DFT, Nyquist theorem, aliasing, and spectral leakage
fs = 44 Hz | Nyquist = 22 Hz | signal f₁ = 5 Hz
5 Hz
12 Hz
0.50
44 Hz
0.10
The Nyquist-Shannon theorem: a bandlimited signal with max frequency f_max can be exactly reconstructed from samples taken at f_s > 2·f_max. Below the Nyquist limit, aliasing occurs — high frequencies appear as lower "ghost" frequencies (f_alias = |f − n·f_s|). The DFT assumes periodicity, causing spectral leakage when signal frequencies don't fit exactly in the window — suppressed by windowing functions (Hann, Hamming, Blackman) at the cost of frequency resolution. Zero-padding interpolates the spectrum without adding information.