Closed-form design of fixed fractional hubert transformer using discrete sine transform

In this paper, the closed-form design of fixed fractional Hilbert transformer (FHT) using discrete sine transform (DST) is presented. First, the DST-based interpolation method is applied to reconstruct the continuous-time signal from the given discrete-time signal. Then, the filter coefficients of the transfer function of fixed FHT are obtained from the DST reconstruction results by using suitable index mapping. The main feature of the proposed method is that the closed-form design can be obtained without performing any optimization procedure. Finally, several numerical examples are demonstrated to show the effectiveness of the proposed design method.