BSTJ 50: 10. December 1971: Design of Digital Filter Banks for Speech Analysis. (Schafer, R.W.; Rabiner, L.R.)

14.1 MB·English

Design of Digital Filter Banks for Speech
Analysis

By RW. SCHAFER and I. RL RABINER

Aan ofbandpasy filer eft sain pefrming abortstne spect
asolyes of epeech stats. Taie paper so ince witht analyse
Wbsign af ig te bats compared of equeiyepacad bendpass ier
ie shown tas etifcont inprarment an the compart ltr bork
feepones can be ah eaed ty poe cero he vee pes 9 he tad
nse filer, The rene are enter wm gone! fe ae conf
feos

Many sproe provessiag systray ev bused ou ee eaeopt of sate
vise apnetram sealysia'” Spectrum analyte for sues ystems often
trnsivt set of beadgace ltrs whoee conebined porsbacds corer &
‘heined feeouency range, Aithoush contzmowetime ft have frudi-
tioraly Seen ued in filtor banas fr se cals, elvan tal a
sions of dice filers are now svailale,? at he yang seh
tbgital tor ofer should be exploited in fir bane design. Thee
fudvanteges Iveludes Moibilily 0 design uf Uh iets
fiter, preesion of realrtion, stability of digital hardwers, wd the
‘ficieney of realization of the Biter binle eared by the possibility
Df rlliplesng the digital ona. Ths iki porta to eonidee
Asin technique for Fle asker auc of gal bandpass

‘To foeue ot the bio concept in Alter bake desi, it Is wel to
sefne sn ideat pier taut spectrum apalszer Tigure t depiets wel &
Str banie composed of digxal Stns whose smpule responses are
denoted by Age), = O01, oy AD, whore 1/7 isthe swopling
iequeney of the input signal Such a flter bank constitutes an ideal
speetzum anaivaer i the inpak ofa) (with possibly further band limit
ing) can be ayatesized exter (within some fixed delay) By oleae

Sachin ese ler yo
08 ru ana sveTEAC TreNTOAL JURA, DECEMBER 1

ig 1k gta Sands Fr,

combination of the bsudpaas filter outputs xin). An example of
Imi a ejstem would bo one ia whieh the filter hal weelaguler
Toandje er with ee aae:a ecrtant gin and lirear phe in their

such

ter bardvidche

fechas sae eno gain ouide. IF the
that he eeuenay sang

{is completely gover wituva wena, then tha input ean be
sec by adding tether sho natgute of the bandos fters
‘he estonia eouractevais af the desl epeetrum snr aro tht
tho frecucnos “pone of the cimtined outpate must exhibit a fst
magnitude response axd 6 Tsar phara, and thovetore the eombined
iimpube roo wii be a delaged digital impulse anit sample
Gaol digital Bers lan whore palsy responses aro aem for
n°. 0) cates have the dasited ideal psn chameteristios and. may
hot hve Ensar phase Therefore ster ban eomocw of ih ters
Ssnuioh asin the eel cheneateatice of fat magnitude remposee and
linear phase In hia paper we wil dsoribe wn approach tthe design
of Ser banks that approsimate the ideal specirim analyser. Hast
We pion dhlailed analein of after banlegoniarstion i whieh
equally spaced, cousl-handwidth digital Biter: ave vod. This anniyis
‘ygestew tehnique for optimising the fier bank: eharacrarities and
ie irton pba sprang tors am ae pray Sear pe
rar ce wk 08

sao songests how he emule ga: be usw che mia bendths
fp desi. Tee teas ae stad with exemple

Semin shot the ulpnes Flare i Mig, 2 hava imple sponses
ofthe form

ker

De ROT, Gon HO) BRAY ora
De Wor;

these an = oy — GTS dant MOLT) Ube inplie expose of
Fits lowpass ier. (leat she = Oloapaee erie eds
fad zy — 0) The aystem funations for tie Seo? bande lors ate

FQ) HD |HOME [DOI a2,
He) ~ (Dy HE. e

a}

Aer

‘he freeveney revpance of these tens 2 obtained attersubattucng
em ein as

Be HE PF |e ste,

se

He} = | Hey

E the trogusaey meeponse of promatyge lowpees filter, He), dscpa
sry, thon i one bo wort fon 14 ta
[HG DB) Owe aT
OD [HOY aw 50.
Te his ous: te Fler bk eumigs 0m ash o MF — 1} aealy nen
Tonia fees wit enti agribsle wees ana Voie
seine anes Fein We fare ewe Ue eal dein
Dandnser tie tom lozpass procoeyoes foe aralstina. eonseniense
‘nd Drearse of the iinpostance nf spectrum saalyae syseme this
Team! Th meal to be eeu apply Tor olla Vandyace wane
feataatio an fen x they pil su of uniFesl spe basins
fiers wit iene! Feenensy characte
(Our objets i tp scan oe youtolype Hops Lar aad the
parameter [Dy], uy dn, andy 29 shat the fer beaks wll loe.y
foprosinnae ths ehacacervties ofthe ideal epsetmima snalvaer, Ta do
{af ne mst corm the reaponae of the oomnpesin tor bank. Pet,
‘i10) ras use sv8TISF TERSHEAL UAL MO

omever, it eure! la interes the individual bandosan feerouepsts
Sa vermy of spss analy eanwiderti
‘Pee inca has outputs are 0° Be

addi — Sanh |D, ROY eMowhakh— T+ 0),

267 | Py [der Ah

phigh can exposed ae
nga) = 2 He 0.X¢a
ze) = We (DAK, ht

‘whore Ds iv fe wor constant defied hy

Di=[Dp[e a
De= [Pale

sod
Xt wi = SS se Tai — oe m

trae quantity Xap. i the diertetime svi of the sher-time
[Fourier tnustuty of 687), Ths, (3) sors te relate the bandgoxs
ltr yutsits 2) us ue ahor-ttac Fourier trauonn.

"The fectoncs nespense and ampules resjnse nthe composite Bee
ng utvaliniced fren

san ~ Eas *
ce io)
son Soenfer om Eve an

Dering
iar, ET Hs ao.

sve observe fron (10) thatthe combine! imple response af the Riler
Take ea be exposed

1) ~ aT) aan 0

ayastions (11) and (12) ane tie asia result of the ange. (Note
‘has ckey cond have heen obtained ively by stammiay the impale
responses (87), sll tie tilve of the fveepretabion of the ser
bys tpt a eerms of th sent ine spetninn)

Taunt (19) shows hat tar ter bath ipbe esponme ie the
product of the prototype owes Hier pun rewonne MT), cd
the suauenge alt) eid be (LL). The hola lows lt depends
tu both tho desir fein aes Ue reg remient o ob
ing lat riagnitile st! linear pase reponse inthe eomapaste Bier
bok. ‘The sequenee dais nlependet of the prota leper
ss afk of regency sqeing the rlaive gains ard phase,
fad tho mamas’ Denne Here Thus fur cen chee of prope
Tinney, eh pammetars cf de) ras ate thir the
Tet approximation te ths fal aertowre anzlearr. To ase hw die
Goer osha | Set sxcanine veal dae ularuelerisas of Se seuss
Sint)

‘A wil eT athe eemaiader of thie amt, a arly es
digg u the eorex ezfEeients Dez 11)

ee ba ee ta 4
a)
vote ia nego.
Hsueh and [Yel =
(The eunivon Dy = 1 imglise tot ee baad caound ~ 0 is rede

Titer Sk: Dy =U szplos tant ts.) 1 cnn Ie so thal
a By 11) omnes

forthe ei

Bain [Mf te Ll eos ol +m), 8)

10D = nai mT

lore = ay $M — 1 2, and ie Lo dentin on wheter
‘or nat te Topas channel rede
"The pimpertioe of che secuence aid) deter he lamas of
8102 Ime buy srerINL Hon Feat, ROR 181
Uh mpage reponse of the her ule Borie of thea pipers ae
imine Rea

{i The paar bite theses mT) By my eam wil
rospeot te BGT)

(ii) Tho segues ov} is wwen svout the sample» = <n jhe
Mot — 40) sl al — nD
(ii) The masunune valu of a(n) neeure nt x = —ng This valne

ie (mnt) ~ 2M + De

(6) TF 2a/CGa) aad ye axe Yul Tales, ther the peuenen
cD) i peed with pore ane abe, AT) WEL We
fs alts perotie espencr hich wil pai p24 em interals
of 2rd

nih ite eprint tn) can i xd by entice a
sins ou ak y = do ad at © vt 9
sel nr Thalia eeioetemmey tage fe 0/7
Safin i onitasin aro tw dts oe oer
Ef Waser ces eon 4 on wr
vin [22GE" aur nt]
Si fate 4 TA
vn [@ EY) as nt]

sala TT

ae) - Lit po ate

Boat 5h

1037 os, the k = O tere ot used, Le. LO and wb Aw)
Tin ele Thom (15H) thal for chose candivons AWD) is w period
feajuece mith posi — 2a ay fase ain ye Una of
cies of a matimnouscime periodic Diciblet kernel as shows i
Fig 20-100 =H Wy/2 and De ~ 1, (a2) bs» period discrete
time impale ean wth impos ceesering wi miles of WT This
ie becavne the aumple pints oa the peridie Dirichlet hors! weour at
"oe mina el the nao erring, sadeatod by desma eels ie
Fig. 25

"The eanditions Zor dw 7) to bo pele ne that Toth w/a and
aaa) be equal 1 intone, To so thi, ne nel exon (11) ix
etal 125i) isun ingen, ae AF iol insger he nae
Dein [A dud? © mP)i20 sim [Sen be 7)/2] in iaie with
Derind 87" ~ 2rd If ye an itoxer ad Wi, the sauce
oe [lay + GACT) Ba | -mgTIT Fe ab perio weit a period
Drei sat ae ase 08

oni a
say betters]
Talaeteat ye

i\
|

Bi epliwoaetiae Ge

thot ie an inser auliple af 26/e. Thom the amie of the we
‘owunnese 4 periedie with poninl e's. ‘The ine ane holes
fie AP ag even ntoger and 2: a we ingens all ag ie
Inuoretion betwee apr emt anes aii de

W oicar 2e/{asT) or ay! ame nit itogene ain) wl tbe
vsrodis, bot wil sil yoce pw Lome leave of 2a, Bul ems
15 dopiced in Pig 2h whors the stmoley 4a} aro mused by the
B10 Te LL eostaae HCL NIE cond mA RL

vl eis ad te dated uv howe the tector
fin IM Sein = P32 Lalo a P21

shen 9 ino. As chown is Ti 2,
Tot GON eseNpla

aT? wil alae have ove sen

tos the posed soto we preted « detalled analy ef a Ger
bate ensipesed of byilly spre ceual-hadsedh hose. In thie
Setiun or nil shaw te avs Ue mln ca De ese
inate ak dei

“The abject ve af Mat anplitude response wid Ena phave be must
tosily aeiovod Uh Iaulpas Whe having those sume proper,
For tie racon, Bevel Geasically Hot daly; Sitors ave ofeen voed
fides banks Tw die easnples some a this pic, we Have asad uta,
fice: obsrined (run Passel pepe desiacs we impulse ivesian.*
TE shoule be note sat ae gal tar obtened this wap dao hee
the oaecly ft eles property. J. Tbseu" ls sown that ehe de
omit of Ye syauem Tesi of eaxiolly fu dia distal ers
Era Gaus hspengimeltis iuarien, Ie teacamnb oto expost hoeever
the for Loc uarmwhael filtee ot iacerest here, ue aiereneer seal
bo ual

“AS an excmple a lial fla cerved frome a aichaneder ese
loupe flier with aryreptete email freyseney of 40 Fix is aon
in Fig, The imple eespomse ie ow Pig hal he arp
sn lis sna acer fx Pig thd Pgh Hor nin
Fp. ens use ina ser maak" wise Colloeng ee of passe
De = 0,7 = Mae, dy IDG), oy — 2s IUD) ey — 0, md
Af — 8b, The svg lle bank eharacveriioe are stone a Fig
Sine aire lank tome response, AnD), ie sci im Pg So hing,
vit the protaljiv hase impilee respozie Bia). Fur tio ata
Choke of panes, fe) eBtanod fom Ge)

in O6len) os

i Olam,

aint

‘wise is peiodie nth perl U0 spies {i ne), wt peaks aeearing
HEAP 0 11D, 130, mice, Prom Pig: ta it oun le see that
Tie poss Hin), the peas of AinT) at a = Owl be
wt sae Ala} Sa sacl sebum 9 Ore the aller band
Darna ware nose 10s

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