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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.