3. Temporal signal truncation: consequences; correction: weighting windows

3.1 Temporal signal truncation

FFT spectral analysis is based on the principle of transforming N temporal signal values into N frequency values "en bloc".

In this section, we focus on the influence of the number of calculation points N on the spectral representation obtained.

Let x (t ) be the analog signal to be analyzed, with Fourier transform X (f ).

The sampling of x (t ) is assumed to respect Shannon's theorem and yields : $x\text{*}\left(t\right)={\displaystyle \sum _{k=-\infty }^{\infty }x\left(k{T}_{\text{e}}\right)T_{\text{e}}\delta \left(t-k{T}_{\text{e}}\right)=x\left(t\right)}$