抄録
When the autocorrelation function of an input signal to a system is Dirac's delta (δ-) function, the impulse response of the system is obtained as the crosscorrelation function between the input and the output of the system. In practice, however, there exist some cases where such an input signal cannot be used because of its lack of power, or because of poor frequency characteristics of the devices actually applying the input. In these cases the impulse response is not obtained simply from the crosscorrelation, but indirectly by a troublesome deconvolution. In the present paper a simple deconvolution method is proposed in which the impulse response is determined from a linear combination of the derivatives of the crosscorrelation function. The method is particularly simple when the autocorrelation function φxx(τ) is given as φxx(τ)=e-λ|τ| or φxx(τ)={1-|τ|/T(|τ|≤T) 0(|τ|>T)
This method does not require the function φxx(τ) to be the δ-function, but to be not differentiable at some τ's. Essentially, the method utilizes the δ-functions appearing when φxx(τ) is differentiated in the sense of the distribution proposed by L. Schwartz. The experimental values obtained by the computer simulation agree well with the theoretical ones, and the errors estimated are negligibly small.
