Hilbert and Fourier transforms of polynomial ratio time signals

Polynomial curve fittings have long been used to smooth data and provide functions from which, at specified times, samples may be obtained. Relationships of these polynomials to frequency content can be determined by including a denominator polynomial which does not essentially affect the fit over the data interval. Both Fourier and Hilbert transforms are found for general polynomial ratios, and their subsequent properties, duals of polynomial ratio frequency functions, are discussed.