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Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect-reconstruction property

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1 Author(s)
Vaidyanathan, P.P. ; California Institute of Technology, Pasadena, CA

Based on the concept of losslessness in digital filter structures, this paper derives a general class of maximally decimated M-channel quadrature mirror filter banks that lead to perfect reconstruction. The perfect-reconstruction property guarantees that the reconstructed signal \hat{x} (n) is a delayed version of the input signal x (n), i.e., \hat{x} (n) = x (n - n_{0}) . It is shown that such a property can be 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.

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Acoustics, Speech and Signal Processing, IEEE Transactions on  (Volume:35 ,  Issue: 4 )