# Elemente der Funktionentheorie by Knopp K.

By Knopp K.

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The results obtained in this way are used both for endurance estimation and for dynamic analyses of the structures. Although such a general random process analysis is relatively complicated and time-consuming, fast modern digital computers with A/D converters have been used successfully in designing universal methods and programmes. This manipulation of random processes has thus been brought into practical use, except perhaps for non-stationary random processes, for which more investigations are needed.

10) is accepted. Be54 cause one can write 5(0) = ó 2 + ì 2 for a stationary process, it is highly improbable that the autocorrelation function will be a function of the absolute time for all time delays (lags) ô except the value ô = 0. Thus from the constant value of variance the stationary nature according the autocorrelation function is also deduced. This assumption is not inevitable, but substantially simplifies the practical test for stationarity because we need examine only the properties of the mean values and variances.

Example of sinusoidal cycle block forming based on level-crossing method. 10. Comparison of probabilities of occurrences of characteristic parameters of processes 1 and 2 from Fig. 08 O06p 0. CH OXKI II 2 48 O02 4 6 610 12 14161820 rLrM I 2 4 6 T? 3 fej COUNTING PROCESS 2 PROCESS 1 METHOD Ãº ! 15L.. 14 16 18 n. 20 i cr^Ü 2 A ao! J 12 H MAXIMA MINIMA li. jfl RELATIVE RANGE METHOD +020 hfl m. 10 +oû3-n Ð t) 10 12 fflJh 14 « 18 20 I h-i-i16 B 20 18 20 M-0J05 2 4 6 8 D ÐÔÃÊ, 12 U 16 From the point of view of practical analysis the counting methods have one important advantage: they can be applied equally well both to stationary and non-stationary processes and no tests are required for preliminary esti49 mations of their properties.