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Theory and design of two-parallelogram filter banks

Lin, Yuan-Pei and Vaidyanathan, P. P. (1996) Theory and design of two-parallelogram filter banks. IEEE Transactions on Signal Processing, 44 (11). pp. 2688-2706. ISSN 1053-587X. doi:10.1109/78.542176.

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It is well known that the analysis and synthesis filters of orthonormal DFT filter banks can not have good frequency selectivity. The reason for this is that each of the analysis and synthesis filters have only one passband. Such frequency stacking (or configuration) in general does not allow alias cancellation when the individual filters have good stopband attenuation. A frequency stacking of this nature is called nonpermissible and should be avoided if good filters are desired. In a usual M-channel filter bank with real-coefficient filters, the analysis and synthesis filters have two passbands. It can be shown that the configuration is permissible in this case. Many designs proposed in the past demonstrate that filter banks with such configurations can have perfect reconstruction and be good filters at the same time. We develop the two-parallelogram filter banks, which is the class of 2-D filter banks in which the supports of the analysis and synthesis filters consist of two parallelograms. The two-parallelogram filter banks are analyzed from a pictorial viewpoint by exploiting the concept of permissibility. Based on this analysis, we construct and design a special type of two-parallelogram filter banks, namely, cosine-modulated filter banks (CMFB). In two-parallelogram CMFB, the analysis and synthesis filters are cosine-modulated versions of a prototype that has a parallelogram support. Necessary and sufficient conditions for perfect reconstruction of two-parallelogram CMFB are derived.

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Vaidyanathan, P. P.0000-0003-3003-7042
Additional Information:© Copyright 1996 IEEE. Reprinted with permission. Manuscript received March 7, 1995; revised May 14. 1996. This work was supported in part by NSF grant MIP 92-15785, Tektronix, Inc., and Rockwell International. The associate editor coordinating the review of this paper and approving it for publication was Dr. Bruce Suter.
Issue or Number:11
Record Number:CaltechAUTHORS:LINieeetsp96b
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6885
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Deposited On:30 Dec 2006
Last Modified:08 Nov 2021 20:37

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