Quarterly Progress and Status Report. Phase dependent pitch sensation

Transcription

1 Dept. for Speech, Music and Hearing Quarterly Progress and Status Report Phase dependent pitch sensation Shupljakov, V. and Murray, T. and Liljencrants, J. journal: STL-QPSR volume: 9 number: 4 year: 1968 pages:

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4 STL-QPSR 4/1968 the property of mechanical selectivity. This means that for each frequency a given point along the membrane exhibits a maximum amplitude of vibra- tion. trauma, Similar inferences have been made from experiments on sound Direct measurements of the discharge of neurons indicate that only up to frequencies of Hz the firing of neurons is synchronized with the input frequencies. The inability of the neurons to generate im- pulses of high frequency provides strong evidence in favor of the spectral hypothesis. On the other hand, experiments by von B6k6sy show that traveling waves spread along the basilar membrane and histological studies point to the fact that receptors connected to the membrane are situated in a very regular pattern. In other words, there is a good reason to consider the basilar membrane as a delay-line with an enormous amount of outputs - an organization appropriate for a time analyzer. One of the most important effects of hearing, the binaural effect, is explicable only if one supposes that each hearing channel measures the phase of the signals not only at low frequencies, but also at frequencies above 1000 Hz. Experiments on the perception of pitch of high-pass and low-pass filtered white noise, Shupljakov (1 967), have shown that for cut-off fre- quencies of 1000 and 1500 Hz the noise signals have a pitch corresponding to these frequencies. In the present paper it is proposed that use is made of the fact that there is a traveling wave along the basilar membrane in order to answer the question whether phase information in signals of high frequencies is used in the auditory analysis. As is well known, von B6kesy made measurements on time delays which are needed for an input impulse to travel from the oval window of the inner ear to a certain point on the basilar membrane (see Fig. 11-A-1). These measurements show, that the sound waves spread along the basilar membrane with a decelerating velocity and the relation between the time delay on a logarithmic scale and a coordinate x along the membrane

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6 where a is a constant, and to is the time corresponding to the coordinate x where Eq. (1) begins to be fullfilled. 0 If the sinusoidal signal: 5 (t) = Asinwt is presented to the auditory system and on the assumption that no damping is present along the x coordinate, the distribution of amplitude as a func- tion of the x coordinate along the basilar membrane will be: 5 (t$ X) = Asin[m(t- T)] = Asin[w(t-too 1 O ~ ( ~ - ~ O ) ) ] (2) or for a fixed time t k: where A, kl, k2, and k are constants. 3 If we present to the ear two periodical signals of the following kind: 5 (t) = Asin[kl(l - kg 1okzt)] and 5 (t) = sin[ kl(l - k3 10-~2~)] i, e., differing only in terms of the sign of time, and choose the values of the coefficients kl, k2, and k3 so that the period of the signal will be smaller than 3 msec, i. e,, smaller than the maximal time delay of the basilar membrane, the distribution of the phases of these two signals a- long the basilar membrane will be different. Provided that the hearing system performs only spectral analysis on the basilar membrane level these two signals will not be distinguished by the subjects because the signals have the same spectrum. If the hearing device uses phase information, these signals will be perceived by the subjects as different signals. By changing the repetition rate of the signals it is possible to determine the boundary frequency above which the phase information is not used.

7 Method and results of the experiments A computer CD 1700 was used to generate the functions (4) and (5),* The computer calculated values of these functions in equal intervals of time, %ti qto 128 At and stored them in the core-memory. These values were then transmitted to the digital-analog converter at a frequency af 37,000 words per second. The generated curve could be observed on the screen of the oscilloscope. The values of the coefficients kl and k2 were fed into the computer with the aid of external controls. By observing the form of the curve on the screen it was possible to choose values for the coefficients that were most compatible with the aim of the experiment. Numbers from core-memory could be read either forwards (F) or in re- verse order (B). Therefore, signals quite identical except for the direc- tion of the time axis, could be generated. Three different forms of curves (forwards and backwards) were used in the experiments, namely: curves consisting of one, two, and three periods (Figs. 11-A-2 and 11-A-3). values of the coefficients k and k were chosen so as to make the final 1 2 value of the curves zero. The signals generated by the computer were recorded on magnetic tape. For this purpdse a 14-channel tape-recorder Ampex with frequency modulation was used. In arder t:, provide for a variable repetition rate on playback the signals from the computer were recorded on different tracks at the tape speeds of 3 3/4, 7 1/2, 15, 30, and 60 inches per second and reproduced at the speed of 60 inches per second. As a result, the repetition frequency of signals could be 292.5, 585, 1170, 2340, and 4680 Hz. The table for the tests contained 48 pairs of stimuli. The table con- tained four different versions of pairs: F-F, B-B, F-B, and B-F, which were recorded in random order. The number of pairs in the table with identical signals was the same as for non-identical signals. The duration of each stimulus and the interval between them were controlled by the com- puter and were exactly the same in all the pairs and fcr different speeds of the tape. The duration of each signal was 560 msec and the interval between them was 20 msec. Each pair was repeated twice, with an inter- val of half a second. For each repetition frequency a different list of stim- uli was recorded. The * The program was written by J. Liljencrants.

8 STL-CPSR 4/1968 REPETITION FREOUENCY Hz i Table 1. The mean values of the number cf wrong decisions in % for each repetitinn frequency and subject.

9 Fig. 11-A-2. Computer-generated signals used as stimuli in psychoacoustic tests on pitch perception. The three waveforms exemplify sinusoidal sweeps of varying frequency extent which all have the same repetition rate. As can be seen the range of the sweeps increase as we go from A, B, to C. The frequency change is from low to high. Fig. 11-A-3. Same as Fig. 11-A-2 but the frequency change is from high to low.

10 STL-QPSR 4/ As shown in Fig. 11-A-4 the spectra of the stimuli of the F-B type obtained with the help of a Kay Electric Sona-Graph, are identical. means, that the signals should not be distinguishable on the basis of spectral measurements. Four subjects took part in these experiments. This Their task was to in- dicate pairs with identical stimuli. The experiments were carried out in a soundtreated chamber, Head-phones of type Koss were used for listen- ing. The intensity of the signals, in order to eliminate nonlinear distor- tions, was chosen around 60 db above the absolute threshold of hearinz. Every list was repeated five times. every repetition frequency was thus 240. The general number of stimuli for The number of wrong decisions for every repetition frequency is given in Table 11-A-1 as a percentage. It can be seen from the table that the subjects distinguished correctly the pairs of signals having different directions from the pairs of signals having the same direction at all the repetition frequencies, including 4680 Hz. increases. The number of wrong decisions rises when the repetition frequency Discussion The experiments carried out suggest the interprctatf:n that use was made of a phase information in signals whose repetition frequencies was increased in steps u;? to Hz. It is quite natural t3 assume that a sim- ilar mechanism ic use2 als? in 2erceiving signals more like everyday sounds. What parameter of the traveling wave could correspond to the perceived pitch of a pure tone of the period T? Taking Eq. (1) into consideration the following relationship exists be- tween the length of the first wave hl counting from the oval window along the x axis and the period T: tott lg-= a(h tx -x ) = to l o o aal During a time interval equal to two periods the wave will travel a distance, equal to two wave lengths, i. e. :

11 khz 1.0 sec. Fig. 11-A-4. Spectrograms of waveforms shown in Figs. 11-A-2 and 11-A-3. In the left member of the pair the frequency change of the (~eriodicall~ repeated) sinusoidal sweep is from low to high. In the right case it occurs in the opposite direction. Note the identical spectral structure.

12 Or by taking (6) into account, the value of A2 is: For t <4 T, A2 is equal to: 0 (9) For the length of the n-th wave: or given condition (9) the length of each wave except the first, is equal to The equations (6) and (12) show that only the length of the first wave, counting from the oval window, depends on the frequency of the entering acoustical signal, The lengths of the other waves depend only on the number of the wave. Different parameters of the traveling wave can be chosen as a possible correlate of the pitch of tones. In the case when one measures the position of the points, at which the phase shift from the oval window is equal to 2n, the linear relationship as specified by Eq. (6) will be maintained. Similar relationship.was obtained in the experiments by Tasaki, Davis, and Legouix (1952) who measured phase differences of the microphonic responses between the outputs of electrodes at various positions along the basilar membrane. A similar mechanism was proposed by Huggins (1952). To have the analysis work according to this principle, the existence of some sort of connections between the beginning of the basilar membrane and every point along its length is necessary. It seems to be simpler to measure the length, for example the second wave, i.e. the wave between phase shifts of 217 and 4n. The length of this wave is invariant with different frequencies, it only changes its place. In this case, the mechanism, measuring the wavelength, must be the same over the whole length of the membrane.

13 STL-CPSR 4/ wave. It is necessary to draw attention to another peculiarity of the traveling At a frequency f', which is twice as small as the frequency f, the length of the first wave A', is acc~rding to Eqs. (6) and (7) equal to Since for every frequency the length of A 2 is the same and equal to the length :f the second wave A' is also equal to A +A4, i. e., the length 2 4 of the second wave corresponding to the frequency - f is equal to the sum 2 of the third and the fourth waves corresponding to the frequency f, which is an octave higher. Provided that a mechanism measuring wave length actually exists in the hearing process, the reason why the two frequencies differing by one octave are perceived as similar signals becomes clear. This phenomenon is very difficult to explain from the point of view of spectral hypothesis. It seems appropriate to consider another fact well-known from the literature, which until now has been very difficult to explain. It concerns the fatigue curves measured by Gershuny (1949). A very strong tonal signal (125 d ~ was ) given to the subject's ear during five minutes. Imr~e- diately after this the threshold intensity of the tones was measured by dif- ferent frequencies. In the case when the perception of the pitch of the tone is connected with the point on the basilar membrane, which is vibrating with maximum amplitude (spectral hypothesis), the fatigue curves must have a maximum coinciding with the frequency of this tone. However, the experiments have shown that the maximum of the fatigue curves does not coincide with the frequency of the strong tone but is as a rule situated higher on the frequency scale. In view of the wave length hypothesis such a result seems quite natural. According to the measuriments by von B&k6sy, the position of the excita- tion maximum is situated at a place corresponding to a phase shift of ZIT. 3 This means, that the maximum is situated closer to the oval window or higher on the frequency scale than the second wave.

14 STL-QPSR 4/ The main argument against such point of view is the fact that the vibrations of the basilar membrane partitions just after the maximum are strongly damped. This has been shown many times by data on masking. But at the same time Tasaki, Davis, and Legouix (1952) could measure with certainty phase shifts up to 5n. References: (1) von BBkCsy, G, : Experiments of Hearing ( ~ew York 1960). (2) Gershuny, G. V.. "About the Changes of Hearing Function by the Action of Sound", Problems of Physiological Acoustics - 1 (1949), pp (in ~ussian), (3) Huggins, W. H. : "A Phase Principle for Complex-Frequency Analysis and its Implications in Auditory Theory", J, Acoust. Soc. Am, - 24 (1952), pp (4) LicMider, J. C. R. : "' Periodicity' Pitch and ' Place' Pitch", J. Acoust. Soc.. Am, - 26 (1954), p. 945(~). (5) Miller, G. A. and Taylor, W. G. : "The Perception of Repeated Bursts of Noise", J. Acoust. Soc. Am (1948), pp (6) Ohm, G. S.?' fiber die Definition des Tones, nebst daran gekniipfter Theorie der Sirene und ghnlicher tonbildender Vorrichtungen", Ann. Physik (1843), pp (7) Shupljakov, V. S, : "Analysis of Stationary Fricative Cons~nants by Hearing", thesis work in Russian (1967). (8) Tasaki, J., Davis, H., and Legouix, J.P. : "The Space-Time Pattern of the Cochlear Microphonics (Guinea pig) as Recorded by Differential Electrodes", J.Acoust.Soc.Am. 24 (1952), pp