Contributions to low-complexity maximally decimated filter banks

Abstract: Filter banks are systems of several filters with a common input or a commonoutput. They are used whenever a signal needs to be split up into differentfrequency bands. The first filter banks were introduced in theseventies, and about ten years later it was shown how to design filterbanks which do not introduce any errors to the signal. Such filter banksare called perfect reconstruction (PR) filter banks. Since then, the theoryof filter banks has developed and today there exist numerous ways todesign filter banks for different applications. However, earlier work has toa large extent been on the transfer function level, while here, efficientrealization and implementation, important in e.g. low-power applications,is in focus. Further, most of the work has been focused on the PR case,which is for many application an unnecessarily severe restriction.In this thesis, four different classes of near-PR (small but acceptableerrors are allowed in order to further decrease the arithmetic complexity)maximally decimated filter banks are proposed. They are all opitimized tohave as low arithmetic complexity as possible, meeting frequency-selectivechannel filter specifications. A number of design examples areincluded in order to demonstrate the benefits of the new filter bankclasses. The four classes are preceded by some introductory theory tomaximally decimated filter banks.The first class treats the two-channel case. The conventional quadrature-mirror filter (QMF) bank theory is combined with the frequencyresponsemasking (FRM) technique to get a linear-phase FIR filter bankwith narrow transition bands and simultaneously a low complexity.The second class is a combination of the cosine and sine modulationtechnique and a new version of the FRM approach. This theory holds foran arbitrary number of channels and the filters are nonlinear-phase FIRfilters.