On the Designs of Variable Fractional Hilbert Transformers

Abstract

In this brief, the designs of variable fractional Hilbert transformers (VFHTs) are presented. First, the definition and properties of FHT are briefly reviewed. Then, the fact that the frequency response of FHT with order $v$ can be obtained from the linear combination of those of the two FHTs with different orders $p$ and $q$ will be shown. Based on this fact, a new VFHT structure is derived, in which the phase response of FHT can be easily changed by adjusting the linear combination coefficients without redesigning the FHT. Finally, numerical examples are demonstrated to compare the proposed method with conventional Farrow structure method in terms of design error, computational complexity, and memory storage requirements.