A new method of determining correlation functions of stationary time series

The paper presents what is believed to be a new approach to the problem of determining correlation functions of stationary time series. The method is based on an expansion of the correlation function in a suitable orthonormal system. The coefficients in this expansion are shown to be simply related to the convolution integrals which arise when the given time series are applied to linear filters whose impulse responses are members of this orthonormal system. A very simple scheme for measuring these coefficients is proposed. It is further shown how a complex filter, whose impulse response is of the same shape as the desired correlation function, can be built up in a systematic way when these coefficients have been determined. Two examples of filter systems whose impulse responses are members of a Laguerre system are presented, and finally a description of a practical auto-correlator built around one of these filters, and some results obtained with it, are given.