appld Physcs c. 3, Vol. Iss. 5, PP. -8 Assssmnt of Spch Intllgblty by Formant-Modulaton Mthod Arady Produs Acoustcs and Acoustolctroncs partmnt, Natonal chncal Unvrsty of Uran (Kyv Polytchnc Insttut, 9/6, Ac. Yangla Str., 356 Kyv, Uran Abstract- tald dscrpton of spch ntllgblty assssmnt by proposd formant-modulaton mthod s prsntd n th papr. Analytcal xprssons for xpctaton and varanc of stmators of a modulaton coffcnt and ffctv sgnal-to-nos rato ar obtand. wo stuatons whch ar most ntrstng n ngnrng applcatons ar consdrd: a prdomnant nos dsturbanc and a prdomnant rvrbrant dsturbanc. Convnnc n ngnrng applcatons uatons, whch prmt fndng ffcnt tst sgnal duraton for rurd masurmnt xactnss, has bn obtand. Computr modllng and xprmntal tstng hav confrmd ffcncy of th formant-modulaton mthod. Kywords- Spch Intllgblty; Formant-Modulaton Mthod; Assssmnt; Masurng Exactnss I. INROUCION h nw nstrumntal mthod of spch ntllgblty assssmnt, whch had bn offrd n wors [, ], was calld "formant-modulaton" as t was supposd that nw mthod would jon bttr faturs of formant [3] and MF [, 5] mthods. h da of calculaton of probablty of corrct undrstandng of spch lmnts (phonms, syllabls, words, phrass was savd from formant mthod, and th da of applcaton of th modulatd tst sgnal, whch allows tang nto account both nos and rvrbrant dsturbancs, was borrowd from an MF mthod. Man purpos of th papr s vrfcaton of ffcncy and assssmnt xactnss of th proposd mthod. II. SHOR ESCRIPION OF FORMAN-MOULAION MEHO Whn thy ma an acoustc xamnaton of apartmnt wth th us of nstrumntal (objctv mthods of spch ntllgblty valuaton, thy radat a tst sgnal x ( t n a crtan pont of apartmnt (announcr locaton, and n othr pont of apartmnt (lstnr locaton thy accpt a sgnal y ( t, whch s xposd to spcal procssng for calculatng on or fw numrcal paramtrs, whch charactrz spch ntllgblty of ths apartmnt [3 6]. Whn an apartmnt has mpuls rspons h ( v, whch dscrbs rvrbraton, and whn thr s ntrfrng nos n ( t n th sam apartmnt, thy watch a sgnal y ( t n th rcpton pont: y( t h( v x( t v dv n( t. ( At th us of formant-modulaton mthod [, ], thy calculat artculaton ntllgblty A n th sam way as n a formant mthod [3]: K A p P ( E, ( whr p s formant probablty dstrbuton on fruncy bands; P ( E s spch prcpton coffcnt; E s ffctv prcpton lvl of spch sgnal n -th fruncy band f. A dffrnc btwn formant-modulaton and formant mthods conssts n dffrnc of sgnal-to-nos assssmnt. Whn usng formant mthod, thy us a tst sgnal x ( t, whch s statonary stochastc procss and powr spctrum of whch s l long trm spch spctrum, and thy stmat E n accordanc wth uaton: whr s partal sgnal-to-nos rato, fruncy band. Whn usng formant-modulaton mthod, thy stmat E lg( s n, (3 s and n ar rspctvly varancs of statonary sgnal and nos n -th E n anothr way, whch s usd n modulaton - -

2 Journal of Basc and Appld Physcs c. 3, Vol. Iss. 5, PP. -8 mthod and whch prmts tang nto account prsnc of rvrbraton dsturbanc [, 5]. In accordanc wth ths way, thy us non-statonary stochastc procss tst sgnal x ( t, varanc of whch x ( t s modulatd on harmonc law wth modulaton fruncy F : x( t ( t f ( t, ( f ( t cos Ft. (5 x (t x (t x(t ( cos Ft, (6 whr ( t s statonary stochastc procss wth varanc and wth powr spctrum, whch s l long trm spch spctrum; s xpctaton symbol. It s vdnt that modulaton coffcnt m of varanc x ( t s ual to n ths cas. Varanc y (t of procss y ( t wll also b modulatd on harmonc law wth th sam fruncy F, but as a rsult of acton of rvrbrant and nos dsturbancs, modulaton coffcnt m of varanc y (t wll b lss than. ruly, substtutng h( v ( v n E. (, whr ( v s rac dlta functon, w gt: Sgnal-to-nos rato valu follows from E. (8: y(t ( cos Ft n, (7 m ( n. (8 SNR lg( n lg[ m ( m]. (9 At th untd acton of nos and rvrbraton dsturbancs, analytcal xprsson for th modulaton coffcnt m of varaton y (t appars mor dffcult, as compard to E. (8, and dpnds not only on nos varanc n, but also on standard rvrbraton tm 6, and vn on modulaton fruncy F. MF mthod authors suggstd usng of a st of modulaton fruncs F for mtaton of non-statonary charactr of th ral spch sgnal varanc. hy also ntroducd concpt of ffctv sgnal-to-nos rato: SNR, SNR, ( SNR, m ( F lg. ( m ( F whr m ( F s modulaton coffcnt of varanc y (t of sgnal y ( t n -th fruncy band [, 5]. SNR, s calculatd on formula, whch dscrbs th nos dsturbanc acton, whl th modulaton coffcnts m ( F carry on thmslvs th sal of acton by not only nos but also rvrbraton dsturbanc. Avragng of SNR, on th numbr of modulaton fruncy also varanc of th stmaton dmnshs. F n E. ( rsults n a doubl ffct: nflunc of F on th rsults of masurng s rprssd, and It bcoms clar n ths conncton, why t s suggstd n a formant-modulaton mthod to stmat th ffctv prcpton lvl E of spch sgnal n accordanc wth uaton: E SNR. ( As far as stmaton of modulaton coffcnts m ( F, t s xpdnt to produc t by mans of Fourr transformaton bcaus of harmonc modulaton of varanc y (t [5]: A ( F m ( F, (3 A( - -

3 Journal of Basc and Appld Physcs c. 3, Vol. Iss. 5, PP. -8 jft A( f y( t dt, ( wr s absolut valu symbol; s duraton of procss y( t h( v x(t v dv n(t ; x( t ( t cos F t s modulatd band-pass wht nos n th -th fruncy band. III. ANALYSIS OF MEASURING EXACNESS If w suppos that formants probablty dstrbuton on fruncy p and prcpton coffcnt P ( E ar nown wth hgh xactnss, thn t follows from Es. (, (, (5, ( (, that a bas and varanc of ntllgblty stmator ( ar compltly dtrmnd by statstcal proprts of magntuds A ( and A ( F A. Prvalng Influnc of Nos. In th bgnnng w shall ma a statstcal analyss of a par of stochastc varabls A ( and A ( F n th supposton that nos dsturbanc s prvalng abov rvrbraton dsturbanc. In ths cas modl of a sgnal n -th fruncy channl can b prsntd as: y(t (t cos( F t n (t, (5 whr ( t and n ( t ar normal band-pass (n -th fruncy band f wht and statstcally ndpndnt statonary stochastc procsss wth zro xpctatons; s unnown ntal phas. At frst lt's analyz xpctaton of magntuds A ( and A ( F (5, w rcv: A( f whr y ( t jft dt ( n jf Sa( f j j( f F. Omttng, for smplfcaton, ndxs n Es. ( and Sa[ ( f F ] j j( f F. Sa[ ( f F ] Sa( x sn( x x. At mplmntaton of condton r F, whr r s arbtrary postv ntgr, t follows from (6: (6 A( n, (7 A( F A( F. (8 As can b sn, uaton r F s a condton of an unbasd stmator of artculaton ntllgblty ( by mans of formant-modulaton mthod. W wll now fnd varanc of magntuds A ( and A ( F. In gnral cas: jf ( t t A( f y ( t y ( t dtt y jf ( t t y ( t y ( t dtt, (9 ( t y ( t y ( t y ( t n R ( t t f ( t f ( t Rn ( t t, ( n whr R ( and R n ( ar corrlaton coffcnts of statonary stochastc procsss ( t and n ( t rspctvly. Snc R ( Rn ( Sa( f cos f, ( whr f s fruncy bandwdth of procsss ( t and n ( t, f s cntral fruncy of ths band-pass, aftr rathr buly - -

4 Journal of Basc and Appld Physcs c. 3, Vol. Iss. 5, PP. -8 calculatons, undr th assumpton f, t s possbl to gt nxt fnal formula: whr s sgnal-to-nos rato. n, ( n 3 A( A( F f It follows from E. ( that Estmator (, gnratd by a formant-modulaton mthod, s consstnt. It wll b usful for ngnrng applcatons nxt formulas for rlatv varancs, whch dscrb an assssmnt rlatv rror: A( 3, A( f ( h dagrams of rlatv varancs (3 for A( F 3 (3 f A( F f =9 Hz ( f =5 Hz and =6 s ar rprsntd n Fg.. Invstgatons of cross corrlaton of magntuds A ( and A ( F ar also accompand wth th rathr buly calculatons, thrfor w only brng fnal rsults. (a Fg. Rlatv varancs of A ( (a and A ( F (b (b For small ( sgnal-to-nos ratos, at mplmntaton of condtons f and r F ualty may b wrttn:, th approxmat K A( A ( F KA( F A (, (.. magntuds A ( and A ( F ar practcally uncorrlatd ( s symbol of complx conjugat. And du to th cntral lmt thorm t s possbl to consdr ths magntuds as statstcally ndpndnt. For larg ( sgnal-to-nos ratos th approxmat ualty may b wrttn: K A( A ( F KA( F A ( f. (5 It follows from Es. (5 and ( that magntuds A ( and A ( F ar statstcally dpndnt, and factor of thr cross corrlaton s clos to magntud.66: R K A( A ( F A( A ( F 3. (6 A( A ( F spt of corrlaton of magntuds A( and A( F, th concluson about a consstncy of an Estmator (, gnratd by a formant-modulaton mthod, rmans n a forc. In vw of wa corrlaton of magntuds A( and A( F, t follows from E. (3 that undr condton r F - 3 -

5 Journal of Basc and Appld Physcs c. 3, Vol. Iss. 5, PP. -8 m ( F n m, (7.. stmator of modulaton coffcnt s unbasd. Expctaton of modulaton coffcnt stmator suar s: m ( F A( F A( F A( F. (8 A( A( A( ang nto account Es. (7, (8 and (, w can gt from Es. (7 and (8 th xprsson for modulaton coffcnt stmator varanc: It s asy to fnd from (9: 3 f [ m ] 3. (9 f [ m, lm ], [ m 5 lm ], [ m 6 ], f f f thrfor t wll b convnnt to us n ngnrng applcatons th followng smpl formula: u to unbasdnss of an stmator m (undr condton r [ m 6 ]. (3 f F, sgnal-to-nos rato stmator m SN R lg m. (3 s unbasd too undr th sam condton. As w can s from (3, varanc m ] s small for, so w can gt nxt approxmatly tru uaton: ang nto account (3 and [ w drv sutabl for ngnrng applcatons uaton: It may b shown for E. (3 []: f df ( m [ SNR ] [ m ] ; (3 dm m f ( m SNR lg. m df ( m,3,3 dm m( m [ SNR 3 ],SNR, SNR,, SNR, SNR. (33 f [ ] 38. (3 f Whn comparng Es. (33 and (3, w can suggst that formant mthod may b prfrabl for cas of prvalng nflunc of nos. Computr modllng shows truth of th suggston. Rlatv rror of formant mthod word ntllgblty - -

6 Journal of Basc and Appld Physcs c. 3, Vol. Iss. 5, PP. -8 stmator (Fg,a s about.5-. of th formant-modulaton mthod rror (Fg,b. Formant mthod stmaton tm s about of formant-modulaton mthod stmaton tm. (a Fg. Rlatv rrors of word ntllgblty stmators for formant mthod (a and formant-modulaton mthod (b B. Prvalng Influnc of Rvrbraton Whn consdrng th cas of prvalng nflunc of rvrbraton, th -th fruncy channl sgnal pattrn can b prsntd as y ( t h ( v x( t v dv, (35 whr x( t ( t f( t ; h ( v h( v h ( z v dv ; h ( v s room mpuls rspons and h ( v s -th band-pass fltr mpuls rspons. Expctaton of A ( F s: (b A( F jf t y ( t dt, (36 y( t h ( t h ( t ( ( f( f( dd Procss ( t n E. (37 s band-pass ( f f wht nos wth varanc, thrfor. (37 ( t (t Sa( f (, (38 f whr ( s rac dlta functon. W gt from Es. (37 and (38, undr condton r F : A ( F f h ( v jf v dv. (39 It follows from E. (39 n th spcfc cas F : Now lt s analyz th varanc of A ( F. W can gt aftr buly transforms: A ( F H ( f H ( f F df H ( f H ( f F f f A ( h ( v dv. ( f H ( f F df H ( f H ( f F H ( f F df f, ( - 5 -

7 Journal of Basc and Appld Physcs c. 3, Vol. Iss. 5, PP. -8 A ( H ( f df f H ( f H ( f f F df H ( f H ( f f F df, ( whr j fv H ( f h ( v dv. It wll b mor convnnt to us n ngnrng applcaton th xprsson for uppr bound of varanc: B ( d f f h 3 3 A ( F A ( H ( f df, (3 jf Bh ( h (t h (t H ( f df. ( Undr th assumpton of w corrlaton of magntuds A( and A( F, t can b gottn from Es. (3, (39 ( th formulas for xpctaton and varanc of modulaton coffcnt stmator: m h ( t jf t dt h ( t dt. (5 [ m ( F ]. (6 f It follows from E. (6 that stmator of modulaton coffcnt s consstnt. Whn comparng Es. (3 and (6, w can s that uppr bound of varanc for rvrbraton cas s much mor than for nos cas on. It s ncssary to ma addtonal rsarch n futur for gttng mor prcs rsult. hr s obvous smlarty btwn E. (5 and nown Schrodr formula [9]. IV. COMPUAIONAL MOELLING RESULS In ordr to rduc duraton of computatonal modllng, t s xpdnt to us band-pass procsss nstad of procss ( t, whr ar rsults of fltrng of ( t by mans of octav fltr ban. So, w had usd xprsson nstad of E. ( for numrcal modllng. x( t ( t f( t (7 Multplyng x ( t by spcally chosn coffcnts a, w provd a smlarty of long-trm spctra of tst and spch sgnals. Componnts n ( t of nos n ( t ar gnratd smlarly, wth an only dffrnc that coffcnts b ar usd n plac of coffcnts a. It allows gnratng of rurd colord nos. Anothr fatur of schmatc rprsntaton of nos gnraton s absnc of modulaton blocs, whr multplyng on f ( t s mad. Modulaton coffcnts stmaton s mplmntd n accordanc wth Es. (3 (, and ffctv sgnal-to-nos rato stmaton s xcutd n accordanc wth Es. ( (. Artculaton ntllgblty stmaton s fulflld n accordanc wth E. (. h obtand stmaton s rcalculatd n wordy ntllgblty [3]. At frst w shall consdr rsults of modllng of a stuaton, whn rvrbraton dsturbanc s absnt, and th nos dsturbanc acts only. h valuaton rsults of a wordy ntllgblty obtand by a formant-modulaton mthod for varous ntgratd sgnal-to-nos ratos and for varous colord noss ar ndcatd n Fg. 3,a. Smlar dagrams for formant mthod ar shown n Fg. 3,b. As w can s, both mthods lad to practcally dntcal rsults, dspt of ssntal dffrnc of tst sgnals and stmaton mthods. It mans that th dvlopd computr modl of th masurng systm ralzng a formantmodulaton mthod s ffcnt and nsurs drvng corrct outcoms n cas of a prvalng acton of a nos dsturbanc. Now w shall consdr rsults of modllng of stuaton whn rvrbrant dsturbanc s prvalng. agrams of wordy ntllgblty for room wth rvrbraton tm, 6 s ar shown n Fg.,a, and analogous dagrams for room wth 6 rvrbraton tm 6 s ar shown n Fg.,b. As could b watd, ncrasng of rvrbraton tm lads to spch ntllgblty rducng. hs rducton s most notcabl for mddl and small sgnal-to-nos ratos. h rducton of spch - 6 -

8 Journal of Basc and Appld Physcs c. 3, Vol. Iss. 5, PP. -8 ntllgblty s lss notcabl for sgnal-to-nos ratos ovr 5-7 db. It s also ntrstng that th dgr of ntllgblty rducton dpnds on color of nos dsturbanc: thr s mnmum rducton for brown nos and maxmum rducton for wht nos. hat fact may b xpland by mans of som low-fruncy fltrs as y bloc of rvrbraton procss gnraton modl [, 5]. (a Fg. 3 Intllgblty stmators for nos dsturbanc: formant-modulaton(a and formant (b mthods (b (a Fg. Intllgblty stmators: 6, 6 s (a and 6 s (b (b V. ARICULAION ESING RESULS h artculaton tstng was ralzd n two rooms of Natonal chncal Unvrsty of Uran Kyv Polytchnc Insttut : small (8 m 3 laboratory wth rvrbraton tm 6, 6 s and larg (69 m3 lctur hall wth rvrbraton tm 6 s. h artculaton tsts wr conductd n th corrspondnc wth th rcommndatons of GOS [7]. hr spars and thr audtors partcpatd n tstng, and ach spar rad on 5 syllabl tabls (wth 5 syllabls n ach tabl from GOS [8] n ach ssson. wo xprmnts wr ralzd n ach room. A bacground nos was usd as nos dsturbanc n th frst xprmnt. A wht nos, gnratd by computr and mttd by acoustc systm, was addd to a bacground nos n th scond xprmnt. Emttng loudspar was placd btwn spar and audtors, on a dstanc of.5 to m from audtors. Undrctd mcrophon G57 was usd for rcpton of a sgnal and th accptd sgnal was rcordd on th scond computr ds. h faturs of rcordd nos and spch sgnals ar pontd n th abl : P n s ntgratd lvl of a nos dsturbanc; P s s ntgratd lvl of a spch sgnal; SNR P s Pn s ntgratd sgnal-to-nos rato; S s syllabl ntllgblty. h magntuds S appropratd to outcoms of th sparat spars n Exprmnts and 3 (bacground nos, ar rprsntd n Fg. by astrss, and th outcoms of thr avragng ar rprsntd by a small suar. h magntuds S appropratd to outcoms of th sparat spars n Exprmnts and (bacground nos + addd nos, ar rprsntd n Fg. by crcls, and th outcoms of thr avragng ar rprsntd by a small trangl. 6, s ABLE FEAURES OF SIGNALS AN NOISES Nos P n, db P s, db SNR, db.6 bacground bacground +addd bacground bacground +addd S - 7 -

9 Journal of Basc and Appld Physcs c. 3, Vol. Iss. 5, PP. -8 It s obvous that thr s a good nough concordanc of modl and xprmntal rsarch rsults. VI. CONCLUSIONS Effcncy of proposd formant-modulaton mthod s confrmd by analytcal and xprmntal nvstgaton rsults of th papr. Euaton r F, whr r s arbtrary postv ntgr, s a condton of an unbasd ntllgblty stmator for formant-modulaton mthod. Formant-modulaton stmator s consstnt,.g. ts varanc tnds to zro whn stmaton tm tnds to nfnty. Analytcal rsarchs and computr modllng show that formant-modulaton stmator s wors compard to formant mthod for cas of prvalng nflunc of nos: rlatv rror of formant mthod word ntllgblty stmator s about.5-. of th formant-modulaton mthod rror and formant mthod stmaton tm s about of formant-modulaton mthod stmaton tm. Analytcal rsarchs show that uppr bound of varanc for rvrbraton cas s much mor than on for nos cas. hs rsult s prlmnary and t s ncssary to ma addtonal rsarch n futur for gttng mor prcs rsult. ACKNOWLEGMEN h author s thanful for th studnts group of Acoustcs and Acoustolctroncs partmnt, Natonal chncal Unvrsty of Uran (Kyv Polytchnc Insttut, spcally Mr. V. Klmov for partcpaton n computr modllng and also thanful for L. ronzhvsaa and. Shagtova for partcpaton n artculaton tstng xprmnt. REFERENCES [] A. Produs, On Som Evoluton Faturs of Objctv Mthods of Spch Intllgblty Masurmnts, Elctroncs and Communcaton, thmatc ssu "Elctroncs and Nanotchnology," vol., pp. 7-3,. [] A. Produs, On Possblty of Advantags Jon of Formant and Modulaton Mthods of Spch Intllgblty Evaluaton, n Procdngs of th VI Intrnatonal Confrnc MEMSECH, Lvv, Polyana, pp. 5-59,. [3] N.B. Porovsy, Calculaton and Masurmnt of Spch Intllgblty. Moscow, USSR: Svazzdat, 96. [] H.J.M. Stnn and. Houtgast, Bascs of th SI-masurng mthod [Onln]. Avalabl: [5] H.J.M. Stnn and. Houtgast, RASI: A ool for Evaluatng Audtora [Onln]. Avalabl: [6] A.N. Produs, V.S. dovsy and M.V. dovsaa, Acoustc Examnaton of Spch Communcatons Channls. Kyv, Uran: Imx-L, 8. [7] GOS Audtorums. Mthods of dtrmnaton of spch ntllgblty. Мoscow, USSR: Izdatlstvo standartov, 983. [8] GOS Spch ransmsson on Communcaton Channls. Mthods of Evaluaton of Qualty, Intllgblty and Cognzanc. Мoscow, USSR: Izdatlstvo standartov, 996. [9] K. Jacob, Corrlaton of Spch Intllgblty sts n Rvrbrant Rooms wth hr Prdctv Algorthms, J. Audo Eng. Soc., vol. 37, ss., pp. -3, c [] A. Produs, L. ronzhvsaa, V. Klmov and. Shagtova. Formant and Formant-Modulaton Mthods of Spch Intllgblty Assssmnt. Part. Assssmnt Exactnss and Spd, Elctroncs and Communcatons, vol. 6, ss. 6, pp. 6-,. Arady N. Produs s profssor at th Acoustcs and Acoustolctroncs partmnt, Natonal chncal Unvrsty of Uran Kyv Polytchnc Insttut (NUU KPI. H rcvd an Engnrng ploma from th NUU KPI, Kyv, Uran, Ph from th Stat Scntfc Rsarch Insttut of Hydrodvcs, Kyv, and a Sc from th NUU KPI, Kyv. H s th frst author of th boo Exprt Systms n Mdcn publshd n 998. H s also th frst author of th boo Acoustc Examnaton of Spch Communcatons Channls publshd n 8 and th frst author of th boo Computr Procssng of Acoustc Sgnals publshd n. H has publshd numrous scntfc paprs and patnts