The fractal dimension of a test signal: implications for system identification procedures.

Abstract:

:The experimental identification of a non-linear biologic transducer is often approached via consideration of its response to a stochastic test ensemble, such as Gaussian white noise (Marmarelis and Marmarelis 1978). In this approach, the input-output relationship a deterministic transducer is described by an orthogonal series of functionals. Laboratory implementation of such procedures requires the use of a particular test signal drawn from the idealized stochastic ensemble; the statistics of the particular test signal necessarily deviate from the statistics of the ensemble. The notion of a fractal dimension (specifically the capacity dimension) is a means to characterize a complex time series. It characterizes one aspect of the difference between a specific example of a test signal and the test ensemble from which it is drawn: the fractal dimension of ideal Gaussian white noise is infinite, while the fractal dimension of a particular test signal is finite. This paper shows that the fractal dimension of a test signal is a key descriptor of its departure from ideality: the fractal dimension of the test signal bounds the number of terms that can reliably be identified in the orthogonal functional series of an unknown transducer.

journal_name

Biol Cybern

journal_title

Biological cybernetics

authors

Victor JD

doi

10.1007/BF00354987

subject

Has Abstract

pub_date

1987-01-01 00:00:00

pages

421-6

issue

6

eissn

0340-1200

issn

1432-0770

journal_volume

57

pub_type

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