Lineare Systeme mit gesteuerten statistischen Impulsquellen

Summary From the communication engineers point of view the paper deals with networks consisting of linear filters and a special sort of controlled statistical pulse generators (SIG). The SIG responds to an analog signal with a sequence of Dirac impulses, where the probability for an output impulse at a given time depends on the instantaneous value of the input signal only. In connection with linear filters, however, systems can be realized in which the whole past of the input determines the statistical structure of the output. Therefore systems consisting of linear filters and SIGs (SIG networks) become interesting as models of biological systems, because in biological information processing transformations from analog signals into pulse trains occur very often. An example concerning the application of SIG systems in behavioural sciences will be discussed in a subsequent paper. In the present paper a theoretical analysis of the SIG and SIG networks is carried out by means of Statistical Communication Theory and Theory of Stochastic Processes. It is shown that under certain conditions very complex SIG networks can be treated with Correlation Theory. For one case not satisfying these conditions a solution on the base of Markoff processes is given.

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Auszug aus einer von der Fakultät für Maschinenwesen und Elektrotechnik der Technischen Hochschule München genehmigten Dissertation.Herrn Prof. Dr.-Ing. H. Marko danke ich für das Interesse und die fördernde Kritik während des Entstehens der dieser Arbeit zugrundeliegenden Dissertation. Der Deutschen Forschungsgemeinschaft ist für die finanzielle Förderung der Untersuchungen zu danken. Die numerischen Berechnungen wurden auf der Rechenanlage TR4 des Leibniz-Rechenzentrums der Bayerischen Akademie der Wissenschaften durchgeführt.