Postfiltering versus prefiltering for signal recovery from noisy samples

Pawlak, M.; Rafajłowicz, Ewaryst; Krzyżak, Adam

doi:10.1109/tit.2003.820013

Cited by 38 publications

(22 citation statements)

References 30 publications

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“…Nevertheless, one can consider interpolation as a simple remedy to these deficiencies. It yields a global and continuous model of the nonlinearity and can be easily refined with the successively incoming measurement data; see Remark 8 (in the numerical experiments in Section 5.1 we demonstrate potential advantages of an interpolation scheme (see also, e.g., Pawlak et al, 2003;Śliwiński, 2013).…”

Section: 3)mentioning

confidence: 90%

A simple scheme for semi-recursive identification of Hammerstein system nonlinearity by Haar wavelets

Śliwiński¹,

Hasiewicz²,

Wachel³

2013

International Journal of Applied Mathematics and Computer Science

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A simple semi-recursive routine for nonlinearity recovery in Hammerstein systems is proposed. The identification scheme is based on the Haar wavelet kernel and possesses a simple and compact form. The convergence of the algorithm is established and the asymptotic rate of convergence (independent of the input density smoothness) is shown for piecewiseLipschitz nonlinearities. The numerical stability of the algorithm is verified. Simulation experiments for a small and moderate number of input-output data are presented and discussed to illustrate the applicability of the routine.

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Section: 3)mentioning

confidence: 90%

A simple scheme for semi-recursive identification of Hammerstein system nonlinearity by Haar wavelets

Śliwiński¹,

Hasiewicz²,

Wachel³

2013

International Journal of Applied Mathematics and Computer Science

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“…Some techniques have been proposed thereafter to tackle the effect of different types of added noise and improve the robustness of Shannon. We note [10], [11] which contain a list of references. However, those papers were dedicated solely to Shannon's method.…”

Section: ¦ ¦mentioning

confidence: 99%

Evaluation of several reconstruction methods of bandlimited signals

Ahmad

Tarczyński

2008

2008 2nd International Conference on Signals, Circuits and Systems

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“…Previous treatment of reconstruction in the presence of noise includes analysis of the noise effects in existing reconstruction systems [9]- [12], and concrete reconstruction methods from noisy samples [13]- [16]. However, the suggested algorithms tend to focus on the bandlimited setting and are typically not specified to be optimal from the point of view of statistical estimation theory.…”

mentioning

confidence: 99%

“…A class of reconstruction methods that was proposed in [14], [16] in the context of bandlimited sampling is based on convolving the noisy samples with a finite-impulse-response (FIR) filter prior to reconstruction. Under certain conditions on the sampling and reconstruction spaces, we show that FIR reconstruction is admissible if and only if the filter impulse response is symmetric, and its Fourier transform satisfies .…”

mentioning

confidence: 99%

Mean-Squared Error Sampling and Reconstruction in the Presence of Noise

Eldar

2006

IEEE Trans. Signal Process.

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Abstract-One of the main goals of sampling theory is to represent a continuous-time function by a discrete set of samples. Here, we treat the class of sampling problems in which the underlying function can be specified by a finite set of samples. Our problem is to reconstruct the signal from nonideal, noisy samples, which are modeled as the inner products of the signal with a set of sampling vectors, contaminated by noise. To mitigate the effect of the noise and the mismatch between the sampling and reconstruction vectors, the samples are linearly processed prior to reconstruction. Considering a statistical reconstruction framework, we characterize the strategies that are mean-squared error (MSE) admissible, meaning that they are not dominated in terms of MSE by any other linear reconstruction. We also present explicit designs of admissible reconstructions that dominate a given inadmissible method. Adapting several classical estimation approaches to our particular sampling problem, we suggest concrete admissible reconstruction methods and compare their performance. The results are then specialized to the case in which the samples are processed by a digital correction filter.

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Postfiltering versus prefiltering for signal recovery from noisy samples

Cited by 38 publications

References 30 publications

A simple scheme for semi-recursive identification of Hammerstein system nonlinearity by Haar wavelets

A simple scheme for semi-recursive identification of Hammerstein system nonlinearity by Haar wavelets

Evaluation of several reconstruction methods of bandlimited signals

Mean-Squared Error Sampling and Reconstruction in the Presence of Noise

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