The sampling theorem made visual — reconstruct a signal from discrete samples
12 Hz
4 Hz
15
Nyquist freq: 6.0 Hz
Signal freq: 4.0 Hz
Aliased: No
Max error: 0.00
Nyquist-Shannon sampling theorem (1949): Any bandlimited signal with max frequency f_max can be perfectly reconstructed from samples taken at rate f_s > 2·f_max. Reconstruction: x(t) = Σ x[n]·sinc(f_s·t − n) where sinc(x) = sin(πx)/(πx). Below the Nyquist rate, aliasing occurs — high frequencies "fold" back and corrupt the signal.