System for Measuring Cross Power Spectra or Cross Correlation Function

摘要

1,179,711. Evaluating correlation functions. USTAV PRO VYZKUM MOTOROVYCH VOZIDEL. Feb.21, 1967 [Feb.22, 1966], No.8143/67. Heading G1U. A system for developing co-efficients for use in evaluating the cross power spectrum or cross correlation function of two functions x(t), y(t), incorporates two phase shifting networks 2, 5 to which the two functions are applied as inputs, the phase shifters operating to establish a phase difference of either m# or (2n + 1)#/2 between the two functions, which are then combined in an adder 7. The outputs from the adder are passed to a band pass filter set 9 whose output is applied to an r.m.s. detector 11. It may be shown that the cross power spectrum Sxy(jwo) may be calculated from the two r. m. s. values M 1 , M 2 derived from the arrangement for the inphase and quadrature settings of the phase shifters respectively in accordance with the equation: Where A, B are the transmission constants of the system and Wo is the mean angular frequency in the transmission band, #f of the filter set. Alternatively by determining M 1 and M 2 in the different frequency bands within the range covered by the filter set, the cross correlation function may be determined from the expression: where M 1 (W oi ) and M 2 (W oi ) are the in phase and quadrature outputs in frequency band i, N is the number of filters and W hi , W di are the upper and lower limit frequencies of the band i.