Properties of Continued Fractions Approximations of Fractional Analog and Digital Operators

This paper establishes a link between the Lagrange's continued fraction expansion (CFE) and two CFEs the author recently introduced for approximating the operators s(nu), 0 < nu < 1, and their discrete realizations. The zeros and poles of these new approximations alternate on the negative real half-axis of the s-plane (in the case of analog realizations) and on the real segment inside the unit circle of the z-plane (in the case of discrete realizations). Finally, the paper shows that the discrete approximations of s(nu) have poles and zeros enjoying a nice symmetrical distribution on the z-plane.