REPRESENTATION AND ANALYSIS OF SIGNALS PART XXI. THE INTRINSIC DIMENSIONALITY OF SIGNAL COLLECTIONS

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Abstract
In this work, the dimensionality of a collection of signals is defined as equal to the number of free parameters required in a hypothetical signal generator capable of producing a close approximation to each signal in the collection. Thus defined, dimensionality becomes a relationship between the vectors representing the signals. This relationship need not be a linear one, and does not depend on the basis onto which the vectors are projected in signal measuring processes. It represents a lower bound on the number of coefficients required to describe the signals, no matter how sophisticated the representation scheme, and thus provides an index of the redundancy in a given representation. A computer program for estimating this dimensionality from the signal coefficients on an arbitrary orthogonal basis is developed. The validity of the program is verified by using it to estimate the dimensionality of signals of known structure, and therefore of known dimensionality.

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