Perfect reconstruction recursive QMF banks for image subband coding

A scheme for implementing a perfect reconstruction QMF (quadrature mirror filter) bank is considered. The scheme is based on a uniform DFT (discrete Fourier transform) L-band analysis filter bank realized using a polyphase decomposition of a lowpass L-th band filter (composed of stable allpass subfilters) followed by an L-band synthesis filter bank (realized using the transpose of the analysis filter bank with the allpass filters replaced by their inverse filters). In the subband coding of finite-length sequences, the instability problem of the inverse filters can be avoided by using the original stable allpass filter in each branch of the synthesis bank with time-reversed input and output. Conditions for perfect reconstruction are derived and illustrated with examples