Theorem on Stieltjes correlation

A theorem on Stieltjes correlation is formulated, in which it is shown that, in theory, Stieltjes correlation techniques do not produce any distortion of the true correlation function, provided that the two inputs are stationary, ergodic and have a normal joint distribution function. The errors due to finite averaging time are discussed, and it is shown that an analytical evaluation of the signal/noise ratio of a practical Stieltjes correlator requires knowledge of the autocorrelation function of the product function, which is dependent on the quantiser characteristics.