Improved accuracy in the singularity spectrum of multifractal chaotic time series

Existing algorithms for accurately estimating the f( ) singularity spectrum from the samples of generalized dimensions Dq of a multifractal chaotic time series use either linear interpolation of the known Dq values or nely sample the Dq curve. Also, the derivative in the expression for Legendre transform necessary to go from Dq to f( ) is approximated using rst order centered di erence equation. Finely sampling the Dq is computationally intensive and the crude linear approximations to interpolation and di erentiation give erroneous end points in the f( ) curve. We propose using standard min-max lter design methods to more accurately interpolate between known samples of the Dq values and evaluate the Legendre transform. We use optimum (min-max) interpolators and di erentiators designed with the Parks-McClellan algorithm. The new min-max approach exhibits computational reduction and improved accuracy. Examples are provided that show improved accuracy for attractors that contain multifractal behavior.