非線形最適化手法による音響放射系のインパルス応答の合成

抄録

An acoustic radiation system like a loudspeaker can be thought as a linear time invariant system. In this paper, it is tried to express the impulse response mathematically. It is generally difficult to find out analytically the impulse response of such system, but it is very significant to get the mathematical expression of the system characteristics. Accordingly, a mathematical expression of the impulse response of the acoustic radiation system is introduced as a sum of many decayed sine waves which have different frequencies, phases, amplitudes decay factors and time delays, respectively. In order to determine the values of these five kinds of unknown parameters, a nonlinear optimization method is used. At first, the impulse response is practically measured, then each optimum value of unknown parameters of the synthesized impulse response is looked for by means of the Hooke-Jeeves' method. These optimum values can be obtained when the mean square error between the synthesized and measured waveform becomes minimum. As a result of an experiment about edge-clamped circular p;ate radiator with baffle board, the impulse response of the system can be expressed mathematically by a sum of fourteen decayed sine waves. In this case, the error factor indicating the degree of agreement between the synthesized waveform and measured one shows the value of 1. 25%. For an applied example, it is shown that the pole-zero configuration of system can be obtained from the mathematical expression of the impulse response.