An easily implementable sampling procedure for certain fractal and other non-band limited signals
Lafon, Stéphane ; Lévy Véhel, Jacques
HAL, hal-00746531 / Harvested from HAL
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.
Publié le : 2004-06-09
Classification:  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
@article{hal-00746531,
     author = {Lafon, St\'ephane and L\'evy V\'ehel, Jacques},
     title = {An easily implementable sampling procedure for certain fractal and other non-band limited signals},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00746531}
}
Lafon, Stéphane; Lévy Véhel, Jacques. An easily implementable sampling procedure for certain fractal and other non-band limited signals. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00746531/