Waveform computations by the time-series method

Compared with conventional means the time-series method offers a great reduction of the computing work involved in solving many of the practical waveform or ¿transient¿ problems of cascade-connected linear 4-terminal networks. The basis is that any waveform arising from a system of limited bandwidth can be represented exactly by a time series, or sequence of equidistant ordinates of the waveform, having an interval equal to half the reciprocal of the bandwidth. It is pointed out that the advantages of the method can be exploited, not only when a limitation of bandwidth is a physical property of a given system, but also when a limitation arises merely from a restriction of interest in the performance of the system to a given range of frequency. Such a restriction can be applied to a waveform by an arithmetical filtering process without recourse to spectrum analysis. An elementary description is given of practical procedures for dealing with time series, including serial multiplication (equivalent to convolution), serial division, differentiation, integration, filtration and an interpolation method for reconstituting a waveform from its time series. These are illustrated by examples chosen from the field of television transmission.