An algorithm for the stable operation of a digitally-implemented fractionally-spaced adaptive equalizer

Gitlin, Richard D.; Meadors, Howard C.; Weinstein, Stephen B.

doi:10.1109/icassp.1982.1171458

Cited by 7 publications

(12 citation statements)

References 3 publications

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“…Similar results can be obtained by constraining the adaptive filter weights by modifying the cost function as [39] (12) where is a weighting on the control effort. Following the derivation of the FXLMS algorithm, the update algorithm can be derived as (13) where is the leakage factor and This leaky FXLMS algorithm also reduces numeric error in the finite-precision implementation [4], [40]. The introduction of a leakage factor has a considerable stabilizing effect on the adaptive algorithm, especially when very large source strengths are used [39], [41].…”

Section: Filtered-x Lms Algorithmmentioning

confidence: 99%

Active noise control: a tutorial review

Kuo

Morgan²

1999

Proc. IEEE

1,066

529

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Active noise control (ANC) is achieved by introducing a canceling "antinoise" wave through an appropriate array of secondary sources. These secondary sources are interconnected through an electronic system using a specific signal processing algorithm for the particular cancellation scheme. ANC has application to a wide variety of problems in manufacturing, industrial operations, and consumer products. The emphasis of this paper is on the practical aspects of ANC systems in terms of adaptive signal processing and digital signal processing (DSP) implementation for real-world applications. In this paper, the basic adaptive algorithm for ANC is developed and analyzed based on single-channel broad-band feedforward control. This algorithm is then modified for narrow-band feedforward and adaptive feedback control. In turn, these single-channel ANC algorithms are expanded to multiple-channel cases. Various online secondary-path modeling techniques and special adaptive algorithms, such as lattice, frequency-domain, subband, and recursive-least-squares, are also introduced. Applications of these techniques to actual problems are highlighted by several examples.

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Section: Filtered-x Lms Algorithmmentioning

confidence: 99%

Active noise control: a tutorial review

Kuo

Morgan²

1999

Proc. IEEE

1,066

529

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“…Using this decomposition the effect of the well-known observation [4] that leakage in essence increase the eigenvalues of the input autocorrelation matrix can be observed directly. For a small , the addition of to the denominators in (28) will greatly reduce the eigenfilter weight.…”

Section: Ltat In the Frequency Domain-fir Casementioning

confidence: 99%

“…The controllability grammian and the observability grammian are defined as solutions to and . For any nonsingular , a new state-space realization of the filter can be found with a transfer function (4) It follows that and . Observe that the eigenvalues of the product of and are equal to the eigenvalues of the product of and , .…”

Section: A Balanced Model Reduction-general Casementioning

confidence: 99%

“…The leakage to a target tap-weight adaptation is (17) which biases the tap weights toward the target vector . The standard leakage algorithm [3], [4], [21] can be thought of as LTAT where the target vector is (the null vector) and . That is, the leakage algorithm biases each of the tap weights toward zero.…”

Section: A Leakage To a Targetmentioning

confidence: 99%

“…Fractionally spaced equalizers (FSE's) constitute another class of equalizers that experience a magnitude response peak problem, as shown in [3] and [4]. Since an FSE samples the input waveform at a rate higher than the symbol rate, there is no signal energy between and , where symbol rate; FSE sampling rate; rolloff factor.…”

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confidence: 99%

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Magnitude response peak detection and control using balanced model reduction and leakage to a target

Benson

1997

IEEE Trans. Signal Process.

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Abstract-Adaptive filters are often used in systems that need to adjust to unknown environments. Communication channels with frequency nulls, signals that lack energy in a frequency band, and transducers with a finite bandwidth present special problems since adaptive filters can develop a large gain at frequencies where excitation is lacking. Such magnitude response peaks can cause problems if unchecked. This paper suggests a procedure for detecting and controlling magnitude response peaks that uses a balanced model reduction technique to form a low-order IIR filter that approximates the performance of the filter. The poles are then studied to determine if magnitude response peaks are present. If a peak is detected, then "leakage to a target" is used to gradually reduce the peak with minimal effect on the equalizer's response at other frequencies. Several useful bounds on the equalizer frequency response magnitude are derived, and the frequency domain behavior of the leakage to a target algorithm is analyzed. A case study is provided.

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Unbiased and stable leakage-based adaptive filters

Nascimento

Sayed

1999

IEEE Trans. Signal Process.

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The paper develops a leakage-based adaptive algorithm, refered to as circular-leaky, which in addition to solving the drift problem of the classical least mean squares (LMS) adaptive algorithm, it also avoids the bias problem that is created by the standard leaky LMS solution. These two desirable properties of unbiased and bounded estimates are guaranteed by circular leaky at essentially the same computational cost as LMS. The derivation in the paper relies on results from averaging theory and from Lyapunov stability theory, and the analysis shows that the above properties hold not only in infinite-precision but also in finite-precision arithmetic. The paper further extends the results to a so-called switching-algorithm, which is a leakage-based solution used in adaptive control.

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An algorithm for the stable operation of a digitally-implemented fractionally-spaced adaptive equalizer

Cited by 7 publications

References 3 publications

Active noise control: a tutorial review

Active noise control: a tutorial review

Magnitude response peak detection and control using balanced model reduction and leakage to a target

Unbiased and stable leakage-based adaptive filters

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