In this paper, the vibration system of a piano string and a sound board (Fig. 1) is analyzed by the finite element method (Fig. 2). The string is stretched with constant tension P between the upper bearing and the lower bearing, and is assumed to be completely flexible. The mass point m are distributed along the string at equal distances, and m_1 indicates the upper bearing, m_&lt103&gt the lower bearing, m_&lt97&gt the equlivalent mass of the sound board, and k the spring constant. It is also assumed that the mass-point of the hammer m_H collides with the point m_N on the string with an initial velocity x^^^. _H, that they repel each other according to Newton's law, and that m_N is decelerated by the tension P. Then it collides with m_H again, and this series of motions is repeated. These motions of all points m_i, m_H, m_N are expressed by Eqs. (1), (2), and (3). The flow diagram of the program is shown in Fig. 6. The calculated values by this simulation program and the measured values of an actual piano are presented in Figs. 7 and 8. Comparisons between them show good agreement.

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For the observation and development of undersea resources reliable transmission of information underwater is a necessary prerequisite. Recently a grate deal of effort has been expended in the design and development of underwater acoustic telephone equipment. It can be foreseen, however, that there will be a demand for the transmission of digital as well as analog information underwater in the near future. The efficient transmission of digital information underwater may be accomplished by using such a specific data transmission system as the PSK system, as is the case with digital data transmission on the ground. An appealing alternative, when the required rate of transmission is not too high, is to utilize acoustic telephone channels as the transmission medium for the digital information. Modulation techniques that can be used for the acoustic telephone system include AM, SSB, FM, PM, PPM, PCM, etc. However, if, in the design of such a system, the important design criteria include low cost and simplicity, as is the case with underwater communications equipment, then PPM is a logical choice for the modulation technique. Although Gaussian noise processes are common sources of interference in communication problems, background noise of impulsive character also occurs frequently in underwater acoustics. The aim of the present paper is to study the effects of the mixtures of Gaussian and impulse noise accompanying acoustic signals on the probability of bit errors that occur when binary data are transmitted via a PPM acoustic telephone channel. A block diagram of the modem that is used for the analysis is shown in Fig. 1. Section 3. 1 presents the derivation of an approximate expression for bit error probability due to impulse noise. A simple noise model for the impulse noise referred to as the Poisson noise model is employed. First, a pdf(probability density function)for the time of occurrence of the anomaly in the i-th frame is obtained and then it is converted to the pdf p(V) of amplitude V of the PAM pulse in the i-th frame (eq. (14)). The pdf p(V^^^~) given in eq. (24) of the demodulator output V^^^~ which is a weighted sum of overlapping filtered PAM pulses is calculated with the help of a characteristic function (20) and semiinvariants (22) Two kinds of error probabilities P_r(e|S) and P_r(e|M) are finally obtained in eq. (28). Section 3. 2 and 3. 3 deal with the bit error probabilities due to Gaussian noise and the mixtures of Gaussian and impulse noises, respectively. The method of analysis is similar to that of Section 3. 1. In Chap. 4 some results of numerical calculation of the error probability expressions are presented graphically (Fig. 10). One can observe the threshold characteristic and the effect of impulse noise on the error probabilities.

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The behavior of adaptation-type neurons to unsteady sounds (tone bursts, amplitude-modulated tones, frequency-modulated tones and combinations of these) was investigated using an electronic model of the auditory nervous system (Fig. 1). When a tone burst is applied to the model, the response of the adaptation-type neurons with CF approximately corresponding to the stimulus frequency gradually reduces after an initial response. However, the response of the neurons distributed at the peripheral part of the responding neurons is phasic, in spite of the fact that the neurons are of the same response type (Fig. 6). That is, a neuron behaves differently according to the relation between the stimulus frequency and the C. F. of the neuron. This phenomenon is observed in the responses of primary and secondary neurons of the sustained type (Fig. 3, 4, 5). Furthermore, for a tone burst with two Frequency components, the response of the adaptation-type neurons varies from adaptive response to on-response depending on the frequency interval and the relative intensity of the two components (Fig. 7). In the adaptation-type neuron model, the coefficient and time constant of the inhibitory connections are greater than those of the excitatory connections, so that the end part of the response of the secondary neuron is suppressed and the duration of the response is shorter than that of the input stimulus (Figs. 8 and 9). For an amplitude-fluctuated tone, therefore, the adaptation-type neuron behaves so as to segment its response at each peak point (Fig. 10). Such a function is one of the important signal processing functions of the adaptation-type neuron and is characterized as temporal sharpening. In the response of the sustained-type secondary neuron to a compound tone that is composed of a pure tone and a frequency-modulated tone the frequency of which changes toward that of the pure tone, the response to the pure tone and to the FM tone are separated spatially in the response pattern. This is the effect of spatial separation. Furthermore, the response to the pure tone is segmented in a temporal response pattern, since the neuron is inhibited when the FM tone is in the inhibitory area. This is the effect of temporal segmentation (Fig. 11, 12). Adaptation-type neurons emphasize the spatial separation and the temporal segmentation. It is concluded that the behavior of the auditory upper nervous system is to funnel the response at the neurons with CF corresponding to the frequency components of the stimulus and to segment temporally the response to the sequential stimulus.

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M-sequence method and pulsed method giving range resolution to Doppler method are being applied to the measurement of blood velocity profile in a human heart. In these methods, however, the product of maximum Doppler frequency and measurable range is limited to less than half the sound velocity in the medium. To remove this limitation, two methods named double M-sequence Doppler method and M-sequence pulsed Doppler method were devised. In experiments with a model target, Doppler signals of reflected wave from desirable distance were successfully obtained, separating these signals from signals of targets at undesirable distances. An elementary ultrasonic Doppler system with range resolution is shown in Fig. 1. The carrier signal generated by an oscillator is modulated with a pseudo-random signal, and applied to a transmitter. The received signal from reflective bodies is demodulated with a delayed pseudo-random signal. After filtering the output of the demodulator, a Doppler signal is detected. An M-sequence signal shown in Fig. 2 can be used as a pseudo-random signal. Owing to the power spectrum of this signal, shown in Fig. 3, the product of maximum Doppler frequency and measurable range is restricted by the relation (5). In case of pulsed Doppler method, the same relation holds. When this limitation is disregarded, undesirable signals will be dominant. In order to overcome this difficulty, two methods are devised. These methods reduce undesired signals to a level enabling measurement of the Doppler velocity of the desired object. One is the double M-sequence Doppler method with the signal shown in Fig. 4(c). This method expels a great part of the undesired signal power from the measuring Doppler frequency band (Fig. 5). The other is the M-sequence pulsed Doppler method with the signal shown in Fig. 8(b). In this method, a gate does not let great undesired signals into the receiver. For the test of these methods, a steel ball of 10mm in diameter was moved back and forth from 6. 5cm to 10. 5cm in front of the oscillator surface. The Doppler signal from the ball was analysed. Fig. 9(CW) shows the Doppler frequency in case that a continuous sinusoidal wave is transmitted. With the double M-sequence method, the Doppler signal at the range of 9cm is obtained intensively as shown in Fig. 9(DM1). Fig. 9(MP1) and (MP2) show the signal from the ball at 9cm, and the signals from other ranges disappear or are dispersed.

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