Free Books

Fourier Series Special Case

In the very special case of truly periodic signals $ x(t) =
x(t+NT)$, for all $ t\in(-\infty,\infty)$, the DFT may be regarded as computing the Fourier series coefficients of $ x(t)$ from one period of its sampled representation $ x(nT)$, $ n=0,1,\dots,N-1$. The period of $ x$ must be exactly $ NT$ seconds for this to work. For the details, see §B.3.

Next Section:
Normalized DFT
Previous Section:
Spectral Bin Numbers