Browsing by Author "Van Veen, Barry D."

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    Efficient Methods for Identification of Volterra Filters
    (1994) Nowak, Robert David; Van Veen, Barry D.; Digital Signal Processing (http://dsp.rice.edu/)
    A major drawback of the truncated Volterra series or "Volterra filter" for system identification is the large number of parameters required by the standard filter structure. The corresponding estimation problem requires the solution of a large system of simultaneous linear equations. Two methods for simplifying the estimation problem are discussed in this paper. First, a Kronecker product structure for the Volterra filter is reviewed. In this approach the inverse of the large correlation matrix is expressed as a Kronecker product of small matrices. Second, a parallel decomposition of the Volterra filter based on uncorrelated, symmetric inputs is introduced. Here the Volterra filter is decomposed into a parallel combination of smaller orthogonal "sub-filters." It is shown that each sub-filter is much smaller than the full Volterra filter and hence the parallel decomposition offers many advantages for estimating the Volterra kernels. Simulations illustrate application of the parallel structure with random and pseudorandom excitations. Input conditions that guarantee the existence of a unique estimate are also reviewed.
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    Low Rank Estimation of Higher Order Statistics
    (1995-12-01) Nowak, Robert David; Van Veen, Barry D.; Digital Signal Processing (http://dsp.rice.edu/)
    Low rank estimators for higher order statistics are considered in this paper. Rank reduction methods offer a general principle for trading estimator bias for reduced estimator variance. The bias-variance tradeoff is analyzed for low rank estimators of higher order statistics using a tensor product formulation for the moments and cumulants. In general the low rank estimators have a larger bias and smaller variance than the corresponding full rank estimator. Often a tremendous reduction in variance is obtained in exchange for a slight increase in bias. This makes the low rank estimators extremely useful for signal processing algorithms based on sample estimates of the higher order statistics. The low rank estimators also offer considerable reductions in the computational complexity of such algorithms. The design of subspaces to optimize the tradeoffs between bias, variance, and computation is discussed and a noisy input, noisy output system identification problem is used to illustrate the results.
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    Matrix Based Computation of Floating-Point Roundoff Noise
    (1989-12-01) Van Veen, Barry D.; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
    A matrix based procedure is presented for computing the output roundoff noise power for filters implemented with floating-point arithmetic. The filter's computational structure is represented in terms of a product of matrices, known as a factored state variable description. The quantities needed to compute the output roundoff noise power are obtained from the factored state variable description via matrix manipulation. The expression for output roundoff noise power is shown to be of the same form as that for fixed-point arithmetic roundoff noise. Comparison indicates that, under very general conditions, fixed-point arithmetic provides better roundoff noise performance than floating point. Several examples are provided.
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    Tensor Product Basis Approximations for Volterra Filters
    (1996-02-01) Nowak, Robert David; Van Veen, Barry D.; Digital Signal Processing (http://dsp.rice.edu/)
    This paper studies approximations for a class of nonlinear filters known as Volterra filters. Although the Volterra filter provides a relatively simple and general representation for nonlinear filtering, often it is highly over-parameterized. Due to the large number of parameters, the utility of the Volterra filter is limited. The over-parameterization problem is addressed in this paper using a tensor product basis approximation (TPBA). In many cases a Volterra filter may be well approximated using the TPBA with far fewer parameters. Hence, the TPBA offers considerable advantages over the original Volterra filter in terms of both implementation and estimation complexity. Furthermore, the TPBA provides useful insight into the filter response. This paper studies the crucial issue of choosing the approximation basis. Several methods for designing an appropriate approximation basis and error bounds on the resulting mean-square output approximation error are derived. Certain methods are shown to be nearly optimal.