by Ton Wempe AN EXPERIMENTAL SEGMENT SPECTROGRAPH BASED ON SOME NOTES ON FREOUENCY ANALYSIS OF SPEECH SEGMENTS ='===============:=: SI]MMARY

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1 r PROCEET}F{GS F R O M T H 8 N S T l U T E O F P T T O N E T C S C E N C E S O F T T E U N V E R S T Y O T A M S S g R D A M A U $ T E R D A M :

2 AN EXPERMENTAL SEGMENT SPECTROGRAPH BASED ON SOME NOTES ON FREOUENCY ANALYSS OF SPEECH SEGMENTS ='===============:=: by Tn Wempe S]MMARY Crnrnnly used dsplays f sgnat segment spect.ra lke '1ne spectrar mstly ffer pr readablty f varus speech sgnal parameeers. Sme deas fr btanng spectra wth greatly mprved readablty are descrbed. Experments usng hardr^rare were carred ut fr mplementatn f these methds. Fr estmatn f naccuracy n practce, artfcal fspeech sgnals' wth knwn parameters were used. Sme f ther spectra are shr^m as examples. Addtnalllr, spectra f sme natural speech segments are dsplayed whch resulted frm the methds as descrbed. The cnstructn f a segment spectrgraph based n ne f the methds was fnshed n 1976 and has been n regular use snce.. NTRODUCTON n general, the analvss f segments f speech sund s nt fundamentallv dfferent frm a descrptn us ng a set f unversal

3 - 45'- parameters. Hwever, parameters sutable fr the nvestgatn f certan segments f speech (whch s nn-statnary) maybe unsutable fr ther segments, dependng n the lcatn and duratn f the selected segment. Besdes, the chce f parameters depends n the am f the analyss. A partcular set f parameters may result n an analyss whch culd be cmpletely satsfyng fr a mathematcan but nt necessarly fr a physcst. T meet the acustc phnetcan's requrements fr an analyss we have t answer the questn: what d we want L measure? Or n ther wrds: when selectng a speech segment, what are \^/e lkng fr? When speakng f frequency analyss we naturally cncentrate n the mre statnary speech sectns n rder t gve the term tfrequencyr sme physcal relevance. S we are partcularly cncerned wth the vced segments. The determnatn f frmant frequences n the descrptn f ths class f speech sund stll plays an mprtant part. Defnng frmants as the maxma n the system functn f the vcal tract cnfrnts us at nce wth the prblem f extractng frmants frm the speech sgnal. n the speech prductn mdel the exctatn surce (g1tta1 pulse) drves the lnear flter system cnsstng f the vcal tract flter and the radatn flter. The frmants as defned abve, are system parameters, whereas, frm the utput, nly sgnal parameters can be extracted. Ths wuld nt be a prblem f the exctatn surce culd be cnsdered t delver a sutable test sgnal r, at east,3 sgnal wth knvrn parameters. The fact that ths s nt the case s the man reasn fr the dffcultes n frmant extractng. Frm a sgnal analyss pnt f vew the prblem desnft exst: f a frmant s undetectable wng t the prpertes f the ex-

4 -46- ctatn surce, the sgnal present cntans nsuffcent nfrmatn fr ext.ractng that frmant. Therefre we cntend urselves wth frequency dstrbutn dagrams whch are vald fr the selected speech segments. Lke many thers, we wll call the peaks f these dagrams rfrmantst fr the sake f cnvenence... Althugh theretcally frequency analyss s applcable t any length f the sgnal segment, t s mstly shrt segments we are dealng wth n rder t be able t make a mre detaled analyss by means f many cntguus shrt tme frequency spectra alng the tme axs rather than a lng tme average spectrum f a large sgnal prtn. A rapdly varyng frmant culd change wth a velcty f 30 Hz/msec (accrdng t an example frm Markel, 1972), whch means that the frequency shft between tw sequental perds f the fundamental frequency f a male vce culd be abut 300 Hzl n ur effrl n makng the analyss mre detaled, we wuld lke l shrten the segments t be analysed. Hwever, f we cntnue t shrten the sgnal tme ntervals, the term tfrequencyt becmes gradually mre meanngless. Accrdng t the uncertanty prncple the naccurac.y f the determnatn f a frequency cmpnent s abut 1 /t tl, where T" represents " the length f the segment analysed. n cases f rather steady parts f vwel sunds, t seems therefre advsable t take segments f lnger duratn n rder t be able t measure frequency peaks wth greater accuracy. Because f the perdcty f the sgnal wthn the steady segment, we rnght just as well stre ne F'-perd n a sgnal memry, whch s afterwards scanned repetvely s that a cntnuus perdc sgnal arses f any desred duratn. The frequency dman representatns f perdc sgnals hwever, are tlne spectrat wth cnstant lne dstances equal t FO Hz.

5 -47- A spectrum f ths knd s t be cnsdered as a sampled versn f a cntnuus spectrum f ne F'-perd. t wll be clear that as far as the accuracy f frmant extractng ges, there s n pnt. n takng segments f lnger duratn than ne F'-perd. The frequency cmpnents n the frequency dman representatn f sgnals are f nf nte duratn rnrhereas the sgnal segments are defntelv nt s. f we thnk f a sgnal segment as beng the result f a multplcatn f a cntnuus tme functn wth a rectangular 'wndwt functn f unt ampltude and f the same duratn as the sgnal segment, the spectrum f the segment s fund by cnvlvng the ndvdual spectra f the multpled functns. The spectrum f a rectangular twndw' functn s a (snnft'/nft') functn and has zer cmpnents at multples f /TO. The result after the cnvlutn s a spectrum wth addtnal maxma and mnma ('1bes'). Because the readablty f frmants can be pr wng t the ccurrence f these t lbes t, a number f dfferent twndws t have been appled (Gauss, Hannng, Hanrnng) n rder t elmnate these 'lbes' r reduce ther ampltudes. n addtn varus (cmputerzed) smthng technques have been develped t smthe ths'f^-rpple'r t cnvert the fspectral u " FFT-prgram nt a cntnuus graph. lne'utput f the Frm a physcal pnt f vew we shuld prefer erhaps the use f tme-lmted snusdal cmpnents, each wth a length equal t the speech segment, rather than cntnuus nes. Apart frm the ac,curacv f frequency determnatn, the dfferent lengths f the segments then have n further cnsequences as regards the shape f ther spectra. Anyway, ur am was t try t develp relatvely whch shuld: smple hardware l. apprxmate the ampltude spectrum f ne F.-perd wth p-

6 tmum readablty f the frmants and wth knwn naccuracy. nfrmatn abut the frmant ampltudes and bandwdths are thus ncluded; handle segments f varus lengths (.e. dfferent F^perds) be easy t perate. at ptmum reslutn; 2. FRST APPROXMATON The nsertn f tme (T") nt each perd (TO) f the fundamental frequency f a perdc vwel sund was the frst dea n apprxmatng the cntnuus spectrum. The effect f ths s that the dstances between the spectral lnes s decreased because the mdfed fundamental (tot) equals l/(t^+t^). The mre T- s ncreased, the better the cntnuus u a a spectrum apprxmatn becmes. T get sme nsght n the shape f the cntnuus spectrum f ne F^-perd f a vwel sund, we defne a smplfed speech segment U ' as a damped snusd, whch s started at t=0 and truncated at t=t^: U -Af (l) g(t)=e snllt 0 < t < T Usng Euler s relatn g(t) changes t: c(r)= +[. (cr-jr) t -(cr+jurr) rl J 0 < r < T ts Furer transfrm s: +v" (-cr,+j1-j) t G(trl) = dt,1. ; (--jurr-j) t - l e J.f

7 - l, - Evaluatng leads, (2) c(ur)= 7Jl L t: -[+5(ur1)J r -[+j (+r)] T 1-e l-e +j (-urr) 61+ j (+1) Ths can be wrtten as the subtractn f tw functns; (3) c(trl) =ce (ur) - c*(), where: G" () =,T [ r - r - l L*j (r-rr ) + j (ur+1) J c*() = g - (+ rrl) T - 2j jrr l e l_+j (ur-r ) _jrr _ e l 6x+j (ur+1),l 0r, n trgnmetrc frm: (4) c t'r,r\= - \'g \uj,/ ()1 (5) G (trl) = e m' - t'cr+ r,r\ T (cl+j) sn trlrt+trtr cs trtrt (cr+ jtl) 2+ur! The latter functn becmes zer f Tn tends t nfnty, s that G^ (t) represents e ^ the Furer transfrm f an untruncated damped s nusd. Frm the superpstn prperty f the Furer transfrm t fllws that: g(t)=ge(t) - Cm(t) whch causes S -m (t) t be: 8*(t) =e (See fg. 1) -nf s nl t T < t <

8 -50- ge(r) g(t)=e"(t)-sr(t) Fg.1

9 - 5l The functn f g"(t) wth gn(t) can be thught f as a tme-shfted versn -ClT *-" an ntal ampltude f e and a phase-shfted rgn. The ampltude spectrum f G"(trl) s determned by: (6) lc^ E (ur) l= (r)t V('*r?- u2)2+4u2u2 Ths functn expses maxlma at (7) (l)=u) = + m u?-a2 (B) The magntudes f these maxma are 1/2a. T derve the 3 db bandwdth f the peaks we slve the Jl _ l *l-- 2a\12 whch delvers: n ul?-cl2+2urr '"1 As lng as 2q,2<<L - Z*r, we may wrte: n 6f +6x2+2rrl = + (r +) = +(trrr-)

10 whch means that ujh-uj= 2A (9) r: B= 9 Hz The naccuracy f the apprxmatn n cases f practcal values f trtr and, s rather sma1l: fr example n the unfavurable case f fl=300 Hz and c=00 n, the devatn amunts t less than 32. The shape f lc.() s utlned n fg. 2. The shape f the functn C*() depends n the phase anqle LrT^. - U f rto = nn(where n s an nteger): ( t0) lc,n, {) l=. -CT "; c" t,) and n ths case lcr(ul) s srnply an attenuated versn f lc.tl l. tf 0rTO = n(n+!): (u) lc,r(ur)l = qf lc"', () lc*r() nly equals lcr, (ur).r 2 - l.2, vz at the maxma f lc*, (ur). Fr values f where u)2>>a.2 the l c*, () ncreases lnearly wth 6 db/ ctave. specrrum c'., (r) cmpared t mlncreasng uj, accrdng t Maxma ccur at (1 2) max r: u2 max (u?+za2)2 - d 2 Fr practca 1 values f tr and 0, we may neglect the term 4clq n

11 -53- respecr f (u?+2a2)2 s that '.,2 w max tl?+cl2 and (13) max!+2 The heght f the max j-ma rs:,^.., -, f Gm2 (tr') l*"*= \ / ^ V zutr t!r'r*a'-r, J Agan we may wrrte: c*, {,^,) lfu" 2@?+2a"2)-zu 4a2 ( 14) Hence: c*, {r) l,n"* = - 2a Whch s equal t the maxma f lc"(ur) l. The 3 db bandwdth can be fund by slvng the equat ln: a"'*tj' (cl2*?-t.r2 )2+4a2u2 4trr 6l+4a2 -ujl whch delvers: 'lr= zp'-'?-'* f +3p 4-4u-rf p 2 ^1= 2P'-'?-a2- t lf+:p4-4'?1 2 ( 5) where ul+4a2

12 -54- Let be fr= *+y and ull= x-y, then: -, 'r 0"-0,=\/**y -\/"-y N V ' V (u1-trr) z= zx-\ r *2-y2 s that (0trl.-ul,.*h *1,)2= 'Y 4l 2-2u?-26y2-2\ -w - v t -t Substtutng f (15) and sme mnr manpulatns yeld: (t \r-01 )'= +r,\f',*?- zu?-zaz Fr practcal values f tl.lr and 0, apples: 4a2ul( -\f*4$ << (ur?*a') ' Ths al1ws the smlfcatn: (rn-t )'= +r r! r', *F - 4w2r- 4a2 Agan we wrte: (t1-r)'= $l*fu', ** 4a4-4wl-4a2 and neglecr -4,4: (rrln-rrlr)2= +fu*zu2)-qu?-+a2= 4u2 (16) Hence, 0h-01= 2a r B = 9Hz S, n practce the bandwdth f the peak s case f lc^crll. (See fg. 3 fr urlnes f ' g ' ' Other values f the phase angle trlrt' result smewhere between these extreme curves. the same as lc,n, () and n ampltude n the c*, () spectra lr.

13 -55 ta-- Fle.2 rt6.3 -.//4: _. -tr- -'-'-' l6mr(ar)l / a,",t ]'-'.- \ lc(ar)l = t le c(c.r) -G F6. q tt\. t' t'-l' lc(r^r)l- t lg3() -6r0. F. s \ ----

14 T fnd the arnpltude spectrum f g(t), each frequency cmpnent f Gr(trl) has t be subtracted frm the crrespndng cmpnent f C"() whle accuntng fr the relatve phase shfts. Accrdng t the tme shft prperty f the Furer transfrm a tme shft f TO secnds crrespnds t a phase shft f -TO radans (hence the fact. "-jt n equatn 5). Thus when subtractng Gr(ul) frm G"(), rnaxmum devatns frm lc"(ur)l ccur when crrespndng cmpnents have equal r ppste phase. Ths accunts fr the tf.-rpplet n the spectrum f g(t). (See fgs 4 and 5). The rperdr f ths rpple s 2r/tO rad/sec. The lwer the factr e-t, the lwer the rrpple ampltudet. The methd used here may appear rather unsphstcated, but t has prbably the advantage that t ffers a detaled nsght vsually. T test ths tme nsertn n practce and experence the effect f the'f^-rpplet n the readablty f frmants, a smple artu -- fcal vwel generatr was made whch prduced tw damped snusdal vltages as frmants and was ftted wth adjustable TO and T-. The resnance frequences as well as the bandwdths were made a presettable. The utput \^/as cnnected wth a swept sgnal narrw band spectrum analyzer (General Rad wave analyzer Lype 1900A). Bref descrptn f the artfcal vwel generatr (see fg. 6). A pulse generatr s made by means f tw cupled mnstable mu1- tvbratrs OS and OS2, each ne trggered at the end f ts ppnent's cycle. Cncdng wth the begnnng f the T'-cycle a very shrt pulse s generated by OS3 (T6= l25psec). Ths pulse exctes tw resnance crcuts smultaneusly, GC and GC2, whch start prducng ther damped snusds. The resnance crcuts each cnssts f a gyratr, ts tw gates cnnected wth capactrs. These crcuts are equvalent t an LCR-crcut. A gyratr used as a resnance crcut has the advantages f beng stable, beng easy

15 F\ (5 u-

16 t cnstruct and has ts resnance energy cntaned n nly tw capactrs. (See chapter 4 fr a descrptn f the gyratr prncple). At the end f a T.-cycle, a T.-cycle s started durng whch the capactrs f the gyratr devces are shrt-crcuted, causng the utputs f these devces t becme zer. The result s a wave-frm srner,hat lke f g. 7. The effect f the exctatn pulse n the purty f the damped snusds s neglgble: the ampltude spectrum f ths pulse beng prprtnal wth sn lt6/t6 has ts frst zer at ul= 2nlr6 r at f= l/t6= 106/125 Hz = 8000 Hz: s that n the vcnty f the frmant frequences the rsurce spectrumr s almst f1at. The crrespndng spectra f sme f the varus sgnals wth dfferent parameters we measured n ths way are shr^m n the fgs 8 thrughl4. The utputs were prduced by a chart recrder (General Rad type l52lbql) whch s mechancally cupled wth the narrw band sdectrum anat.vzer alreadv mentned. The tme-nsertn prcess causes the average vltage f a sgnal t decrease wth a factr equal t T6/T0. n rder t acheve cnvenent dsplays, the utput vltage f the spectrum analyzer was ncreased accrdngly n cases f sgnals wth tme-nsertn. Naturally, the sgnal t nse rat f the measurng system decreases wth the same amunt; n practce the S/N rat f selectve measurements hwever, s very hgh (here B0 db) cmpared t the S/N rat f taped sgnals. f ne bears n mnd that durng the tme T the nse level at the nput f the sdectrum analyzer d can be kept very lw, eventual- cmpnents due t nse n the spectrum can be cnsdered as beng entrely caused by the rgnal sgnal tself. Frm the fgs 8 thrugh 14 the cnclusn can be drawn that the tme-nsertn prcess s a valuable methd fr accurate measurng f frmants frm sgnal segments wth relatvely 1w fnal ampltudes (.e. F^-perds f male vwels). Fr ths last class f sgnals the U ' frms 7 and 9 are qute applcable.

17 U z u z!l g td E u. N rn ll e\ N F\ tl N ts N tl \./. g (d d.rl r+t s \ a{,t Af tl +J q) h r E e l!! n tj l-< 4 l f;h; r Nr HsNdSSu t! HHh '; u t tr HeR '-g g: H;l - ( -\ - Ī \5 (.n

18 -60- u v z u2 ld f r? L tr E N N l +J tr OJ aa OJ.Fl +J d..p 'r{ F t\, (1 ll b0 (H lr q-.1 Fl (d - rl 5.:s (t s, qj aa rj q-l tf.lj a 0) (0 r F O T J O F t! J O z 80 Nr 3SNOdSSU uj lrj l c z H =" (! F \ O tr Zl - l < ] J. t r f t ), L,. l u.t u J (! - 6 = F a - =utr rll :.J O : l uj :-4 t :1.tr t z-l t l l ;l l T ; : : l l :.'t', -:-- t,.-j-..,. -.-.'_')^

19 -61 C) Y = z uj f l! cr l! N ts tn ll N N -r tl N F c\ tl H E r--{ b0 t+{! +J q) (t) b0 80 Nr SSNOdSSU r t r F t u = J O z tr ('! r tr ul G u.l ; - u, G F O E.J ( r O z = = UJ u l ( L F 0) rt z E =tr l U ft J a z

20 Y = z lrj f uj (r l! N \ \ tl - d. rj t'r 0) 'r"{ c).rl p {J F q-.1 tr q-1 r--f (d - b0.rl 0) {J r+-{ tr lj a c) b0 'rl go N 3SNOdSSU E F O ttl! ;! J O z tu ul k ( E F c E u r - (r() = -r' =)l:, - t 1,-'. z - :, l\ : ' tr lul l l6 l uj ll t ' ul t! u)- = F c E * =! (\ tr (')!! f LlJ :{ a =

21 -63- C) Y = z UJ f, ul (r l.l. t.l O rn tl ftl N F \ tl fr{ N c{ l (d F, b0 (') l+l! lj c) U) b0 go Nl :lsnodssu E F O UJ t! J O 4 z E z ul t llj ;l (L = ( E F O E U J z = = uj l.! O. F a f 1 z F tr- = n N n! u l a (t T-t z 1, : 1 {l r ' : t 1_

22 -64- = z u.l l g u.l E. L N ts -$ tl d. +J tr q) 'rl c.) +J d. ]J.Fl F b0 'rl LH tl q{ r-.l (0 d. 0.F{ CJ - +J q-l tr 4J a qj a0 l r t r F O t! ;! J ( f z l,, l l l, l l ' : r l a 5--l*-**. uj l r r l l : l a l ; " l l r, l l, lur '---1 l,, r : l'' : '-', t.t-;,:;.-:-..t O N SSNOdSSH UJ ut F E...1 uj llj a O r._l z ; cc. =! N r"t U J (7) T-t = J - l, 1,...r--*.-..-.^ b0

23 , ANALYZER *-$ BANDWTDTH tr3!10 ---^*---;"* - f *1."'" -*; RECORDER charr speed N,/MN -- c0 = uj a z (L a UJ cc L**.*. *._...: RECORDER WRTNG SPEED --",!1 fl 10.. L t=tzv,- -.; ln/sec -!-.' '..* -.'' - -,M*'4q!'lzlt4.@'.<.!r -,;*, r * B, D D '...: :ns +tr:1 +t! :1 +! RECORDER CHART SPEED N/MN t- m = uj Q) Z l. (.t) : r! : cc. RECORDER ]WRTNG SPEED : *;*_;!1 [t _-.*,tr3!20 - rn/sec. - - Fg. Spectrum f s gnal 5F, F =24OHz, F,=4O0Hz, F,=7 \OHz Fg. la Spectrum f sgnal 5F wth rme-nserrn, FL=l4.4n,

24 ANALYZER --*;-_-t BANDWDTH -^ L_l ru -50 t---*,, : t ;;;;;;;; CHART SPEED N/MN Q).-.-. "...", ,.".-...-, U.,. : J ,^.-...._. -_.*-...- RECORDER 'Wntf tng SPEED n1!t tr3 n20 N/SEC -..;...-'..-.".- -,.,-. m r] = u 6) z {-] (r t r T Tr- T r T.ANALYZER F'*'**; BANDWDTH l 3 n10, t 1, _".*-,. -. RECORDER CHAHT SPEED N/MN = u a z - u) rl tr...***r***---, -..*...*,* RECORDER WRTNG SPEED - L D10 : l]3 a20. N. SEC ) Fg. 2 Spectrumf s gnal 2l'1, F =160H2, F,=540H2, Z =86OHz Fg.12a Spectrum f sgnal 2M wth tme-nserrn, =l4.4hz f,f

25 u3 D10 '. l l,.-,.---. ",..-- -,-l..: RECORDER "**r speed, _: NMN _;--_" r. r : f" " -_ WRTNG SPEED *,---nt lll f 3 _2 rn'sec -,* -""^_*1" m = ul a z - a J (r E, U t- L! l f f t l T 1 T T - f* :.., **-.,.:;**:-**..-,. -.. : RECORDER CHART SPEED *-^:"** N/MN r'e ccfdt***"- *...-*-,",,..--*::*.f*"-. ^* t r t "--.--: :-.-.-;:- RECORDER l c0 z : lfl U). z.: llj j 't WRTNG SPEED tr1!10 Fg. 3 Spectrumf Fg. 3a Spectrum f sgnal 7F, F F,=580H2 =Z4OHz,, Fr=93OHz s gnal 7F w th tme-ns er tn, F t-=1 4.4Hz

26 Y = () z JJ f uj TL N 6l tlc{ Fll N co C.l lt N \t C-'t tl rt, --l cd a'j.f{ ct) (H tr +J q) b0.fl 8C Nt 3SNOdSfU

27 N $ \f tl r t +J tl c) u) d 'rl c.) F -. +J 'r F b0 tt-.{ q-.1 F'l (d d..rl a.) -. ]J q.{ tr ]-J 0) L l $ b0.rj Y = C) z uj : U E. tl 80 Nt SSNOdSSH

28 The F'-rpple f spectra frm sgnal segments wth cnsderable fnal ampltude (fgs loa and l4a) culd ccur t such an extent that the readablty f the frmants rnruld be rather Dr, especally when mre than tw sgnfcant frmants are present. Furthermre, the lmtatns f the methd fr frmant extractng frm lne spectra usng fhe prnc.ple f a weghted average f maxma and ther neghburng cmpnents (Ptter and Stenberg, 1950) are clearly dsplayed partcularly n the fgs l3 and l3a. The hgh-frequency behavur f spectra f the type as shvrn n the fgs la and l2a s caused by the fnal ampltude step present n the crrespndng sgnals. n practce, when gatng a sgnal segment, ampltude steps can easly be avded b1r takng care that the segment starts and ends al zer-crssngs, s that the spectra f fgs lla and l2a are n fact academc nes (and wth them the functn Grr(ur)). 3. SECOND APPROXMATON The cnnnnly used methd fr elmnatng r attenuatng the rnterval rpple' n spectra f tme-lmted sgnals s multplcatn f the nterval wth sme rrndw functnr prr t the transfrmatn nt the frequency dman. Hwever, f ths s appled t the shrt ntervals f the F.-perds, large sgnal prtns f these are greatly attenuated, especallv n the ntal parts, where the sgnals have ther majr ampltudes. Frm chapter 2 we knr,,r that the rrpple ampltudet s prprtnal t the ntal ampltude f the mdfcarn functn g*(t). The bvus way t attenuate the -0Tn " ntal arnpltude (whch equals e rf'-rpple' s decreasng ths tmes the ntal ampltude f g(t)) by multplyng the sgnal wth an expnental func tn: (17) s, (r) = "-"' -n [O<t]

29 - 71 Nw, culd be thught f as the sum f the natural and artfcal dampng: g(t) = e - (crrr+c") TO s].n (r), t t The ampltude f the mdfcatn functn alters t: -(cl ' +a )T n a' Or^,. e lg^(ur) f " culd be gven an ndvdual value fr each segment t be measured, t wuld be pssble t keep the factr -(a ' n+a a )t ' e cnstant fr all dfferent segments. f -(cl - n +a )T a - e = k, then the spectrum ccurs between (l+k) lc.(rrr) and (l-k) lc.() l. e tg"rthmc ampltude scale causes a cnstant rpeak-t-peak rpple value': (r8) ur = 20 g j* uu Chsng k = /20 yelds the rpple t be wthn db. -(d +c[)r t a' " (19) Therefre " =* f fr mst vwels ct' s valued at 250 and fr TO s wrtten l/f', then frrn (19) the rule-f-thumb can be btaned: (20) 6x =3F^-250 U Of curse the accuracy f the dspl-ayed frmant decreases wth ncreasng cl. anc frmula (20) therefre ffers a cmprmse between rpple smthng and acc.uracy f the frequency measurement. Fr a twrse caset example, assume! F^ = 240 ltz, then: Ct = 0 +d = 3F^ = 720 n a u

30 Substtutn f ths nt (7) tgether wth the fl l = 300 Hz as used befre gves: ur---=ff=f42 max 'wrse' value r: f = Hz. max The errr s abul 7.52, whch s lw cmpared t the famlar frmant extrac.tn errrs f ths type f sgnal. Besdes, because the devatn frm f, s knwn, a crrectn s pssble f des red. Of curse the 3 db bandwdth s cnsderably ncreased. n ths example t amunts t abut 230 Hz (B = 9). Tr' ' Evdently, t check ths methd n practce, the same test set-up as descrbed abve s applcable, f the dampng f the snusds s adjusted accrdng t: J cr = 3FO = -.F Sme spectra btaned frm measurements as carred ut n ths manner are dsplayed n the fgs 15, 16 and 17, whereas the spectra f the crrespndng sgnals wth 'nrmalt values fr s. (.e. wthut addtnal dampng) are depcted n the fgs 1/s, l3a and l4a. As a result f applyng ths fexpnental wndw', the readablty f the ffrmantst s mprved cnsderably. Usng the cnvlutn therem t can be stated that multplcatn f the tme functns results n the cnvlutn f ther ndvdual spectra. Thugh ths s nt exactly Lrue fr ampltude spectra, the errr culd be sgnfcant nly n the vcnty f zer frequency (Randa11, 1977), The prcess f a measurng flter scannng the entre frequency range can be cnsdered as the practcal analgy f the prcess f cnvlvng the nput spectrum wth the measurng flter characterstc. Then f the flter pass band curve culd be made equal t the spectrum f the expnental wndw, ths methd wuld gve results very smlar t the expnental wndw methd.

31 '"*- BANDWDTH n3 [10 Lr 50 t- RECORDER CHART SPEED N/MN.."_".,* '*_-t = ul U> v 0- ) ul tr RECORDER WRTNG SPEED _-,r, n3 ttt /ctr^ --t l 10!20.A\AL T 4trN *.*.**; BANDWDTH tr3 n10 Tl 50 : : : "-.t "..,.-" RECORDEH CHART SPEED lnrmln.----.'- ; ,.-. c0 = ul a 7- (-') uj (r RECORDER WRTNG SPEED tl r -l 10!3 Llz N,'SEC : : Fg. 5 Fg. 6 Spectrum f the sgnal frm fg. 12 (sgnal 2M) r^rth tmemultplcatn, cr"= 200 nsertn and exnental wndw Spectrum f the sgnal frrn fg. l3 (sgnal 7F) wth tmernultplcatn, cx,"= nsertn and expnental wndw )50

32 ! ( ) 0 J ^ Y q O (( - d z. l J \ v.rt z B a JJ - d d F l llj t d r.r- cd.'r h n ^ v ( / ) { J r l t \ t F. B.d "(, q { t 'r d E ^ H r'-r q.r (d "l r--r P A / tr) t a Q ' X AJ CJ d. d. (f.t $ ^ d. F -. d q lr.,j +J tf c ) 0 J ( n ^ 4 (.1) ' Fl : b0.rl rr, t-

33 t " The ampltude spectrum f the functn e to < tl s equal t: A smple secnd rder resnance crcut wth a bandr,qdth f matches ths functn apart frm the asynnnetry when pltted C -nz 1T na lnear frequency scale. Althugh ths methd seems qute realsable, we thught t easer at the tme t apply the expnental wndw methd snce n that case we culd use the narrw band spectrum analyzer agan whereas we therwse had t cnstruct a spectrum analyzer wth a cntnuus adjustable bandwdth. The tme nsertn prcess and the expnental wndw methd were als appled t natural vwel sgnals. Fr ths purpse the fllwng measurng set-up was made (see fg.l8 ): Frm the vwel sgnal t be measured ne perd f the fundamental frequency was slated wth the ad f the tprecsn Gatet 1976) and stred n a dgtal sgnal memry (1000 x B bt). The memry length was made 20 msec whch s suffcent t stre any F^-perd f vwel sgnals. Thus after the sgnal perd zeres U ' were stred. (Wempe, The cntents f Ehe memry were repettvely scanned at the same rate as durng the recrdng, cntrlled by an external tmng crcu t. The bnary equvalents f the sequental samples were cnverted nt ther rgnal values by a multplyng dgtal-t-analg cnvertr. The DACrs reference nput was cntrlled by a devce whch -cr t prduced the functn e ts,a was made adjustable. The tmng -cl^ t 4 crcut caused the functn e t start frm ts rgn (t = 0) at the begnnng f each memry scannng cycle. Besdes, ths crcut als actvated an analg swtch n such a way that the analg utput f the DAC was cnnected t the spectrum analyzer nly durng ne ut f three scannng cycles, whch caused an addtnal tme nsertn.

34 Ea Ft{ F r.j r lr> r/l< t- E e < ; 5S s 5 ar.u L U Lttr '.5L z - E g F \ J '9r OU J F z 3 <vl lj U r./'t! j U A Z < lrj!!(j - r ) ;. 9 E A E l! e LJ JJ g U F Fe. 8

35 " r t ' t ' t +F- -r +rr+ _. FREQUEN 0 l : u J FREQUEN Fg. 9 Fg. 9a Spectrum f male y] wth tme-nsertn, F=95H2, Spectrum f the same vwel wth tme-nsertn and wndr^r multplcatn, ^= 50 Ft =14.4H2 expnental

36 Y = UJ f n [l E l! N l N O c.l tl -, +J tl q) a4,.fl q) 'rl.u -. P qj r-4 (d (+-l tl.lj c\l.fl Fr : j t '".^'** ' T E. F O t! N ; L J O 4 z ; z < < c [r f] : _ -_j -_j_- BO Nt 3SNOdSfH : ^ ; l ',. : u l : : U t,! t t r J : n - - N, ' tf tlj.^.) v / t - a - s t^_-.--.,..*--:.* -",..- uj! u ul - a. ; a cc z : _ - = r : u l = 'ul F _ r!.(r Btr

37 d..f{.u tr q) a d..r{ U J J d a c{.r. + J b 0 ( 0 'F O tf-l. rl r--r l r r J q-.1 tl. cd..1 E F QJ r+ +J 'rl.lj q-{ tr d. t r X lj c) 0J. c\ 0 tr{ f r L a N ; t l z < _ : < (D L_.1 Lt ' l : t l ec Nr SsNdsSH u l, H :!! :!*"*"...-. ' -. v) r > : ; t l t z ; u. - r (r O.! n : t l l l ^ - N cc 6,, : -* -.* tu l- J Ur.; ' 1. r t z u) : - 7 r ( J - ( 9 - cc =L :

38 -80- Y 4 z LU f lr.l E L N ll N -\ c! tl a..1 t{ qj d. 'rl c).rl.lj -.lj.fl GJ r-"r CS qj q-.1 q-l t lr ]J a.) 6l b0.fl Er r{r SsNdstu -**1 ( F O llj N = -l > 5 ' J O z, l,-' :!: tll e ul ; -, 4 6 *!. 4. l J. h ; F. '() ( l(r z.l"*'*--1*' : l, t. l 1 ; u J l t t : l ^ - N : c c O ul!! l!.-- ';E O u), t Z \t ; 2. O = - c D - '; =utr l

39 - 8l -f jj_ Y = z uj f E u- -,.r{ +J tr qj U) d. q) O! s J (.d c! B < J N t r.rt. -{.lj l O, q-.{ 'rl.lj r A J B r--r O CJ q-r CJ.ll ttl 'rt F Fr 'Fl 'lj tr d.! X lj qj aj.d c,)(s (0 c{ : r" 1 l EO N SSNOdSU tll l* ur '- 1 r n Z ; ;(r F \ l O E z r.! l r n r u ) u.t O - - ' r ( ' ' - t u! ) E z ' v F cr =tr, J j, ' : N : u r.r.l "-.,j a, l. l \! z l t c ' - l f r l..-:,,"..^.:.":.

40 (The resultng fundamental perd T' was slghtly mre than three scannng cycles wng t a tme delay between cnsecutve scannng cycles. The fnal Ff therefre was equal t 14.7 Hz). The effect f the adjustable factr Oa n the tme functn f the speech nterval was made vsble n an scllscpe. Cancellng f the multplcatn functn was pssble wth the swtch S. Frm the sgnals v/e measured n ths manner a few are dsplayed n the fgs 19 thrugh 2l. The fgs 19,20 and 2l were made wthut the use f the expnental wndw, whereas the effect f the expnental wndw s shr,an n the f gs l9a,2oa and2la respectvely. 4. THRD APPROXMATON The cnsderable amunt f tme necessary fr plttng a cmplete spectrum and the ptmum adjustment f cx," smetmes beng dff cult were the majr dsadvantages f the prevus methd. Althugh bth prblems can be practcally elmnated by respectvely adaptng hgh speed analyss and determntb " autmatcally frm the length f the segment, at ths stage an exper.ment f a dfferent methd fr frequency analyss r,cas started. The fllwng rnay explan the prncple f ths methd. Cnsder the practcal case f a measurng flter respndng t a tme-lmted sgnal prtn. Frm a tme dman pnt f vew the j-nfluence f the sgnal length n the respnse f the flter nly starts after the mment the sgnal segment ceases. n fact the sudden change at the end f the segment cntrbutes t the flter respnse nly frm that mment n. The'frmant maskngt sde lbes n the cntnuus spectrum (r n ts practcal apprxmatn) are therefre slely caused by ths sudden change at the segment end. Nw the dea was t mdfy the tme nsertng methd frm chapter 2 'enablng' by the measurng flter nly durng the ccurrence f the sgnal segment wthn each perd f the flter nput sgnal. 'Dsablng'f the flter was ntended t be acheved by wthdrawng the energy frm t s that

41 -83- the flter respnse shuld start frm zer at the begnn.ng f each sgnal perd. Usng narrw band flterng mples that n ths way the flter utput vltage s kept cnsderably belw ts steady state value. The spectral nfrmatn hwever, can be extracted frm the varus peak vltages f the flter utput at dfferent center frequences. Real zatn. Fr the practcal mplementatn f ths dea the cnstructn f a specal purpse spectrum aaalyzer was necessary wng t the unusual requrements. The measurng prcedure culd be rughly descrbed as fllws: Frm a sgnal, an nterval wth 20 msec length s recrded nt the sgnal memry n such a way that the fundamental perd r ther segment t be analysed frms part f the memry cntents. Durng repettve replay f the memry cntents, the wanted segment can be selected by means f cntrls whch cause the passng f the sgnal va an electrnc swtch nly durng the ccurrence f the segment nvlved. (en scllscpe serves as a mntr necessary fr adjustment f the cntrls). The sgnal passng thrugh the electrnc swtch s fed t the nput f the measurng flter f the analyzer. After each replay cycle f the memry, the central frequency f the measurng flter s ncreased ne step. The cntrl vltage fr the electrnc swtch serves als as a cntrl sgnal fr the'enablng'and the fdsablng' f the measurng flter. (lsablng ccurs by shrtcrcutng the vltages f the flter va electrnc swtches). tmemry cmpnents wthn the The flter utput s cnnected t a full-wave peak rectfer whch s reset befre each new replay cycle s started. The utput vltage frm the peak rectfer s fed t a strp chart recrder thrugh a lgarthmc cnvertr. After a number f replay cycles f the memry, the flter has swept ver the frequency range f nterest and the plttng s cmpleted.

42 -84- Bandwdth. n rder t attan an utput vltage f sme mprtance frm the nterrupted flter, ts respnse tme shuld nt be t lng cmpared wth the segment duratn (T),.e. narrw band analyss cannt be appled. Hwever, ths desntt mply a lss f reslutn: the hghest pssble reslutn s lmted by the nherent 'pu1se bandwdth' f 1/THz. Obvusly durng ne spectrum plttng a cnstant bandwdth s requred. Althugh the chce f the bandwdth sn't crtcal here, t shuld preferably be made prprtnal t /T n rder t avd the spectral ampltudes beng dependent n the segment length. As the bandr^rdth s cnstant, a lnear frequency scale s justfed. (The pssble reasns fr applyng a lgarthmc frequency sweep are cmpletely gne when analysng shrt sgnal segments). Tunng culd be dne by scannng the memry cntents at dfferent speeds and leavng the flter unaltered. Althugh ths culd be realzed very easly and cancels the prblem f makng a tunable flter, t mples a measurement wth a resultng cnstant percentage bandwdth nstead f a cnstanl bandwdth. The prblem f stepwse crrectng the bandwdth beng cmparable wth the prblem f rnakng a tunable flter, we decded t slve the latter, partcularly n accunt f the taylr-made prpertes f the gyratr band pass prncple. Ths may be explaned by the fllwng descrptn f the gyratr band pass flter prncple: A gyratr (Tellegen, l94b) bascally cnssts f tw mutually cupled 'transcnductance amplfers' (see fg, 22 ). The utput current f an deal amplfer f ths srt s prprtnal t the nput vltage, whereas the nput mpedance s nfnte. One f the amplfers s an nvertng type whch thus causes a negatve feedback. Each amplfer utput frms a termnal (gate) wth regard t the cnrnn cnnectn. Let bth amplfers have equal transcnductances (g). f ne gate s laded wth an mpedance 2,, the effected mpedance (Za)

43 Fg. 22 q l V2 Fg. 23

44 _ 8 6 _ at the ther gate can be cmputated as fllws: A current flwng thrugh the effected mpedance Za causes a vltage v ccurrng acrss t: Z, = v/. The upper amplfer utputs a current, = g.v, whch s flwng entrely thrugh 2,. Hence v, = g.v.zl. The lwer amplfer utputs a current ^=-g.v, =-g2.v.2,. z - l - l As the amplfer nput current s zer t can be stated that 2=-.Hence: - g'.v.z, = - and as Z. = v/l: " l E t (21\ \-./ Z "t = l/p'7., ul f fr Z, a sngle capactance (C) s used, (21) changes t: C / = 1lt\ - t Jw g ' whch behaves lke a self-nductance: a (22) = -"- g2 t wll be clear that a smple resnant crcut can be made by cnnectng the left gate wth a capactance as well. ts resnance frequency results frm: (23),.=G=fl$=t assumng that the tw capactances have equal values. Ths resnance frequency can easly be adjusted by varyng g, whch culd be accmplshed by means f a varable attenuatr at each amplfer nput. n ths way, lnear tunng s very smple t realze. f Zl cnssts f a capactance and a resstance (R) n parallel, Z, changes t: 2 _ R t - Fl,r,cR

45 , 6rr.l! L- = - = -. grzr + trlcr grr Nw Z* can be cnsdered as cnsstng f tw cmpnents t cnnected n seres, namely: a resstance r = + and a g,r self-nductance accrdng t (22). The applcatn f ths means that the flter bandwdth can be determned by ratng the resstrs cnnected acrss the capactances. A schematc set-up f ths s shwn n fg. 23. The fllwng equatns are vald:, = 8'v, 2= E(v. - vr) v, = r'z, v, = fz, Sme substtutns result nt: v g'22 (24) 2= t t+g2zl and v g z 1= t t+g2zl ^7nere,l = R ;JA,CR. 2 1 Wrtng,, = E and, fr 15 changes ths t: (25) Zr = c1;1;; Substtutng (25) nt (24) yelds:

46 uj2 r 62+ (a+j) 2 r, slghtly mdfed: (26) v 2 = g v. C (cl+j) 2 n a smlar wav can be fund: (27) v l = g V, C ]-.+ju) u.r2+(+) 2 r Apart frm the t"r* these results are equal t the cmplex f; spectra f damped snusds wth ntal phases f O and { radans respectvely, as calculated n chapter 2. f the nput vltage f the gyratr flter s dvded by g, ts ampltude respnse s prprtnal wth the ampltude spectra f the damped snusds. Therefre what s fund n chapter 2 cncernng the maxma and bandwdth s cmpletely vald fr the flter respnse. Mrever, f ths tlzpe f band pass flter s used, the 'naccuracy' f the spectral peak lcatns as calculated n that chapter s decreased and even cmpletelv crrected when the flter bandwdth equal s 2cl. f the sgnal gatng s carred ut accrdng t the fnal remark n chapter 2, ptmum crrectn ccurs when v, s cnsdered as the flter utput vltage. Wth reference t the functnal dagram (tg.2a) the wrkng prncple f the segment spectrgraph can nw be descrbed n sme detal. After the recrdng f a part f a sgnal nt the sgnal memry ('transent recrderf) as already descrbed, the sgnal s replayed repettvely at a cnstant rate. The analg utput (Y) f the

47 b 0 + J t r O.Fl ( / ) q J +J A 'F{ $ r r F l { $ 0 t l 0! ]. ( d +J A.rl. l t t O t r A! F l q ) ( d $ t r r r d H V tr.r.r{ 0J.lJ A A F l v b O l J t r. F r a. / l B F r 6 lrl g c d a u ll f.t \ t J a -9 t-g sg td <a G2 l'cl 6 9 Y = t,a F ( J d z l r ja U &!, f- E Z E rrr ;6 r J d a F t! - a g l e c l - j ( n u J l- 2 6 ul ul vt : a &, Z Al lj', l-c * u 33 8! E e a J3 9 v', H gp : F(/' g 0 0. rg l{ A lj tl J J U 0l llr e 6 ul l- J Z b. l E 6 ta a t- d a E A t v d F = \ J a. v d ; ( 4 v A ] g fe ;.$ N b0.rl

48 transent recrder s attenuated by a dgtally cntrllable dvder (usng a multplyng dgtal-t-analg cnvertr) and then led t the nput f the gyratr band pass flter. Tw multplyng dgtal-t-analg cnverrrs serve as dgtally cntrllable attenuatrs, makng the central frequency f the flter prprtnal t the same dgtal number (A) as used fr the nput dvder. The utput vltage f the gyratr s taken frm v, va a buffer arnplf er. Ths results n flterng f the utput frm the transent recrder wth a flter respnse whch s prprtnal t equatn (6) where 0l s prprtnal t A and cx, s cnstant ( = *T). Durng ne cmplete scannng f the transent recrder the number A remans cnstant. The replayed samples n the transent recrder are cunted by a sample cunter. The cuntng result s cmpared wth a number (Nl) whch s preset wth the ad f fthumb wheelt swtches. When bth numbers are equal, a flp-f1p s set, carrsng an analg swtch t cnnect the utput f the transent recrder wth the scllscpe nput. n addtn the flp-f1p enables a prgrarunable cunter whch als cunts the utput samples. After a preset number (NZ) f samples, ths cunter generates a pulse whch clears the flpflp causng the scllscpe nput vltage t becme zer. The desred fundamental perd, r ther segment, can be selected vsually therefre by adjustng N, and Nr. As any sample number belw 1000 can be preset, the adjustment reslutn s 20 psec (the cmplete cntents f the memry beng 1000 samples f a 20 msec sgnal nterval). The nverted utput f the flp-flp cntrls tw analg swtches smultaneusly whch keep the tw capactances f the gyratr flter shrt-crcuted except durng the replay f the selected segment. The number (A) whch determnes the tunng f the flter s frmed by a bnary cunter (9 bt) and s ncremented by ne at each pulse frm a tmng crcut. The same pulse serves t restart the transent recrder scannng cycle and the sample cunter. The peak

49 - 9l vltage f the gyratr flter utput s btaned by a full-wave peak rectfer whch s reset befre the next tunng step. A sample-and-hld crcut changes the vltage drectly frm ne measured value nt the next ne, thus preventng unnecessary large excursns f the wrtng pen f the chart recrder, whch s cnnected va a lgarthmc amplfer. The peak rectfer reset cmmand and the sample-and-h1d cntrl are generated by the trnng crcut. Ths crcut ensures a tme lapse between cnsecutve tunng steps whch s suffcent fr plttng the spectrum accurately n spte f the relatvely lw wrtng speed f the chart recrder. The tmng crcut s drven by the same clck frequency as the ne whch cntrls the utput rate f the transent recrder. Durng the tme 1apse, the flp-flp s nhbted n rder t prevent the gyratr flter frm respndng t mprper nput sgnals. The replay velcty f the transent recrder s made prprtnal wth the length f the selected segment by makng the utput clck frequency equal t the prduct f a reference frequency and the number N, (acheved by usng the 'phase-lcked-lp' prncple). The reasn f ths may be explaned by the fllwng: Reducng the replay velcty by a factr k causes a decrease f the sgnal frequency cmpnents by the same factr. As the tunng steps and the bandwdth f the gyratr flter reman the same, the result s equvalent t flterng wth ncreased bandwdth and tunng steps bth by the factr k. Hence the flter respnse tme and frequency reslutn s matched wth the selected segment length. The peak vltages frm the flter utput therefre are ndependent f the segment length. Because the trnng crcut s slwed dwn at the same tme, the tunng tme s rased by the same factr. The result s that the sweep speed remans cnstant. As the chart speed f the recrder remans unaltered as we1l, the frequency scale f the btaned spectra s ndependent f the segment length. Furthermre the frequeney range ncreases wth the same factr n cnsequence.

50 n rder t avd any prblems caused by spurus capactances, the frequency sweep f the gyratr flter has been shfted t a lwer area tgether wth the utput clck frequency. Owng t the lmted wrtng speed f the chart recrder the tme nsertn between cnsecutve tunng steps s large enugh t a11w fr replayng at slwer rates wthut the cnsequence f ncreasng the analyss tme. The actual value f k s chsen t be 5 when a l0 msec sgnal segment s selected (.". N2 = 500). n that case the utput clck frequency equals l0 khz (whch accunts fr scannng the cmplete memry n 100 msec). Therefre the reference frequency equals l0 k[z/500 = 20 Hz. The reslutn bandwdth and tunng step wdth at a l0 msec segment were made 50 Hz and 162/" Hz respectvely J (the number f tunng steps wthn ne bandwdth was chsen t be 3). That causes a lo Hz bandwdth and a 31 / " tt, tunng step wdth 5 fr the gyratr flter as n ths case k = 5. The chart speed beng 2 nm/sec and a frequency scale f 200 Hz/ cm cause the requred tunng speed t be 40 Hz/sec. f the tunng step wdth s 1621rH", J the tunng speed requres 40/162/3 = 2.4 steps/sec. Thus the utput clck frequency (10 khz) must be dvded by 4167 t bt.an the requred step frequency. Cmputatn f sme prpertes f the respnses f the nterrupted flter system t the smplfed artfcal vwel sunds as used befre ddn't seem a verv smple matter and therefre we decded t check whether r nt ths system wuld at all functn satsfactrly n practce. At a later stage the theretcal behavur culd be wrked ut. The fgs 25 thrugh 29 shw sme utputs btaned frm ths nterrupted flter system at dfferent nput test sgnals. The utputs frm a few natural vwel perds are represented by the fgs 30 thrugh 32. t can be cncluded that the 'sde lbest have cmpletelv dsappeared and the frmants are dsplaved cnvenentlv.

51 L -93- "lf l-t f-.1 t^ l l t l T T 1 'l {- L t-- h t--. t tr, h T - -T-- tr- -T J L r-r t l l : t -l fe t_, l t l l f---t \ J J J -1 f + J t 1 J \, \ l E f \ ' t / T l L L \ L 4 E \ :-\ 4 tf.r r tll _l tt l! \ \ --f j l l j Fg. 25 A: Spectrum f 2O perds f l000hz snusd (T=20msec) B: Spectrum f 2 perds f l000hz snusd (T=2msec)

52 -94- ) E.$ tl H (u F 0,, l{ cl u rt (a N rn N t}{ t lr A ' r q..l a }{ +J C, A tn!?,-l:l-

53 -95- Fg.27 r_ l t, Spectrum f the sun f Fr=1450H2, T=lTmsec 2 danped snusds, Fl=l2OOHz, Fg. 28 Spectrum f the sum f F,=40OHz, T= Oms ec 2 danped snusds, E r=250h2,

54 -96- :T-]-*T-T* r- t t t t t l l --l--r- -l l L r l. l l l l t l t l --+ +#--l] sas--l _t _J l_ l l l 1,1 1 l +"-t Fs.29 A: Spectrum f the sum f 2 danped F2=l500ttzr T=8msec snusds, Fr=850H2, B: As A except T=3msec

55 -97 - r f 1 l l, r l r l - ", l :--f q) t Fr --l E ] -;----l : l t :----r ---'l ] t s l t l-_'l a f > t '_ - l l t --- Fl d l r r *rr r l l, F;- \ l r-r N f f t, t t,j lj') 1 r l r l \ r l l r : l l \. t :'+--F; tl l ', l r- 1,, llt \ l l + { ; - - A / +J --;- A a : t n :-:-- ' (a t). r.l t' l\; )- \ l :1- _L a,l r l U \ -l t ( -r L 1 ',,t tr { 1 l T a : t t l l l L, l : l ) r L --l- --L- T U u 0. F F tr e

56 -98-, E Or.f, tl ts ) ql trl c) tl{ r+{ E a lr TJ & u)

57 r \ l l"-- ^ L ts"-* T L ctl3 a l t-- T- t-- J t ] 5 t u \ 00flz t, Ī l A 3 \ jl t \ t l _0_ { j -t l< :\ OmnlScrlhe* charr rype Ec-r Fg.32 Spectrum f fenale [], T =5.3 msec

58 Even at a segment length f ne r tw perds f the tfrmant frequencyt, ts detectn s pssble, althugh ts spectral peak shfts smewhat t a lwer value. As ths shft s a functn f the segment length, the measure f a nt aceunl. crrectn mght be taken 5. CONCLUSON The expnental wndw analyss and the nterrupted flter analyss as descrbed prve t be valuable methds fr the analvss f vced speech sgnal segments. The latter methd cmpletely cancels the nfluence f the fundamental frequency n the spectrum (the well-knrnm tsde lbes') f ne perd f the fundamental frequency f the sgnal s selected. Addtnallv the frequency reslutn s lnted by ether the segment length r the ntrnsc frmant bandwdth and nt by the analyss methd. The segment spectrgraph devce based n the nterrupted flter methd therefre can be cnsdered as a useful tl fr frmant extractn f speech sgnals per perd, hgh-ptched sgnals ncluded. Thus fr example relable frmant trajectrv measurements culd be carred ut. The requrements as mentned at the end f the ntrductn therefre can be cnsdered as fu1f1led. Naturally, the applcatn f the devce culd be extended t ther speech sunds such as frcatves and furthermre t sgnals utsde the speech fe1d. Acknwledgments. rd lke t thank all peple wh, n ne way r anther, helped t carry ut ths prject and n partcular Drs.A.C.M.Retveld fr hs stmulatng c-peratn n an early stage f the experments and Mr.A.W.van Maanen fr hs mprtant rle n the cnstructn f the segment spectrgraph.

59 - l0l BBLOGRAPHY l. Brch, J.T. and Olesen, H.P. On the frequency analyss f mechancal shcks and sngle mpulses Brel & Kjar Techncal Revew n Engelsn, M. Spectrum Analyzer Measurements Tektrnx nc Lynn, P.A. The Analyss and Prcessng f Sgnals Macmllan Markel, J.D. Dgtal nverse flterng, a new tl fr frmant trajectrv es tmatn EEE Transactns n Aud and Electracustcs 1972, AU-20,129-t37 5. Nerp, D.J.P.J.van, P1s, L.C.W. and P1mp, R. Frequency analyss f Dutch vwels frm 25 female speakers Acustca Y7.29 Hett Papuls, A. The Furer ntegral Mc Graw-Hll 1962 and ts Applcatns 7. Ptter, R.K. and Stenberg, J.C. Tward the specfcatn f speech J.A.S.A. v1.22 n 6 p Randall, R.B. Frequency Analyss Brel & Kjer 1977

60 -tz- 9. Randa11, R.B. Hgh speed narrw band analyss usng the dgtal recrder type 7502 Brel & Kjer Techncal Revew n event 10. Tellegen, B.D.H. The gyratr, a new electrc netwrk element Phlps Research Reprts n 3 l94b p. 8l l. Wempe, A.G. A system fr gatng segments f taped speech wth great precsn PrceednBs 4, nsttute f Phnetc Scences Amsterdam, 1976