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

Vaidyanathan, P. P. (1987) Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect-reconstruction property. IEEE Transactions on Acoustics, Speech, and Signal Processing, 35 (4). pp. 476-492. ISSN 0096-3518. https://resolver.caltech.edu/CaltechAUTHORS:VAIieeetassp87a

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Abstract

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 signalhat{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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/TASSP.1987.1165155DOIArticle
Additional Information:© 1987 IEEE. Manuscript received May 19, 1986; revised September 8, 1986. This work was supported in part by the National Science Foundation under Grant ECS 84-04245 and in part by Caltech's Program in Advanced Technology sponsored by Aerojet General, General Motors, GTE, and, TRW. We wish to acknowledge encouraging and useful discussions we have had during the ICASSP'86 with R. E. Crochiere of the AT&T Bell Labs, T. Barnwell, III, of the Georgia Institute of Technology, T. E. Ramstad of the Norwegian Institute of Technology, and M. Vetterli of the Ecole Polytechnique Federale de Lausanne.
Funders:
Funding AgencyGrant Number
NSFECS 84-04245
Aerojet GeneralUNSPECIFIED
General MotorsUNSPECIFIED
GTEUNSPECIFIED
TRWUNSPECIFIED
Issue or Number:4
Record Number:CaltechAUTHORS:VAIieeetassp87a
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:VAIieeetassp87a
Alternative URL:http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=26209&arnumber=1165155&count=32&index=10
Official Citation:P. Vaidyanathan, "Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect-reconstruction property," in IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 35, no. 4, pp. 476-492, April 1987. doi: 10.1109/TASSP.1987.1165155
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5460
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:18 Oct 2006
Last Modified:02 Oct 2019 23:23

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