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 : $x * (t) = \sum_{k = - \infty}^{\infty} x (k T_{e}) T_{e} δ (t - k T_{e}) = x (t)$

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Temporal signal truncation: consequences; correction: weighting windows

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References

(1) - MAX (J.) et coll - Méthodes et techniques de traitement du signal et applications aux mesures physiques. - 4e édition, Masson (1989).
(2) - Agilent. The fundamentals of signal analysis. - Application note 243.
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