Design of fractional Hilbert transformer with consideration of noise attenuation

In this paper, an approach to the design of finite impulse response (FIR) fractional Hilbert transformer (FHT) with consideration of noise attenuation is presented. The design is based on the maximization of signal-to-noise ratio (SNR) at the output of the fractional Hilbert transformer under the constraint which ideal frequency response and actual response have several same derivatives at the prescribed frequency point. The optimal filter coefficients are obtained from the generalized eigenvector of a pair of matrices corresponding to the maximum eigenvalue. Several numerical examples are demonstrated to show the proposed FHT design method has higher SNR than the conventional FHT design methods without considering the noise attenuation.