Wideband digital fractional Hilbert transformer designs based on interlaced and derivative sampling methods

• Design of wideband fractional Hilbert transformer (FHT) is presented.
• The closed-form designs of wideband FHT are obtained.
• Lp-norm minimization method is applied to design optimal wideband FHT.
• Sparse wideband FHT is designed by orthogonal matching pursuit method.

In this paper, the design of wideband digital fractional Hilbert transformer (FHT) is presented. First, the wideband digital FHT is designed by using the reconstruction formula of interlaced sampling method and derivative sampling method. The closed-form design is obtained, so the filter coefficients are easily calculated. Then, the Lp-norm minimization method is applied to design digital wideband FHT whose solution can be obtained by using convex optimization tool. Next, the orthogonal matching pursuit method is used to design sparse digital FHT for reducing arithmetic complexity. Finally, several examples are demonstrated to show that the proposed FHT has smaller design error in high frequency band than the conventional digital FHT.