The Design of Equal Complexity FIR Perfect Reconstruction Filter Banks Incorporating Symmetries

In this report, we present a new approach to the design of perfect reconstruction filter banks (PRFB’s) which have equal length FIR analysis and synthesis filters. To achieve perfect reconstruction, necessary and sufficient conditions are incorporated directly in a numerical design procedure as a set of quadratic equality constraints among the impulse response coefficients of the filters. Any symmetry inherent in a particular application, such as quadrature mirror symmetry, linear phase, or symmetry between analysis and synthesis filters, may be exploited to reduce the number of variables and constraints in the design problem. A novel feature of our new approach is that it allows the design of filter banks that perform functions other than flat passband band-splitting