A simplified method for detecting information on linear correlation latent in random noise or vibration waves

It is well-known that linear correlation information is very useful in establishing the statistical properties of random noise or vibration waves. As the amount of data increases, however, calculating the linear correlation function by the usual multiplicative operations for large amounts of data can be very troublesome, and so some simplified practical methods of detecting the correlation function are desirable. In this paper, a practical method of detection of a linear correlation function latent in random noise or vibration waves is proposed, based on use of the conditional probability distribution. First, a general expression for the bivariate joint probability distribution for discrete level sampling is introduced in the form of a series expansion in orthonormal functions. The expansion coefficients give principally the information on linear and non-linear correlations, so that a general expression for the correlation function can be derived by conditional averaging. A new simplified version of this detection method is then presented, which does not require higher order statistical information. Finally, the effectiveness of the method is confirmed experimentally by applying it to some actual street noise in Hiroshima City.