A stability condition for adaptive recursive second-order polynomial filters

Mumolo, Enzo; Carini, Alberto

doi:10.1016/0165-1684(96)00096-5

Cited by 22 publications

(11 citation statements)

References 4 publications

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“…As noted, for example, in [19], recursive models (even in the linear case) may be unstable unless the ANC algorithm is carefully designed, by suitably setting the step size or adopting specific algorithmic modifications, such as the introduction of a 1426 D. DELVECCHIO AND L. PIRODDI leakage factor. BIBO stability conditions have been derived for recursive Volterra filters [34], bilinear models [35], second order polynomial models [36,37], recursive FLANN filters [22], essentially relying on the asymptotic stability of the linear submodel and ensuring the boundedness of the nonlinear terms. Interestingly enough, only the former assumption is necessary for recursive FLANN filters, given the specific bounded structure of the nonlinear terms [22].…”

Section: Models and Methods For Nanc In The Linear Sp Casementioning

confidence: 99%

A dual filtering scheme for nonlinear active noise control

Delvecchio

Piroddi

2013

Adaptive Control & Signal

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Active noise control problems are often affected by nonlinear effects such as distortion and saturation of measurement and actuation devices, which call for suitable nonlinear models and algorithms. The active noise control problem can be interpreted as an indirect model identification problem, due to the secondary path dynamics that follow the control filter block. This complicates the weight update mechanism in the nonlinear case, in that the error gradient depends on the secondary path gradient through nonlinear recursions. A simpler and computationally less demanding approach is here proposed that employs the updating scheme of the standard filtered-x least mean squares (LMS) or filtered-u LMS algorithm. As in those schemes, the calculation of the error gradient requires a signal filtering through an auxiliary system, here obtained through a secondary adaptation loop. The resulting dual filtering LMS algorithm performs the adaptation of the controller parameters in a direct identification mode and can therefore be easily coupled with adaptive model structure selection schemes to provide online tuning of the model structure, for improved model robustness.

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Section: Models and Methods For Nanc In The Linear Sp Casementioning

confidence: 99%

A dual filtering scheme for nonlinear active noise control

Delvecchio

Piroddi

2013

Adaptive Control & Signal

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“…[32], a sufficient, but not necessary, condition to ensure a bounded output requires x(n) to be bounded. Therefore, in nonlinear system identification experiments, the Gaussian input signal is zero-mean Gaussian signal.…”

Section: Nonlinear System Identificationmentioning

confidence: 99%

A hierarchical alternative updated adaptive Volterra filter with pipelined architecture

Pang

Zhang

2016

Digital Signal Processing

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“…(10) By calling the term on the right of (10), and introducing the 's defined above, we have (11) Since the poles 's are inside the unit circle, by induction on the order of the system, one can easily show that this last expression can also be written as follows [9]:…”

Section: Sufficient Stability Condition For General Order Recursimentioning

confidence: 99%

“…In [9], the authors of this letter presented simple sufficient stability conditions for recursive quadratic Volterra filters. In this letter, such stability conditions are extended to the more general recursive Volterra systems of arbitrary order, i.e., the polynomial systems described by the following input-output relationship: (1) It is shown in this letter that, provided that the stability of the linear part is guaranteed, the output of the filters in (1) is bounded for every if the input signal is bounded by a certain value which can be very efficiently computed from the filter coefficients.…”

Section: Introductionmentioning

confidence: 99%

On the stability of discrete time recursive Volterra filters

Mumolo

Carini²

1999

IEEE Signal Process. Lett.

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Many real nonlinear systems are characterized by an infinite input signal memory. In such conditions, system modeling by means of recursive polynomial filters requires a much lower number of coefficients with respect to nonrecursive realizations. However, the main problem of recursive polynomial filters is their inherent instability. This letter describes simple sufficient stability conditions for a class of discrete-time nonlinear systems based on recursive Volterra filters of arbitrary orders

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A stability condition for adaptive recursive second-order polynomial filters

Cited by 22 publications

References 4 publications

A dual filtering scheme for nonlinear active noise control

A dual filtering scheme for nonlinear active noise control

A hierarchical alternative updated adaptive Volterra filter with pipelined architecture

On the stability of discrete time recursive Volterra filters

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