Sampling > Respected Shannon limit

We propose to study a sine function with a frequency of 32 Hz and sampled at a frequency Fe of 512 Hz. The modulus of its FT is present between 0 and 256 Hz (Shannon limit). The aim of the exercise is to sub-sample the sine function. So far as n remains inferior to 8, the Fm Shannon limit (greater than 32 Hz for the analyzed sine function) is respected and the sine function is corrected sampled (the dirac associated with its FT is clearly located at 32 Hz) but badly drawn in time. To correctly visualize a function, it is often necessary to over-sample it (Sub-sampling a seismic section in time and spectral aliasing.).

For a value of n=8, all the samples are zero and they correspond to the conversion from all the zero values of the sine function, the limit of Shannon frequency (32 Hz) having been reached.
The product of a function by a Dirac comb function of period n/Fe translates itself by a periodisation in the frequency domain. So far as the Shannon limit is respected, there are no modifications to the spectrum of the sine function. The spectral modifications brought about by not adhering to the Shannon limit are shown in time and frequency.