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An easily implementable sampling procedure for certain fractal and other non-band limited signals

Abstract : The first step in digital signal processing is analog-to-digital conversion. Classically, the analog signal is sampled via the process described by the Whittaker-Kotelnikov-Shannon theorem (WKS), which requires that the original signal is band-limited. Irregular signals, as are fractal ones, typically do not verify such an assumption. The low-pass filtering necessary to apply the WKS theorem implies then a serious loss of information. Although extensions of the WKS theorem to non-band limited signals do exist, their implementation is typically rather difficult. We propose in this paper a sampling procedure for some classes of non-band limited signal which shares the simplicity of the WKS procedure (involving only bandpass analog filtering and regular sampling). We give a detailed explanation of the implementation of our sampling scheme, and provide some of its theoretical properties. Numerical experiments illustrate the behaviour of the method.
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  • HAL Id : hal-00746531, version 1

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Stéphane Lafon, Jacques Lévy Véhel. An easily implementable sampling procedure for certain fractal and other non-band limited signals. 6th Nordic Signal Processing Symposium - NORSIG 2004, Jun 2004, Espoo, Finland. ⟨hal-00746531⟩

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