Generation of positive real functions.

The role of orthogonal polynomials m obtaining a transfer function whose magnitude or phase approximates that of the ideal low-pass filter characteristic is well recognized. In this paper an attempt is made to generate positive real functions starting from the recurrence relations which are normally used in generating polynomials.
The importance of orthogonal polynomials in approximating a specified frequency response characteristic is well known. For instance, Chebyshev polynomials have been used in deriving a transfer function whose magnitude approximates that of an ideal low-pass filter. Also, the phase of the transfer function given by the inverse of a Bessel polynomial is shown to approximate that of an ideal low-pass filter. Though several polynomials have been successfully used to obtain required transfer functions, no attempts seem to have been made to use them for the generation of positive real functions. In this paper an attempt is made to generate positive real functions starting from the recurrence relations that are usually employed in the generation of polynomials. [ABSTRACT FROM AUTHOR]