LXX.Some relations between transient phenomena in systems with similar frequency characteristics

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Abstract
The accurate determination of the transient response to a given excitation in a linear system requires the knowledge of the whole frequency characteristic. In physical systems this knowledge is of limited accuracy, and is restricted to a part of the frequency scale. Some relations between the limitations of a frequency characteristic and the associated transient errors are discussed. The results apply equally to the method of substituting a similar frequency characteristic in order to facilitate the calculations of transients, which is used in technical applications. Upper limits are obtained for the errors of transient responses to prescribed excitations when upper limits are given for the errors of the characteristic in limited frequency ranges, and when some relatively inferior information is supplied about the rest. In most cases the resulting error limits do not apply to the transients directly, but to related quantities obtained by a mean value process. By the application of this process the frequency ranges of main information are given that additional prominence which is required for obtaining sufficiently definite results.