Design of Modified Second-Order Frequency Transformations Based Variable Digital Filters With Large Cutoff Frequency Range and Improved Transition Band Characteristics

Design of Modified Second-Order Frequency Transformations Based Variable Digital Filters With Large Cutoff Frequency Range and Improved Transition Band Characteristics

Abstract— The frequency transformation based filters (FT filters) provide an absolute control over the cutoff frequency. However, the cutoff frequency range < Final Year Projects 2016 > Ωc range > of the FT filters is limited. The second-order frequency transformations combined with coefficient decimation technique based filter (FTCDM filter) has wider Ωc range c_range compared with the FT filter; however, the ratio of transition bandwidth of the transformed filter to that of the prototype filter, tbw FT /tb, is large over a significant portion of. In this paper, we propose a novel idea of relaxing the one-to-one mapping condition between the frequency variables, to overcome the issue of limited Ωc _range for tbw FT= tbw c_range. In the proposed modified second-order frequency transformation based filter(MSFT filter), we relax the one-to-one mapping condition between the frequency variables and use low-pass to high-pass transformation on the prototype filter to achieve wider _ with tbw FT= tbw mod mod. Design example shows that the MSFT filter provides 3 and 1.22 times wider _ compared to FT and FTCDM filters, respectively.