Home HomeAlbertus C. den Brinker, Eindhoven University of Technology (The Netherlands)
Adaptive filters can be made fault tolerant by overparametrization. Conditions are derived such that no deterioration is caused by the redundancy under fault-free operation and that the deterioration caused by weight failures is minimized.
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Petr Tichavský, Inst. of Information Theory and Automation, Prague (Czech Republic)
Peter Händel, Tampere University of Technology (Finland)
Tracking of slowly varying parameters of multiple sinusoids or cisoids (complex-valued sinusoids) in additive noise is an important problem in many engineering applications such as radar, communications, control, biomedical engineering and others. In some applications the sinusoidal frequencies are piecewise linear or periodic functions of time. Signals with harmonically varying sinusoidal frequencies are encountered e.g. in coherent laser radar technology for remote sensing of vibrational characteristics of objects. In these cases, standard algorithms for tracking of (multiple) sinusoidal frequencies, such as the adaptive notch filter, exhibit a nonzero tracking delay, which can be interpreted as an estimation bias. To eliminate this bias, two novel algorithms are designed, one for tracking of linearly and the latter for tracking of harmonically modulated frequencies. Both of the algorithms simultaneously separate the measured signal to individual components and update signal parameters using estimated phase differencies. Performance of the algorithms is demonstrated by simulations.
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Tyseer Aboulnasr, University of Ottawa (Canada)
Khaled Mayyas, JUST (Jordan)
One common approach to reducing the computational overhead of the normalized LMS (NLMS) algorithm is to update a subset of the adaptive filter coefficients. It is known that the mean square error (MSE) is not equally sensitive to the variations of the coefficients. Accordingly, the choice of the coefficients to be updated becomes crucial. On this basis, we propose an algorithm that belongs to the same family but selects at each iteration a specific subset of the coefficients that will result in the largest reduction in the performance error. The proposed algorithm reduces the complexity of the NLMS algorithm, as do the current algorithms from the same family, while maintaining a performance close to the full update NLMS algorithm specifically for correlated inputs.
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Quanhong Zhu, University of Utah (U.S.A.)
Scott C. Douglas, University of Utah (U.S.A.)
Kent F. Smith, University of Utah (U.S.A.)
Past methods for mapping the least-mean-square (LMS) adaptive finite-impulse-response (FIR) filter onto parallel and pipelined architectures either introduce delays in the coefficient updates or have excessive hardware requirements. In this paper, we describe a pipelined architecture for the LMS adaptive FIR filter that produces the same output and error signals as would be produced by the standard LMS adaptive filter architecture without adaptation delays. Unlike existing architectures for delayless LMS adaptation, the new architecture's throughput and hardware complexity are independent of and linear with the filter length, respectively.
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Markus Rupp, Lucent Technologies (U.S.A.)
Scott Douglas, Lucent Technologies (U.S.A.)
Recently, two simple gradient-based algorithms for unbiased IIR system identification in the presence of zero-mean correlated output noise were derived and shown to perform well in simulation. In this paper, we study the stability and robustness of these two adaptive filters, deriving strictly positive real (SPR) conditions on the overall unknown-plus-adaptive systems to guarantee convergence of the coefficients to their optimum values. Unlike other algorithms for unbiased IIR adaptive filtering, the stability of each of these algorithms depends on the initial values of the filter coefficients. However, near the optimum coefficient solutions, both algorithms are locally-stable, irrespective of the unknown system. Simulations verify the results of our analyses.
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Parthapratim De, University of Cincinnati. (U.S.A.)
Howard Fan, University of Cincinnati. (U.S.A.)
Most filters, adaptive or not, formulated using the delay operator, have no limit when sampling becomes fast and therefore they will have numerical problems. We will show that one reason that the normalized lattice filter has less numerical problems is because that it has a limit as the sampling period tends to zero. The transfer function in the $s$-domain obtained as a limit of the normalized lattice filter will, however, will have only every other power in the denominator polynomial. We propose a modified normalized lattice filter that can realize any arbitrary transfer function in the discrete ($z$) domain and its order-recursive limit as the sampling period tends to zero can realize any arbitrary transfer function in the $s$-domain. Various stability properties of the new lattice are also studied.
ic971941.pdf ic971941.pdf TOPJohn S. Bodenschatz, University of Southern California (U.S.A.)
Symmetric (alpha)-Stable (SAS) processes are used to model impulsive noise. Wiener filter theory is generally not meaningful in SASP environments because the expectations may be unbounded. To develop a filter theory for linear finite impulse response systems with independent identically distributed SASP inputs, we propose median orthogonality as a linear filter criterion, present a generalized Wiener-Hopf solution equation, and show a necessary condition for a filter to achieve the criterion. For non-Gaussian SASP densities, zero-forcing least-mean-square is the only well-known filter that satisfies the criterion, but others can easily be designed. We present a second algorithm and simulations showing that both converge to the generalized Wiener-Hopf solution.
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Owen E. Kelly, Rice University (U.S.A.)
Don H. Johnson, Rice University (U.S.A.)
The maximum likelihood sequence estimator is the optimal receiver for the inter-symbol interference (ISI) channel with additive white noise. A receiver is demonstrated that estimates sequence likelihood using a variable order Markov model constructed from a crudely quantized training sequence. Receiver performance is relatively unaffected by heavy-tailed noise that can undermine the performance of Gaussian based algorithms such as decision feedback equalization with gradient based (LMS) adaptation.
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Michael McCloud, University of Colorado, Boulder (U.S.A.)
Delores Etter, University of Colorado, Boulder (U.S.A.)
A technique is presented for subband adaptive filtering with nonuniform filter banks. The bandwidth allocations of the subband analysis and synthesis filters are adapted to the spectral characteristics of the input data in such a manner as to minimize an objective function built from the subband error powers. The nonuniform filter bank structure allows for fast convergence times for high order systems with a reduced mean square error relative to the uniform subband scheme. Results are presented for the case of a nonstationary system with time-varying spectral characteristics.
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Sofia Ben Jebara, LSTélécoms, ENIT / ESPPT, Tunis (Tunisia)
Meriem Jaidane, LSTélécoms, ENIT, Tunis (Tunisia)
This paper presents a tracking analysis of the LMS algorithm used in order to identify system variations modeled by a random walk. We prove that the steady state properties are strongly related to the input characteristics. The input correlation degrades the performances. Consequently, best performances are obtained for white input. We justify then the cpoupled adaptive predictive structures with system identification in order to improve classical scheme steady state performances.
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Saul B. Gelfand, Purdue University (U.S.A.)
Yongbin Wei, Purdue University (U.S.A.)
James V. Krogmeier, Purdue University (U.S.A.)
The stability of variable stepsize LMS (VSLMS) algorithms with uncorrelated stationary Gaussian data is studied. It is found that when the stepsize is determined by the past data, the boundedness of the stepsize by the usual stability condition of fixed stepsize LMS is sufficient for the stability of VSLMS. When the stepsize is also related to the current data, the above constraint is no longer sufficient. Instead, both the upperbound and the lowerbound of the stepsize must be within a smaller region. An exact expression of the stability region is developed for single tap filter. The results are verified by computer simulations.
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