Reflected boundary conditions for multirate filter banks

Several methods for applying perfect reconstruction quadrature mirror filter (PR QMF) banks to finite-length signals are described and compared. Although simple periodization produces a transform that does not increase the size of the transformed signal, it has the disadvantage of introducing a jump discontinuity at the signal´s boundary. Various methods of transforming smoother extensions are considered and analyzed in terms of their ability to conserve data storage costs and reproduce the signal in a numerically efficient manner. A complete classification of two-channel schemes based on periodizing symmetric (reflected) signal extensions and using linear phase filters is described, for both even- and odd-length signals. More general techniques based on transforming linear signal extrapolations and truncating the resulting subbands to conserve data size are also presented. An example using reflected boundary extension is discussed