Abstract:

A new method for designing Fractional Hilbert Transformer (FHT) was proposed. The basic idea is to realize the FHT to design the allpass filter with desired phase characteristic. It is well known that the denominator polynomial of a stable allpass filter must be a minimum phase system. By constructing a pure imaginary odd symmetry phase function, and using symmetry properties of the Fourier transform, this method could obtain the cepstral sequence of the denominator polynomial using the relationship between cepstral sequence and phase function of a minimum phase system. Then, from the cepstral spectrum theory, the denominator polynomial coefficients could be determined through a nonlinear recursive difference equation. Approximated ideal and non-ideal characteristic methods were given. Design examples indicate that the proposed filters exhibit good approximation to the desired phase response, and have the advantage of simple, efficient and infinite precision.