Design of Modified Second-Order Frequency Transformations Based Variable Digital Filters With Large Cutoff Frequency Range and Improved Transition Band Characteristics
Sumedh Somnath Dhabu, A. P. Vinod · IEEE Transactions on Very Large Scale Integration (VLSI) Systems · 2015
The frequency transformation based filters (FT filters) provide an absolute control over the cutoff frequency. However, the cutoff frequency range (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_rangecompared with the FT filter; however, the ratio of transition bandwidth of the transformed filter to that of the prototype filter, tbwFT/tbwmod, is large over a significant portion of Ωc_range. 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_rangefor tbwFT≤ tbwmod. 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 Ωc_rangewith tbwFT≤ tbwmod. Design example shows that the MSFT filter provides 3 and 1.22 times wider Ωc_rangecompared to FT and FTCDM filters, respectively.