State-space representation of fractional linear filters

This paper shows that a simple state-space representation for the so-called fractional linear filters, in the form of a system made up of an infinite number of ordinary differential equations, can be derived in a straightforward manner from the Taylor expansion of (1 - z)^d. As an immediate corollary, we also obtain a finite-dimensional approximation of this representation, corresponding to a rational approximation of the fractional filter. These results are applied to continuous time filter with transfer function ((s + b)/(s + a))^d.