Sampling

Sampling is the conversion of a continuously variable signal into a suite of samples. To do that we replace the continuous function by a suite of values which correspond to the integration of the signal over an interval called the sampling interval.

The conversion of an analogic function to a suite of samples (digital function) necessitates a certain number of precautions be taken, and that the interpolation sampled data requires a certain know-how.

This chapter has one aim and that is to familiarize the reader with known problems which occur during the conversion of a continuous function to a discrete function and vice versa. We hope to attract the reader's attention to a certain number of points which one would do well to matriculate.

1) To correctly sample a function, one should respect the Shannon condition (the respected Shannon Limit) that is to say, one should sample a function with a minimum of 2 points per period. This condition guarantees to respect all the information contained in the signal, nevertheless to correctly visualize the function, it is sometimes necessary to use interpolation ( interpolation by truncation in the frequency domain and the so-called Shannon interpolation).

2) All sampling introduces a periodisation and vice versa.

The Dirac is the object of a specific exercise: Phase of the FT of a Dirac.

We will present a 2-dimensional example which does not respect the Shannon condition and that introduces periodisations that are often called aliasing (Sub-sampling of a seismic section in time and spectral aliasing).