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Uwe Meyer-Bäse, HSDAL, University of Florida (U.S.A.)
Jon Mellott, HSDAL, University of Florida (U.S.A.)
Fred Taylor, HSDAL, University of Florida (U.S.A.)
Frequency sampling filters (FSF) are of interest to the designers of multirate filter banks due to their intrinsic low-order, complexity, and linear phase behavior. Fast FSFs residing in smaller packages will be required to support future high-bandwidth, mobile image and signal processing applications. Since FSF designs rely on the exact annihilation of selected poles-zeros, a new facilitating technology is required which is fast, compact, and numerically exact. Exact FSF pole-zero annihilation is guaranteed by implementing polynomial filters over an integer ring in the residue arithmetic system (RNS). The design methodology is evaluated as an ASIC. Based on an FPGA technology, at least an 86% complexity reduction can be achieved with even greater advantages gained as a custom VLSI. An RNS-based FSF implementation of an eight channel cochlea filter bank is presented which demonstrates both the performance and packaging advantages of the new FSF paradigm.
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William M. Campbell, Motorola SSTG (U.S.A.)
Thomas W. Parks, School of Electrical Engineering, Cornell University (U.S.A.)
The design of constrained multirate systems using a relative (l)^2 error criterion is considered. A general algorithm is proposed to solve the problem. One application of the algorithm is the design of a new class of multirate filters for signal decomposition--projection filters. These multirate systems are projection operators that optimally approximate linear time-invariant filters in the (l)^2 norm. A second application of constrained multirate filter design is also presented--optimal design of multistage multirate systems. Examples illustrate the new design method and its advantages over design methods intended for linear time-invariant systems.
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Wayne Lawton, ISS, NUS (Singapore)
Charles A. Micchelli, IBM (U.S.A.)
Conjugate quadrature filters with multiple zeros at 1 have classical applications to unitary subband coding of signals using exact reconstruction filter banks. Recent work shows how to construct, given a set of n negative numbers, a CQF whose degree does not exceed 2n-1 and whose zeros contain the specified negative numbers, and applies such filters to interpolatory subdivision and to wavelet construction in Sobelov spaces. This paper describes a recent result of the authors which extends this construction for an arbitrary set of n nonzero complex numbers that contains no negative or negative reciprocal conjugate pairs. Detailed derivations are to be given elsewhere. We design several filters using an exchange algorithm to illustrate a conjecture concerning the minimal degree and we discuss an application to coding transient acoustic signals.
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Jörg Kliewer, University of Kiel (Germany)
Alfred Mertins, University of Kiel (Germany)
In this paper we derive perfect reconstruction (PR) conditions for oversampled cosine-modulated filter banks. The results can be regarded as a generalization of the known work for critical subsampling. We show that in the oversampled case we gain some additional degree of freedom, which can be exploited in the filter design process. This leads to PR prototypes with stopband attenuations being much higher than in the critically subsampled PR case. The filters designed as PR filters for the oversampled case can also serve as prototypes for critically subsampled cosine-modulated pseudo QMF banks.
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Masaaki Ikehara, Keio University (Japan)
Truong Q. Nguyen, University of Wisconsin (U.S.A.)
In this paper, we present a novel way to design biorthogonal and paraunitary linear phase(LPPUFB) filter banks. The square error of the perfect reconstruction condition is expressed in quadratic form of filter coefficients and the cost function is minimized by solving linear equation iteratively without nonlinear optimization. With some modifications, the method can be extended to the design of paraunitary filter banks. Using this method, we can design LPPUFB with many channels easily and quickly. Design examples are given to validate the proposed method.
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Benjamin W. Wah, UIUC (U.S.A.)
Yi Shang, UIUC (U.S.A.)
Tao Wang, UIUC (U.S.A.)
Ting Yu, UIUC (U.S.A.)
In this paper, we study various global optimization methods for designing QMF (quadrature mirror filter) filter banks. We formulate the design problem as a nonlinear constrained optimization problem, using the reconstruction error as the objective, and other performance metrics as constraints. This formulation allows us to search for designs that improve over the best existing designs. We present NOVEL, a global optimization method for solving nonlinear continuous constrained optimization problems. We show that NOVEL finds better designs with respect to simulated annealing and genetic algorithms in solving QMF benchmark design problems. We also show that relaxing the constraints on transition bandwidth and stopband energy leads to significant improvements in the other performance measures.
ic972081.pdf ic972081.pdf TOPVijay Jain, University of South Florida (U.S.A.)
A unified approach to the design of linear- and nonlinear-phase QMFs is developed. Formulated as an optimization problem, the design procedure is shown to translate into an eigenvalue-eigenvector problem. To find the optimal filter an algorithm is presented, which typically converges in a few tens of iterations. The flexibility of our design procedure permits several practical extensions to be made readily. These are (a) inclusion of frequency-weighted stopband energy criteria, and (b) inclusion of finite word-length constraints which is stressed in the paper. We have successfully used our filters to applications such as image coding and analysis; here, their use in wavelet-series analysis of oceanographic data is demonstrated.
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