1407234 Measuring voltage; power and crosscorrelation using random waveforms NORMA MESSTECHNIK GmbH 3 Aug 1972 [3 Aug 1971] 36288/72 Heading G1U [Also in Division G4] Various functions of one or more unknown voltage waveforms are produced by the use of a random waveform having known statistical properties. The Specification shows that if an unknown voltage waveform e(t), Fig. 5a, shown for example as being a cyclic pulse train, is compared with a random waveform v(t) at regularly spaced instants t 1 , t 2 , t 3 , . . ., Fig. 5b, to produce a pulse train z(t k ), Fig. 5c, having a pulse in those time slots t k in which the unknown waveform e(t) exceeds the random waveform v(t), and no pulses elsewhere, then if the resulting waveform z(t k ) is averaged, using for example, a trigger circuit 9, Fig. 6, and an RC circuit, the resulting D.C. voltage Mz will be related to the unknown waveform e(t) in a manner which depends upon the statistical characteristics of the random waveform v(t), and in particular that if the random waveform is stationary and ergodic with a uniform amplitude distribution then the D.C. level Mz will be proportional to the long term arithmetic mean of the unknown waveform e(t). An arrangement for performing this process is outlined using a random waveform generator 4', Fig. 4b, a comparator 8, a sampler 6 controlled by a clock 7, and an averaging circuit 5 to produce the D.C. level Mz. The Specification also shows how the outputs Z 1 , SPZ/SP 2 , Fig. 7a, of two such circuits receiving unknown waveforms e 1 (t) and e 2 (t) can be combined, providing the random waveform generators are stochastically independent of each other, in a 'not-equivalent' circuit 10 to produce a pulse train z(t k ) having a long term average which is a linear function of the long term mean of the product of the unknown waveforms e 1 (t) and e 2 (t). The legend on Fig. 7a omits the additive and proportionality constants. Finally the Specification shows how it is possible, using combinations of the circuit shown in Fig. 7a, to obtain the square root of the mean of the product of two waveforms e 1 (t) and e 2 (t). Fig. 8a, and hence the r.m.s. value of one waveform, the quotient of the means of two waveforms e 1 (t) and e 2 (t), Fig. 9 (not shown), the correlation coefficient between two waveforms e 1 (t) and e 2 (t), Fig. 10 (not shown) , and the mean of the modulus of a waveform e(t), Fig. 1 la (not shown). The method utilized for evaluating these quantities is typified by a circuit, Fig. 8a, for producing the square root of the mean of the product of two waveforms e 1 (t) and e 2 (t). The unknown waveforms e 1 (t) and e 2 (t) are applied to an arrangement 1 la, 11b, 12a, to produce a pulse train Z as in Fig. 7a, which is averaged 14a, to give a DC level of the form a+be 1 (t)e 2 (t)'. Simultaneously a waveform U R is applied to an identical circuit 11 'a, 11 'b, 12b and 14b, to produce a D.C. level of the form a+bUrSP2/SP, and the waveform U R is adjusted by comparing the D.C. levels so that the D.C. levels are equal, i.e., so that UrSP2/SP=e 1 (t)e 2 (t). Hence the output Z 4 from unit 11'b, which has an average value equal to Ur, equals #e 1 (t)e 2 (t), Ur being constrained to be positive.
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