Quadrature mirror filter banks, M-band extensions and perfect-reconstruction techniques

TLDR

The paper notes that perfect‑reconstruction QMF banks are related to losslessness in transfer matrices. The paper reviews quadrature mirror filters (QMF). The authors review two‑band QMF banks, analyze distortion sources, and present perfect‑reconstruction structures extended to arbitrary channel counts. The study introduces lattice structures that achieve perfect reconstruction even with coefficient quantization and extends perfect‑reconstruction designs to arbitrary channel numbers.

Abstract

In this paper, quadrature mirror filters (QMF) are reviewed. After a brief introduction to multirate building blocks, the two-band QMF bank is discussed. Various distortions caused by the structure, and methods to eliminate these distortions are outlined. Perfect-reconstruction structures for the two-band case are reviewed, and the results are extended to the case of arbitrary number of channels. The relation between perfect-reconstruction QMF banks and the concept of losslessness in transfers-matrices is indicated. New lattice structures are presented, which perform the perfect reconstruction, sometimes even under coefficient quantization.