MEMSTECH’2011, 11-14 May 2011, Polyana-Svalyava (Zakarpattya), UKRAINE Rapid Version of a Formant-Modulation Method of Speech Intelligibility Estimation Arkadiy Prodeus Abstract – In this paper researches of a rapid version of D and with power spectrum, which is like long term speech a formant-modulation method of speech intelligibility ξ estimation are made. It is shown that the version makes it spectrum; ⋅ is expectation symbol. possible to reduce estimation time in fourteen times. As well as in a method STI, they use a discrete set of 14 Keywords – Speech intelligibility, formant-modulation modulation frequencies (F = 0,63, 0,8, 1, 1,25, 1,6, 2, 2,5, method, rapid version, estimation. i 3,15, 4, 5, 6,3, 8, 10, 12,5 Гц) in full version of FM-method I. INTRODUCTION and estimate the effective perception level E of speech k A new instrumental method of speech intelligibility signal in accordance with equations estimation was offered in works [1, 2]. It was called "formant- Ek =SNRk , (5) modulation method" as it was supposed that it will unite better 1 14 features of formant [3] and MTF [4] methods. It was shown in SNRk = ∑SNRk,i , (6) work [5] by means of analytical and experimental researches 14i=1 that formant-modulated (FM) method is efficient and m (F ) sufficiently precise. At the same time the method is SNRk,i =10lg k i , (7) 1−m (F ) insufficient effective in the sense that it demands k i comparatively a lot of time for measurements – from two up mk(Fi ) is modulation coefficient of variance Dyik(t) of to four minutes. It is inconvenient when measurements are signal y (t): ik supposed to be made in music halls which are filled with ∞ listeners. y (t)= ∫h (v)x (t−v)dv+n(t), (8) It is shown in the work that the pointed drawback can be ik ek i −∞ eliminated by using test signals which are similar ones of used ∞ in RASTI method [6]. h (v)= ∫h(v)h (z−v)dv, ek k0 II. FM-METHOD: FULL VERSION −∞ h(v) is room impulse response (IR) and h (v) is band- k0 When using FM-method [1, 2], they calculate articulation pass filter IR for k-th frequency band. intelligibility A in the same way as in a formant method [3]: Because of harmonic nature of modulation of variance (4) K of test signal (2), it is expedient to produce estimation of A=∑p ⋅P (E ). (1) k k k modulation coefficients m (F ) by means of Fourier k i k=1 transformation: where p is formant probability distribution on frequency k 2A (F ) bands; Pk(Ek ) is speech perception coefficient; Ek is m~k(Fi )= ik i , (9) A (0) effective perception level of speech signal in k-th frequency ik band ∆f . T k A ( f )= 1 ∫y2(t)e−j2πftdt, (10) In full version of FM-method, as well as in a method STI ik ik T [4], they use non-stationary stochastic test signal x (t), 0 i ⋅ is absolute value symbol; T is duration of test signal variance of which D (t) is modulated on harmonic law with xi x (t). modulation frequency F : i i It is shown in [5], that acceptable for engineering x (t)=ξ(t) f (t) , (2) i i appendices accuracy of measurements can be reached upon fi(t)=1+cos2πFit. (3) test signal (2) durations near T =16K32s. Meanwhile, in D (t)= x2(t) − x (t) 2 = D (1+cos2πFt), (4) order to realize full measurements cycle it is necessary repeat xi i i ξ i radiation of a test signal for 14 times, changing modulation ξ(t) is stationary stochastic process with variance frequency F each time. It follows from this that in the full i Arkadiy Prodeus – Electronics Department, National Technical version of the FM-method, as well as in method STI, for University of Ukraine (Kyiv Polytechnic Institute), 9/16, Ac. realization of a full cycle of measurements it is required not Yangelia Str., Kyiv, 03056, UKRAINE, E-mail: less than 2…4 minutes. These time expenses at first sight [email protected] seem quite comprehensible. However if it is a task of acoustic examination of intensively maintained concert halls, such time MEMSTECH’2011, 11-14 May 2011, Polyana-Svalyava (Zakarpattya), UKRAINE of measurements can already be near-critical to value, or even p P + p P + p P P = 125 125 250 250 500 500 , inadmissible, especially if measurements are made in a hall 1 p + p + p 125 250 500 filled with listeners. p P + p P + p P + p P P = 1000 1000 2000 2000 4000 4000 8000 8000 , III. RAPID VERSION OF FM-METHOD 2 p1000 + p2000 + p4000 + p8000 P ,P etc. are perception coefficients of octave frequency As it is known [6], it is possible to reach 14-multiple 125 250 bands with the central frequencies of 125 Hz, 250 Hz etc., reduction of time of measurements in method RASTI by using accordingly. a special test signal: x(t)= x (t)+x (t)=ξ(t) f (t)+ξ (t) f (t) , (11) 1 2 1 1 2 2 t 2t 4t 8t f (t)=1+0,4(sin2π +sin2π +sin2π +sin2π ), (12) 1 T T T T 1 1 1 1 t 2t 4t f (t)=1+0,32(sin2π +sin2π +sin2π + 2 T T T 2 2 2 , (13) 8t 16t +sin2π +sin2π ) T T 2 2 ξ(t) and ξ (t) are results of a filtration of pink noise by 1 2 octave filters with the central frequencies 0,5 and 2 kHz, accordingly; T =1s, T =1,43s. 1 2 Obviously, similar reception should be used also at creation a of the rapid version of the FM-method. At the same time, it is possible to show that direct loan of the idea of RASTI method doesn't lead to desirable results. Really, at creation of the rapid version of the FM-method it is reasonable to demand reception of the same, on the average, results of measurements, as for the full version of the FM- method. However modeling researches testify that it is almost impossible to reach such coincidence by using of only two frequency bands (instead of seven octave frequency bands used in the full version of the FM-method). Let's look at results of such modelling researches. Experiment 1 Perception coefficients P (E ) for two octave bands with k k the central frequencies of 0,5 and 2 kHz were used in the first experiment, and probabilities of formant distribution on b frequency were calculated as follows: Fig. 1. Experiment 1: rapid (a) and full (b) versions of FM-method p = p + p + p +0,5p , (14) 1 125 250 500 1000 p = p + p + p +0,5p , (15) 2 2000 4000 8000 1000 p , p and so on are probabilities of being formants in 125 250 octave frequency bands with the central frequencies of 125 Hz, 250 Hz etc., accordingly. Calculation results of wordy speech intelligibility are shown on Fig. 1. When comparing diagrams of Figs. 1,a and 1,b we can conclude that the received results can't be considered as the satisfactory. Experiment 2 Unlike Experiment 1, the weighted average values of perception coefficients P (E ) were used here: k k Fig. 2. Experiment 2: rapid version of FM-method Appropriate calculation results are shown on Fig. 2. As we can see, the results can't be considered as the satisfactory too, MEMSTECH’2011, 11-14 May 2011, Polyana-Svalyava (Zakarpattya), UKRAINE because of diagrams essentially differ from proper diagrams When increasing the analysis time from 16 s up to 32 s, on Fig. 1,b. outcomes of rapid and full versions of a FM-method are close Despite evident failure of attempt to direct taking of method and appear quite satisfactory for engineering applications RASTI idea, decision of the task exists. It is easy to come to a (Fig. 4). conclusion that, for coincidence of results of fast and full The reason of reduced accuracy of a rapid FM-method is versions of the FM-method, it is necessary to spend simple and evident. Only 5, instead of 14 in full version of a measurement in all frequency bands. Thus only the idea of use FM-method, modulation frequencies are used in the rapid of a test signal in the form of the sum of several harmonics is version of a FM-method. It results in rise of a variance of a borrowed from method RASTI. signal-to-noise ratio estimation and, as a corollary, in rise of a Following variants of realization of the rapid FM-method variance of speech intelligibility estimation. are thus possible: − test signal (12) or (13) is used in all seven frequency REFERENCES bands; [1] A. Prodeus, “On Some Evolution Features of Objective − test signals (12) and (13) are both used with alternation Methods of Speech Intelligibility Measurements,” them in frequency bands by some rule. Electronics and Communication, thematic issue The first variant, with usage of a test signal (13), is looking "Electronics and Nanotechnology," 2010, №2, pp.217-223. as simplest for implementation. Thus the modulation [2] A. Prodeus, “On Possibility of Advantages Join of frequencies range from 0,7 Hz up to 11,2 Hz is practically Formant and Modulation Methods of Speech Intelligibility coincides with modulation frequencies range of STI method. Evaluation,” Proceedings of the VI International The calculations outcomes for this variant are shown on Conference MEMSTECH, Lviv, Polyana, 2010, pp.254- Fig. 3. Comparing the obtained results with the diagrams of a 259. Fig. 1.b, we can see that the outcomes of calculations are very [3] N.B. Pokrovskiy, “Calculation and Measurement of close. However there are also some peculiarities: 1) all curves Speech Intelligibility,” M.: Sviazizdat, 1962, 390 p. differ a little from zero at small signal-to-noise ratios; 2) the [4] H.J.M. Steeneken and T. Houtgast, “Basics of the STI- estimation of wordy intelligibility appears overstated measuring method” approximately on 2 % for a white noise. (http://www.steeneken.nl/sti/Basics_STI_web-site.pdf) [5] A. Prodeus, “Formant-Modulation Method of Speech Intelligibility Evaluation: Measuring and Exactness,” Proceedings of the VII International Conference MEMSTECH 2011, Lviv, Polyana, 2011, Даний збірник праць. [5] H.J.M. Steeneken and T. Houtgast, “RASTI: A Tool for Evaluating Auditoria” (http://www.bksv.com/doc/technicalreview1985-3.pdf ) IV. CONCLUSION It is shown the existence of fundamental possibility of essential, in 14 times, reduction of measurements time of speech intelligibility at usage of a FM-method, which allows speaking about existence of the rapid version of a FM- Fig. 3. Rapid version of FM-method for T =16 s method. The outcomes of modeling testify, that the rapid version of a FM-method concedes the full version of a FM-method on accuracy. Thus upon T =16 s the difference had reached 2% in case of a white noise. The difference is practically imperceptible in case of colour (pink and brown) noises, and upon T =32 s it is practically unessential for a white noise too. Fig. 4. Rapid version of FM-method for T =32 s