Design of very sharp Hilbert transformers by multiple frequency transformations

A method for designing very sharp Hilbert transformers is presented. With the proposed method, the desired Hilbert transformer can be determined by the prototype filter and subfilter through frequency transformation. Moreover, the subfilter can be further decomposed into prototype filter and subfilter, and so on. This results in a multi-layered transformation structure and has significant reduction in the overall number of distinct multipliers, especially in the situation of very sharp transition band.