Pole-zero matching techniques

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					Dept. for Speech, Music and Hearing
  Quarterly Progress and
           Status Report




        Pole-zero matching
                techniques
                           ´
             Fant, G. and Martony, J.




               journal:   STL-QPSR
               volume:    1
               number:    1
               year:      1960
               pages:     014-016




http://www.speech.kth.se/qpsr
F.    POLE-ZERO MATCHING TECENIQTJES
              O work i n t h i s f i e l d i s s t i l l i n an exploratory phase.
               w                                                                                 Vowels
a r e studied. by means of t h e ant i-resonance f i l t e r techniques mentioned i n
s e c t i o n I A. Nost of t h e pole-zero matching of f r i c a t i v e s tms made on a
graphical b a s i s comparing t h e spectra of human samples with spectra synthe-
sized numerically from tabulated data of elementary pole and zero curves.
Analog methods based on t h e . use of networks 1~5thvariable poles and zeros
a r e a l s o being investigated, fl standard c i r c u i t f o r representing a pole-
zero p a i r has recently been developed ( ~ r i n g l e b o t n ) . It i s based on t h e                       .

continuous v a r i a t i o n of an inductance by means of feedback amplifier tech-
nique s ,                                                                                                    ~   -
              A match of f r i c a t i v e s in terms of two poles and one zero i s gen-
e r a l l y s u f f i c i e n t f o r r e t a i n i n g a high standard of speech q u a l i t y in a for-
                          1.
mant-coded synthesis (OVE1 )
              A matching of t h e f r i c a t i v e s [ s ] and    [ f ] i n terms of two poles
and one zero i s shown i n Fig.            1-7,    The measured samples p e r t a i n t o sus-
t a i n e d sounds analyzed by a closed loop process with a vmve analyzer of
125-c/s bandwidth.          The pole a t 2700 c/s and t h e zero a t 2500 c/s of t h e
f r i c a t i v e [ f ] c o n s t i t u t e a bound pail. with but small contribution t o t h e
spectrum.      It i s of i n t e r e s t t o see t h a t t h e spectrum l e v e l r i s e s a l l t h e
way up t o 12 kc/s which was t h e upper limit of analysis.                        Spectra of         [f ]
vary much olsJing t o t h e p a r t i c u l a r c o a r t i c u l a t i o n and t o t h e degree of
labiodental c o ~ s i c t i o n .
                  rt
              The main peak of t h e [s]-spectrum of Fig,                 1-7 i s associated with
t h e pole a t 5800 c/s.         The second pole a t 8000 c/s contributes t o b u i l d up
a proper spectrum l e v e l a t higher frequencies. The zero a t 4500 c/s i s
placed higher than the corresponding zero i n t h e measured spectrum in order
t o preserve a correct l e v e l . r a t i o between t h e main formant and t h e low fre-
quency p a r t of t h e spectrum,
              An a d d i t i o n a l inventory of two pole-zero p a i r s r e r e added f o r
matching t h e [s]-spectrum of Fig, 1-8.                 One of t h e s e bound poles, t h e one
a t 2500 c/s, corresponds t o F3 and t h e one a t l+200 c/s t o F5. These weak-
e r formants do not appear t o be necessary f o r t h e synthesis of a good [s].
Fig. 1-7 Measured spectra (broken llnes) and two-mle-one-zero
         synthetic approximations (solid lines) of the fricatives
          C s l and[   f   I.
Fig. 1-8 Pole-zero matching of [                     .
                                      ] and [ s ] Measured spectra are
         represented by broken lines, two-pole-one-zero approximations by
         dotted lines and more complete synthetic representations comprising
         additional bound pole-zero oairs bv solid line curves.
         Free poles are marked X and free zeros are marked 0 .
              The spectrum of a f r i c a t i v e     [I] and i t s pole-zero                  approhtion
i s demonstrated i n the lower part of fig. 1-8,                            The e s s e n t i a l feature of
this particular p a l a t a l r e t r o f l e x sound i s a f r e e zero a t 1000 c/s and a
f r e e pole a t 2800 c/s and one a t 7000 c/s.            A detailed match employing
three additional pole-zero p a i r s associated with the r e l a t i v e l y suppressed
F2, F3, and F6 provides a match within a few dB from 3C0 c/s t o 12 kc/so
                                              t
The dotted curve on the figure r ~ r t a i n s o the a p p r o d t i o n in terms of
the two f r e e poles and the f r e e zero alone. It i s apparent t h a t the re-
sulting exaggeration of the r e l a t i v e l e v e l of t h e main peak i s due t o t h e
absence of the high-frequency attenuation inherent in the two bound pole-
zero pairs. This e f f e c t has been predicted i n e a r l i e r t h e o r e t i c a l work. (1)
I n agreement with r e s u l t s from those e a r l i e r studies                      it i s apparent
t h a t the synthesis can be made on the b a s i s of a r e l a t i v e l y f l a t source
spectrum,
          The pole-zero matchings performed i n Fig. 1-7 and 1-8 allow a
simplified s t r u c t u r a l comparison of the sounds [f] , [s] 9 and There                [I 1
i s a s i m i l a r i t y between [s] and     j
                                             [ ]i n        so f a r a s the spectra of both possess
a free zero of a frequency lower than t h a t of the two f r e e poles,                             T h i s free
zero contributes effectively t o the high-pass structure of the spectrum a-
bove the zero the significant part of which extends approximately 2000 c/s
lower down in frequency f o r [ / ] than f o r [s].                         The mode spectrum of      [f   1
does not possess a f r e e zero and the only f r e e pole i s located a t very high
frequencies and i s generally heavily damped.                          This pattern        explains i n part
the r e l a t i v e l y low overall i n t e n s i t y of     [f   1.
               n
              A alternative i n t e r p r e t a t i o n applicable t o t h e theory of distinc-
t i v e features (2) would be t o oppose             [/I     t o [s] and [f] a s being t h e only
sound t h a t has a f r e e zero below or close t o F                         This i s a requirement f o r
                                                                       2'
emphasizing formants F3 and F4 and also F2 i f the zero i s well below F and
                                                                         2
thus a formant area i n the consonant not f a r above the mean pitch of the
upper formants of a following vowel. This conforms with the c r i t e r i o n of a
major e n e r a concentration i n a centrally located peak a s required by t h e
definition of compactness. After correction cf the [ s ] - and [f]-spectra
f o r the r e l a t i v e l y low s e n s i t i v i t y of the ear i n the high-frequency region
it i s apparent t h a t the [s 3spectrum has a higher center of gravity than the
[ f1-spectrum and [f ]i s thus grave compared with [s 1. However, in sonr:
languages (e. g., i n      we dish) it i s f e a s i b l e t o oppose [ / ] t o . [s] a s .being
more f l a t ( s h i f t down of t h e spectrum) while other f r i c a t i v e s , e.g.,      [p]
take t h e place of t h e compact member of t h e system.
                                                                  G.   Fant, J. a r t o n y




(1) Fant, G, : Acocstic Theory o f . Speech Production ( 's-Gravenhage,                       1960).
(2) Jakobson, R., Fant, G., Halle, K. : PqPreli.minaries t o speech analysis.
              The d i s t i n c t i v e f e a t u r e s and t h e i r correlates", &L I. T.,
              Acoustics Laboratory, .Techn. Rep. No. 13 (1952); 3rd printing.