Nyquist–Shannon sampling theorem
This leads to a natural formulation of the Nyquist–Shannon sampling theorem. If the spectrum of the function formula_36 contains no frequencies higher than B (i.e., its spectrum is nonzero only in the interval formula_37) then samples of the original function at intervals formula_38 are sufficient to reconstruct the original signal. It suffices to multiply the spectrum of the sampled function by a suitable rectangle function, which is equivalent to applying a brick-wall lowpass filter.