Filter banks are systems of several filters with a common input or a common output. They are used whenever a signal needs to be split up into different frequency bands. The first filter banks were introduced in the seventies, and about ten years later it was shown how to design filter banks which do not introduce any errors to the signal. Such filter banks are called perfect reconstruction (PR) filter banks. Since then, the theory of filter banks has developed and today there exist numerous ways to design filter banks for different applications. However, earlier work has to a large extent been on the transfer function level, while here, efficient realization 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 acceptable errors are allowed in order to further decrease the arithmetic complexity) maximally decimated filter banks are proposed. They are all opitimized to have as low arithmetic complexity as possible, meeting frequency-selective channel filter specifications. A number of design examples are included in order to demonstrate the benefits of the new filter bank classes. The four classes are preceded by some introductory theory to maximally decimated filter banks.
The first class treats the two-channel case. The conventional quadrature-mirror filter (QMF) bank theory is combined with the frequency-response masking (FRM) technique to get a linear-phase FIR filter bank with narrow transition bands and simultaneously a low complexity.
The second class is a combination of the cosine and sine modulation technique and a new version of the FRM approach. This theory holds for an arbitrary number of channels and the filters are nonlinear-phase FIR filters.
The two last classes are one IIR/IIR filter bank and one HR/FIR filter bank. Using IIR filters instead of FIR filters is another way to increase the frequency selectivity with retained low complexity. The different filters are generated using cosine modulation and small errors are allowed for the same reason as above. A general design procedure for an arbitrary specification is also given. These two classes are in general asymmetric filter banks which makes them suitable for certain applications.
Linköping: Linköpings universitet , 2003. , 134 p.