The fractal dimension of a test signal: implications for system identification procedures.
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.
Department of Neurology, Cornell University Medical College, New York City, NY 10021.
J D
JD
Victor
D008433:Mathematics; D008959:Models, Neurological; D013269:Stochastic Processes