A unified framework for low-memory and on-the-fly implementation of generic tree-structured M-channel QMF banks

We study the low-memory and on-the-fly implementation of generic tree-structured M-channel quadrature mirror filter (QMF) banks. A unified framework is proposed in which the forward and inverse transforms are addressed as an integral system. To cope with the decomposition of finite-length signals, an on-the-fly treatment of boundary extension is also presented. The proposed unified framework has the advantages of on-the-fly computation, memory requirement independent of the input signal length, adaptability to varied cascading patterns of filter banks (FBs), and most of all, producing exactly the same subband coefficients as those obtained by the conventional global transform that buffers the whole signal. Examples with 2-channel odd-length linear-phase finite impulse response (FIR) FBs as well as lapped transforms are presented to demonstrate the approach proposed. Lastly, a comparison of memory sizes for three typical configurations of tree-structured FBs is also provided to show the flexibility and application of this framework.