Design of computationally efficient cascade-form digital filters and its applications to programmable downconversion in software defined radios

Abstract

In this thesis, optimal methods for designing multiplierless FIR and IIR filters with cascaded prefilter-equalizer structures are proposed using desirable properties of ISOPs. Assuming that an FIR filter consists of a cyclotomic polynomial (CP) prefilter and an ISOP equalizer, in the proposed method the prefilter and equalizer are simultaneously designed using mixed integer linear programming (MILP). The resulting filter is a cascaded filter with minimal complexity. For IIR filters all-pole IIR equalizers are introduced, and a CP-prefilter cascaded with this type of equalizer is designed. In this case, MILP tries to minimize both computational complexity and phase response nonlinearity. Design examples demonstrate that the proposed methods produce a more efficient cascaded prefilter-equalizer than existing methods. We also propose using interpolated second order polynomials (ISOPs) to design an efficient cascaded integrator-comb (CIC)-based decimation filters for a programmable downconverter (PDC) which is a core function for digital channelizer in software radio systems. It is shown that some simple ISOPs can effectively reduce the passband droop caused by CIC filtering with little degradation in aliasing attenuation. In addition, interpolated second order polynomials (ISOPs) are shown to be useful for simplifying halfband filters that usually follows CIC filtering. This allows us to introduce a modified halfband filter (MHBF) which is simpler than conventional halfband filters. The proposed decimation filter for a PDC is a cascade of a CIC filter, an ISOP, MHBFs and a programmable finite impulse response (PFIR) filter. A procedure for designing the decimation filter is developed. In particular, an optimization technique that simultaneously design the ISOP and PFIR filters is presented. Design examples demonstrate that the proposed method leads to more efficient PDCs than existing ones. Finally, programmable downconverters with optimal discrete coefficients ...