Theory and Design of A4-Channel Maximally Decimated uadrature Mirror Filters with Arbitrary

Based on the concept of losslessness in digital filter structures, this paper derives a general class of maximally decimated Mchannel quadrature mirror filter hanks that lead to perfect reconstrnction. The perfect-reconstruction property guarantees that the reconstructed signal f ( a ) is a delayed version of the input signal x (n), i.e., 2 ( n ) = n ( n a,,). It is shown that such a property can he satisfied if the alias component matrix (AC matrix for short) is unitary on the unit circle of the z plane. The number of channels M is arbitrary, and when M is two, the results reduce to certain recently reported 2-channel perfect-reconstruction QMF structures. A procedure, based on recently reported FIR cascaded-lattice structures, is presented for optimal design of such FIR M-channel filter banks. Design examples are included.