NUMERICAL ESTIMATION OF THE FALL-OFF RATE S OF SPECTRAL DENSITIES

Signals with l/f(alpha) spectral densities have traditionally had the exponent cc estimated by linear regression on a log-log plot. This is problematic when the spectrum of the signal crosses zero because this introduces poles in the log plot of the spectrum. We present a method which avoids these extreme values, namely doing a regression on a subs et of local maxima on the same log-log plot. Self-affine functions wit h Holder exponent ct are well known to have the fractal dimension (5-a lpha)/2, and we thus estimate the fractal dimension of the function in troduced by Kieswetter. On smooth functions, the new method is tested on log-log representation of power spectra, but no relation can be est ablished with the fractal dimension of the signal (due to lack of self -affinity). The limitations of spectral analysis methods for estimatio n of algebraic fall-off rates are discussed.