Fast and low roundoff implementation of quadrature mirror filters for subband coding

We propose a fast and low roundoff-noise implementation of alias-free quadrature mirror filters (QMFs) for tree-structured subband coding. When N-tap FIR QMFs are directly utilized, they require 2N multiplications and 2(N-1) additions to obtain a pair of high-band and low-band decimated outputs. Using recursive formulas and the polyphase concept, a QMF implementation is proposed that, for both analysis and synthesis stages, needs only (N/2+2) multiplications and (3N/2+8) additions to compute the same outputs. Furthermore, the proposed algorithm can reduce roundoff error when finite-wordlength processors are used to implement the encoder and decoder. Simulation examples for image coding are also given to demonstrate the differences between the proposed and previously-known algorithms.