Home HomeSanjit K. Mitra, University of California (U.S.A.)
This paper introduces the concept of structural subband decomposition of sequences, a generalization of the polyphase decomposition of sequences, and outlines a number of applications of this concept, such as efficient FIR filter design and implementation, adaptive filtering, and fast computation of discrete transforms.
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Knut Hüper, University of Würzburg (Germany)
Uwe Helmke, University of Würzburg (Germany)
The problem of finding the generalized eigenvalues and eigenvectors of a pair of real symmetric matrices A and B, with B>0, can be viewed as a smooth optimization problem on a smooth manifold. We present a cost function approach to the generalized eigenvalue problem which is posed on the product of the n-sphere and Euclidian space R. The critical point set of this cost function is studied. An algorithm is presented based on constrained optimization. A proof of local quadratic convergence is given.
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Soura Dasgupta, University of Iowa (U.S.A.)
Chris Schwarz, University of Iowa (U.S.A.)
Minyue Fu, University of Newcastle (Australia)
We consider a multi-input, multi-output lattice realization for linear time-varying analysis banks which are all pass. Such a realization has been given for LTI systems; and under certain conditions, we show how it generalizes to the LTV case. Moreover, our implementation is simpler than the existing LTI version. Finally, we describe the anticausal inverse of a lattice realization which is used in the synthesis bank.
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Steffen Paul, Technical University of Munich (Germany)
Josef A. Nossek, Technical University of Munich (Germany)
Numerical algorithms for signal processing and control are quite often constructed by intuition. When the system to be designed contains algebraic or other invariants, then these constraints can be exploited to find appropriate transformations. The transformations in system theory are usually Lie groups. One has to find Lie groups which are consistent with the invariants. We show, how this point of view can be applied to construct pole placement algorithms for symmetric and skew-symmetric realizations. However, Lie group theory only reveals the appropriate transformations but is not able to reduce the design process to a trivial task. The problem discussed here does also show this limitation.
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Klaus Diepold, IDT (Germany)
Rainer Pauli, Technical University of Munich (Germany)
Numerical matrix computations involving actions of noncompact transformation groups are known to produce numerical problems since the elements of the pertaining matrix representations are inherently unbounded. In this case study we analyse numerical problems occuring in a class of algorithms that is based on actions of the pseudo-orthogonal group O_n,m -- a group that is noncompact (hyperbolic geometry) and well established in signal processing (Schur methods). As a major result, it is shown how to exploit the additional degrees of freedom in defining coordinate frames in a Grassmannian setting in order to impose an a priori bound on the norm of the transformation matrices. This way, numerically disastrous situations can be circumvented systematically. Hence, it becomes possible to develop modified algorithms which exhibit superior numerical performance for a large class of problems based on e.g. hyperbolic transformations.
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Rodney A. Kennedy, Australian National University (Australia)
Deva K. Borah, Australian National University (Australia)
Zhi Ding, Auburn University (U.S.A.)
The performance and complexity of blind algorithms in a digital receiver is dependent on the prefilter prior to discretization of the received continuous time signal and the sampling rate. This paper shows that symbol spaced blind equalization algorithms are in general sub-optimal, since a matched filter cannot be used. We show that, for fractionally spaced equalizers, the prefilter can be a general low-pass filter and does not need to be matched to the unknown channel. This flexibility on choosing the prefilter can result in different discrete time models with different complexities for the signal processing algorithms to follow. As for example, a simpler whitening filter design which is needed for the success of several important blind equalization algorithms can be realized using this flexibility.
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Zhuquan Zang, ATRI, Curtin University of Technology (Australia)
Antonio Cantoni, ATRI, Curtin University of Technology (Australia)
Koklay Teo, ATRI, Curtin University of Technology (Australia)
Envelope-constrained filtering is concerned with the design of a time-invariant filter to process a given input signal such that the noiseless output of the filter is guaranteed to lie within a prespecified output mask. In this paper, using Laguerre filters and H_(infinity) optimization techniques, the continuous-time envelope-constrained filter design problem has been reformulated and solved as a constrained H_(infinity) model-matching problem. To illustrate the effectiveness of the design method, a numerical example is presented which deals with the design of an equalization filter for a digital transmission channel.
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Jeroen Dehaene, K.U.Leuven (Belgium)
Nanayaa Twum-Danso, Harvard University (U.S.A.)
Information theoretic criteria for neural network adaptation laws have recently become an important focus of attention. We consider the problem of adaptively maximizing the entropy of the outputs of a deterministic feedforward neural network with real valued stochastic input signals, as considered by Bell and Sejnowski. We give a new explanation for the relevance of output information (entropy) maximization for source separation applications and reinterpret Bell and Sejnowski's approach in a more general context of probability density estimation. This insight is the basis for a generalization of the approach, and we consider a family of gradient based algorithms.
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Kutluyl Dogançay, University of Melbourne (Australia)
Vikram Krishnamurthy, University of Melbourne (Australia)
The paper presents a quick and simplified aggregation method for a large class of Markov chain functionals based on the concept of stochastic complementation. Aggregation results in a reduction in the number of Markov states by grouping them into a smaller number of aggregated states, thereby producing a considerable saving on computational complexity associated with maximum likelihood parameter and state estimation for hidden Markov models. The importance of the proposed aggregation method stems from the ease with which Markov chains with a large number of states can be aggregated. Three Markov chain functionals which have widespread use are considered to illustrate the application of our aggregation method.
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John B. Moore, Systems Engineering, ANU (Australia)
Danchi Jiang, Dept. MAE. Chinese University (Hong Kong)
This paper concerns quadratic programming problems subject to quadratic equality constraints such as arise in broadband antenna array signal processing and elsewhere. At first, such a problem is converted into a semidefinite programming problem with a rank constraint. Then, a rank preserving flow is used to accommodate the rank constraint. The associated gradient formulas are carefully developed. The convergence of the resulted algorithm is also guaranteed. Our approach is demonstrated by a numerical experiment.
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