Noncausal IIR Fractional Hilbert Transformers With Equiripple or Flat Phase Response

Noncausal infinite impulse response (IIR) systems yield a much better approximation of desired response than causal systems of the same complexity. Today's technology also enables their efficient implementation. In the design of Hilbert transformers, the noncausal approach has been exploited only for conventional transformers. This brief presents a method for the design of noncausal IIR fractional Hilbert transformers based on the elliptic approximation of the desired phase shift. All-pass transformers with equiripple and flat phase responses are considered. The method is given in closed form, which makes the design robust and suitable for high-order transformers.