Contains reports on three research projects.U.S. Air Force, Electronic Systems Division (Contract AF19(604)-6102)National Science Foundation (Grant G-10800)National Science Foundation (Grant G-16526)National Institutes of Health(Grant MH-04737-02

Arnold, Jane B.

Heinz, J. M.

House, A. S.

Paul, A. P.

Stevens, Kenneth N.

DSpace@MIT

XV. SPEECH COMMUNICATIONProf. K. N. Stevens Dr. T. T. Sandel S. InomatatProf. J. B. Dennis Jane B. Arnold A. P. PaulProf. M. Halle J. M. Heinz J. R. SussexDr. A. S. House W. L. Henke E. C. WhitmanA. AN AUTOMATIC SPECTRUM MATCHING PROGRAMThe automatic analysis technique that will be described in this report is an extensionof a computer analysis procedure that has been reported previously.1,2 This programis the same as that devised for manual matching of speech spectra 3 except that the deci-sion functions, i. e., the strategy, are carried out by the program. The strategy used bythe automatic program was designed to parallel, as far as possible, that of experi-menters who were experienced in the use of the manual program.In matching vowel spectra, in general, two situations can arise, and a separatestrategy has been developed to accommodate each situation. The first, which is themost difficult but the rarest, occurs when no previous data about the spectrum are avail-able. In this case, the strategy attempts to obtain a rough approximation to the formantfrequencies (within 200-300 cps). The second situation exists when approximate valuesor the results of a previous match of a neighboring sample are available to the program.When the first strategy is used, the approximate locations of the formant frequenciesare found by assembling comparison spectra from a small set of stored curves. A givencomparison spectrum is constructed from a stored set of first-formant (Fl) curves withresonances 100 cps apart and six F2 curves with resonances 200 cps apart. The lattercurves include the effect of a fixed set of higher poles. All 36 possible pairs of F1 andF2 combinations are compared with the speech spectrum, and the values yielding thelowest squared-error score are chosen to be the initial approximation. The frequenciesof F3 and F4 are assigned values that depend on F 2, and average bandwidths are assignedto each formant. Once such a set of values has been determined, the analysis programwill make use of the second strategy.When the second strategy is in effect, there are eight parameters that can be variedby the automatic program: the frequency and bandwidth of Fl, F2, F3, the frequencyof F4, and the value of a real-axis zero, corresponding to a "tilt" or glottal-spectrumcorrection curve. The formant parameters are changed simultaneously at every trial,while the tilt is changed every third trial. The program carries out the followingThis research was supported in part by the U.S. Air Force (Electronic SystemsDivision) under Contract AF19(604)-6102; in part by the National Science Foundation(Grant G-10800 and Grant G-16526); and in part by the National Institutes of Health(Grant MH-04737-02).tOn leave from the Electrotechnical Laboratory, Ministry of International Tradeand Industry, Tokyo, Japan.275TRIAL FORMANT FREQUENCYNCY FREQUENCYFig. XV-1. Comparison of input spectrum and internally generated spectrum for thecase in which there is (a) an error in formant frequency, and (b) an errorin formant bandwidth.(XV. SPEECH COMMUNICATION)operations: (a) compute the frequency increment, 6F i , and the bandwidth increment,th5b i , for the i formant; (b) constrain the increments to prevent unreasonable behavior;(c) tilt; (d) generate trial spectrum; (e) repeat steps 1-5 until a best fit has beenachieved.The basic part of the program is the evaluation of the two functions for computingthe frequency and bandwidth increments. The frequency-increment function is based onan examination of the error curve in the vicinity of the formant frequency that character-izes the trial spectrum. Idealized curves corresponding to a frequency error and abandwidth error are shown in Fig. XV-1. If we let SL = weighted sum of difference-curve values for a specified frequency range to the left of the trial formant frequency,and SR = the same weighted sum to the right of the trial formant frequency, then thefrequency increment is given by0 10 20 30DEV40 50 60 70 80 90IATION (CPS)Fig. XV-2. Cumulative distribution curve of difference betweenformant frequencies obtained by automatic and manualanalysis procedures.2771008060LLI-OZU2000(XV. SPEECH COMMUNICATION)SL - SR6f. K .bw ,1 K jwhere K is an empirically derived constant that is the same for all formants, and bw.is the bandwidth of the analyzing filter nearest the trial formant frequency. The band-width increment is obtained from a similar function, except that a table look-up is usedto specify values of a function 8pi = f(SL+SR). Constraints are placed on the 6f. so thateach 5f. tends to zero with successive trials. The best fit is for the case in which the1squared-error score has a minimal value; recognition of the best match is simplifiedby placing a limit on the number of trials.The new automatic program (MATCH IV) has been used to specify the formant fre-quencies for three adjacent spectral samples taken from each of a large number (360)of vowels spoken by three male talkers. These data were compared with data on thesame spectral samples obtained as part of an earlier study 4 by the manual matchingprocedure. Some idea of the performance of the automatic program as compared withthe manual matching procedure is given in Fig. XV-2. This figure shows, for example,that 75 per cent of the time the values of F1 and F 2 as obtained by the automatic methodsare within ±20 cps of those obtained by the manual procedure. Results such as thesesuggest strongly that the automatic procedure leads to valid data on formant locations.A. P. PaulReferences1. A. P. Paul, Strategy for the automatic matching of speech spectra, S. M. Thesis,Department of Electrical Engineering, M.I.T., August 1961.2. A. P. Paul, Automatic matching of vowel spectra, Quarterly Progress ReportNo. 63, Research Laboratory of Electronics, M.I.T., October 15, 1961, p. 137.3. C. G. Bell, H. Fujisaki, J. M. Heinz, K. N. Stevens, and A. S. House, Reduc-tion of speech spectra by analysis-by-synthesis techniques, J. Acoust. Soc. Am. 33,1725-1736 (1961).4. K. N. Stevens, H. Fujisaki, and A. S. House, Analysis of vowel spectra, Quar-terly Progress Report No. 60, Research Laboratory of Electronics, M.I.T., January 15,1961, pp. 177-179.B. DATA DERIVED BY AN AUTOMATIC SPECTRUM MATCHING PROGRAMThe automatic analysis program described in Section XV-A has been used to extractformant frequencies throughout the vowel portions of a number of utterances. The speechmaterials were drawn from a library of utterances that have been described previously. 1The measurements were made in eight stressed vowels occurring in 15 different sym-metrical non-nasal consonant environments. The words were spoken by three maletalkers. The computer was instructed to determine the formant frequencies for all278(XV. SPEECH COMMUNICATION)2.02.0-1.530 40 50 60SAMPLE NUMBER(a)30 40 50 60SAMPLE NUMBER(b)Fig. XV-3. (a) Example of data on the frequencies of first two formants obtained by theautomatic analysis program. Spectral samples occurring 120 per second.The light lines at samples 33 and 61 represent vowel boundaries obtainedfrom visual examination of spectrograms. (b) Approximations to the datain (a) obtained by fitting parabolic curves to the plotted points within thevowel boundaries. The two curves are completely described by the param-eters F 1 0 , F 2 0 , T 1 , and T 2 , together with the curvature values for theparabolas.spectral samples within the vowel boundaries. The time locations of these boundarieshad been established earlier from visual examination of spectrograms. 2Typical results of the automatic analysis, showing the frequencies of the first twoformants for one utterance, are given in Fig. XV-3a. The curves depicting F 1 and F 2as a function of time for the symmetrical consonant environments used in this studyusually have a form similar to that shown in this figure. Each formant begins at somevalue that is presumably dependent upon the vocal-tract configuation for the initial con-sonant. The curve then proceeds toward a maximum or minimum value associated withsome target configuration, and finally tends toward a value determined by the vocal-tract configuration for the final consonant.Examination of data from a number of vowels has suggested that the plotted pointsfor each formant of each vowel might be approximated by two parabolic segments, onefor the initial portion of the vowel and the other for the final portion. Each segment isof the form279% 1111 11111111111111111111i000oo  he'd ud S Ioo- 0000000000000000000000- 0000000000000000000000000000 1111 11111.01..0OLLU-0.5-)a0:U--'I 1-100 0 100TIME (MSEC)Fig. XV-4.:D0LLWLUFig. XV-5. FrfolforExample of parabolic curves used to specify vowel formantdata. The parameter is the "curvature value."2200180014001000--3 -2 -I 0 1 2 3 4 5 6CURVATURE VALUEequency F 2 0 vs curvature value for various vowels preceded andlowed by the consonant /d/. Each point represents average datathree talkers.280500CPS!I _64-0-4-6(XV. SPEECH COMMUNICATION)F i = ai(t-Ti)2 + Fi0.,where F i represents formant frequency, t is time, and ai, T i and Fi0 are parametersthat are selected to give a best fit; (i = 1 for the first formant and i = 2 for the secondformant). The parameter Fi0 represents the maximum or minimum value reached bythe formant, and T. indicates the point in time at which this maximum or minimum value1occurs. The parameter a i is a measure of the curvature of the formant, and can bepositive or negative. Figure XV-3b shows the parabolic curves that give good fits tothe data points plotted in Fig. XV-3a. The parabolic curves used in Fig. XV-3b wereselected from a set of curves similar to those shown in Fig. XV-4. The parametervalues on these curves will be called arbitrarily "curvature values."Curvature values and frequencies of Fl and F2 can be related either by examiningdata from various vowels in a given consonantal context or by examining data from agiven vowel in various contexts. These two ways of organizing the data are illustratedin Figs. XV-5 and XV-6.In Fig. XV-5 the maximum or minimum frequency of F2 is plotted against the curva-ture value of F2 for each of eight stressed vowels preceded and followed by /d/. Thereare systematic changes in curvature values from negative to positive as the frequencyof F2 decreases from high to low values, and this change differs slightly for the longand short vowels. The point of intersection of the two functions with the point of zerocurvature value is approximately 1700 cps; when the frequency of F2 for a vowel is lessthan 1700 cps its curvature value is positive, and conversely it is negative when F 2 isgreater than 1700 cps. In other words, the value 1700 cps describes the articulatory1.-c) on I.Z C0 c I.F uQ i.Fig. XV-6.5432.10-4 -2 0 2 4 6 8CURVATURE VALUESFrequency F 2 0 vs curvature values for one vowel in varioussymmetrical consonant contexts as indicated. Each pointrepresents average data for three talkers. The straight linewas fitted visually to the data.281f Z d.. f..Sv gS p bI I I I(XV. SPEECH COMMUNICATION)context provided by the postdental stop consonant /d/, that is, the so-called F2 locusof /d/ is at approximately 1700 cps. 3 ' 4In Fig. XV-6 the maximum or minimum frequency of F2 for a given vowel is plottedagainst curvature values associated with various consonantal contexts. The data displaya wide variation in curvature value, and there is a small but apparently systematicincrease in F2 as the curvature values become more positive. If the straight line canbe interpreted as representing a best fit to the plotted points, then the frequency 1220 cpscan be interpreted as the F2 value associated with the unperturbed vowel articulation,that is, 1220 cps is the so-called F2 target value of this vowel. When the curvaturevalue is negative, the maximum value of F2 is less then the target value; for positivecurvature values, the minimum value of F2 exceeds target value. In articulatory terms,this interpretation suggests that there is an effective inertia in the system that givesrise to undershoot in the articulatory processes.K. N. Stevens, A. S. House, A. P. Paul, Jane B. ArnoldReferences1. K. N. Stevens, H. Fujisaki, and A. S. House, Analysis of vowel spectra, Quar-terly Progress Report No. 60, Research Laboratory of Electronics, M.I.T., January 15,1962, pp. 177-179.2. A. S. House, On vowel duration in English, J. Acoust. Soc. Am. 33, 1174-1178(1961).3. P. Delattre, A. M. Liberman, and F. S. Cooper, Acoustic loci and transitionalcues for consonants, J. Acoust. Soc. Am. 27, 769-773 (1955).4. K. N. Stevens and A. S. House, Studies of formant transitions using a vocal-tract analog, J. Acoust. Soc. Am. 28, 578-585 (1956).C. ERRATAIn the report entitled "Reduction of Speech Spectra to Descriptions in Terms ofVocal-Tract Area Functions" by J. M. Heinz, published in Quarterly Progress ReportNo. 64 (pages 198-203), the numbers referred to in the legend of Fig. XXII-7 wereomitted from the figure. They read as follows:Fig. XXII-7a 244 (frequency)-1 (interval size = 2-1 cm)32 (number of interval)Fig. XXII-7b 852-132Fig. XXII-7c 2192-132. J. M. Heinz282

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