Interpolation filters with arbitrary frequency response for all-digital receivers

If the sampling of the received signal is not synchronized to the incoming data symbols, timing adjustment must be done after sampling using interpolation. If the impulse response of the interpolation filter is a polynomial or piecewise polynomial, it can be implemented efficiently using a Farrow structure. The remaining problem is that there exist no good design methods for polynomial-based filters. In this paper we present a new synthesis technique which allows to design polynomial-based interpolation filters with an arbitrary frequency response. This means that we are able to design interpolation filters in the same manner as normal FIR filters. There can be many passbands and stopbands, and for every band we can set the desired amplitude and weight.