スピーカのシステム関数の一測定法

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The measurement method for obtaining the system dynamics of a loudspeaker in the form of the system function is discussed assuming that the loudspeaker is a linear time invariant system. Generally, in a linear time invariant system the relation between the input to the system and the output from it can be represented by its impulse response or its system function. The measurement method of the system function in a frequency domain has some characteristic comparable to these of the impulse response in a time domain. Namely, since the stationary continuous signal is used as the input test signal, the measurement can be performed without the confluences of loudspeaker non-linearity and the measuring system noise. On the other hand, the difficulty of phase measurement comes into question. In this paper, since there exist only a relation between the phase characteristic and the group delay characteristic, the theory of the simultaneous measurement for the amplitude frequency characteristic and the group delay frequency characteristic is investigated to obtain the system function. In this case, the balanced modulated signal as indicated by eq. (2) is used for the input test signal. When the input signal f(t) is introduced into the system, its response signal g(t) is indicated by eq. (8). Using the assumption of eq. (9) and approximation of eq. (10), appearing in the result, g(t) can be represented by eq. (11). Accordingly, A(ω_0) can be measured by comparing the maximum envelope amplitude of g(t) with that of f(t), using the block diagram as shown in Fig. 1 (a). Furthermore, τ(ω_0) can be measured by comparing the time delay between the envelope of f(t) and that of g(t), using the block diagram as shown in Fig. 2 (a). By means of these measurements for all measurable frequencies, it is posiible to obtain the system function. Next, the possibility of the above measurements, in case the amplitude characteristic is subjected to wide fluctuations as a loudspeaker, is investigated. In such a case, the response signal g(t) for the input test signal is indicated by eq. (14), and its waveform is shown in Fig. 5. In this case, since the maximum envelope value of A_1 and A_2, it is seen that A(ω) can be measured with good approximation by selecting a sufficiently small Δω. When the envelope waveform of g(t) is analyzed into its frequency components by using the Maclaurin expansion, eq. (17) and eq. (18) are obtained. As is clear from these equations, since the time delay of the 2Δω component of g(t) is equal to τ(ω_0) as compared with that of f(t), the measurement of τ(ω) presents no problem. The measuring apparatus for the system function was made, based on the theory of the simultaneous measurement for A(ω) and τ(ω). This fundamental block diagram is shown in Fig. 7. The parts for the A(ω) measurement and τ(ω) measurement are used respectively in the block diagrams shown in Fig. 1 (a) and Fig. 2 (a). Measurement results are converted from analog values to digital values and can be used as input data of a digital computer by OFF-LINE intermadiated by punched papaer tape. Fig. 8 (a) and Fig. 8 (b) are one example of measurement results. In addition, echo distortion caused by group delay characteritic has been taken into consideration.
社団法人日本音響学会の論文
1978-05-01

スピーカのシステム関数の一測定法

スポンサーリンク

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