Patent GB-1062966-A (GB)
Title: Signal analyzer systems
IPC: G06F17/15
Filed: 1964-08-10
Abstract: 1,062,966. Electric analogue calculating. BOEING CO. Aug. 10, 1964 [Aug. 19, 1963], No. 32486/64. Heading G4G. [Also in Division G1] In an apparatus for analysing relationships between first and second signals applied as inputs to the apparatus, successions of time related values of one of the first and second input signals are added in a variable summing ratio to successions of time related values of the second signal, the latter succession of values bearing a predetermined time relationship to the former. The sum so produced and the first input signal are operated upon together to form intermediate signal values. From these values are detected the occurrence and polarity of deviations from a predetermined reference level of the mean product of the sum and the first signal. The variable summing ratio is varied in accordance with these deviations in a sense to maintain the mean product signal equal to the reference level, and the variations in the ratio are monitored. The Specification defines three functions, related to the correlation functions and power spectra functions normally used to analyse relationships between signals, which do not depend on the r.m.s. values of input signals or upon the magnitude of the correlation between, or the power common to, the two signals. The functions, which are said to provide more significant information than those previously made use of, are as follows:- (i) The correlation ratio function where # 12 (#) is the correlation function for various values of delay # between two time varying signals S 1 (t) and S 2 (t) and # 12 (##) is the correlation coefficient for a fixed reference delay ##. The reference is usually chosen according to the value of # for which R 12 (#, ##) is a maximum. (ii) The cross-power ratio function where C 12 (#) is the cross-power spectrum of two signals S 1 (t) and S 2 (t) for various frequencies # and C 12 (##) is the cross-power ordinate at a particular reference frequency ##. The crosspower spectrum C 12 (#) is derived from the correlation function by Fourier transformation, so that This function consists of real and imaginary parts and may be written To simplify calculation, the cross-power coordinate ratio function is defined as (iii) The cross-power function i.e. the ratio between the cross-power spectrum of two signals S 1 (t) and S 2 (t) to the mean square of the undelayed or reference signal S 1 (t). In an embodiment of the invention, relating to an arrangement for determining R 12 (#, ##), (Fig. 1) for two signals S 1 (t), S 2 (t), the two signals are applied at the inputs 10a and 10b respectively. Two variable delay arrangements 12 and 14, delay the signal S 2 (t) by # and # respectively. The system may operate with continuous input signals, in which case the delay arrangements may be a recording and playback system, or with sampled input signals. The delayed signals, S 2 (t + #) and S 2 (t + ##) are passed to an adder 16, the signal S 2 (t + ##) passing via a potentiometer circuit which provides a variable proportion K of the signal as output. It is arranged (by means of inverter 20) that K may vary between Œ1. The adding circuit 16 thus delivers a signal S 2 (t + #) + KS 2 (t + ##) which is supplied to the input B of a mean product polarity indicator 22, to whose other input A is supplied the undelayed signal S 1 (t). The unit 22 comprises a multiplier 24 and averaging circuit 26, so as to produce the mean product which is shown on the indicator 27. The wiper of the potentiometer 18 is adjusted so that the indicator shows zero deviation. Under these conditions, the factor K, shown on the potentiometer scale 31, is equal to the correlation ratio function, because The potentiometer may be adjusted automatically by means of a feedback loop (Fig. 1a, not shown). The function is generated over a period of time during which # remains constant while # is varied. # can be adjusted until the correlation coefficient # 12 (##) is a maximum. Since the only function of the main product polarity indicator is to indicate when, and in which polarity direction, the mean product of the input signals deviates from the zero reference, the multiplier 24 may be simplified. (Figs. 2 and 3, not shown). Alternatively, a quartersquare type arrangement may be utilized, wherein the A and B signals are added and passed to a squaring (or other non-linear) circuit and averaged and also - A and B signals are treated in the same way in a further circuit (Fig. 4, not shown). The difference between these signals, which is proportional to #AB, is used to control a null seeking servo arrangement which adjusts K as necessary. An arrangement for determining H 12 (#, ##), the power spectrum co-ordinate ratio function, is described with reference to Fig. 5 (not shown). This is similar to the arrangement already described, but with the inclusion of units in the paths from the variable delay units which weight the signals in the two channels by variable amounts g and #g. g represents the expression cos ## while g represents cos ##. In the evaluation of this function, all the parameters T, ##, #, ## are varied in cyclical fashion, i.e. # varies as well as T. It may be shown that the value of K, the setting of the potentiometer 18, when a null output is obtained from the mean product polarity indicator, corresponds to the required function H 12 (#, ##). It is arranged in the operation of the arrangement that the weighting functions g pass through at least three cycles of their own per cycle of delay time variation, and the variations in g are correlated with the associated delay time changes. A system for deriving one component of the cross-power function F 12 (#) is described with reference to Fig. 6 (not shown). In this arrangement the channel for computing a reference cross-power spectrum is omitted, and the signal S 1 (t) is applied to the potentiometer circuit. The signal derived from the adder 16 is therefore gS 2 (t+#)+KS 1 (t), and the system balances so that [S 1 (t)][gS 2 (t+#)+KS 1 (t)]=O, i.e. which is as required to provide the function F 12 (#).