F(ω) is called spectrum of the signal f(n). The spectrum has complex values, so it can be represented in the form:

where |F(ω)| is the amplitude spectrum or magnitude spectrum, and φ(ω)=arg(F(ω)) is the phase spectrum.

Spectral frequencies in images

Let us assume that f(n₁,n₂) is a static image. n₁ is an index of samples in horizontal direction (x axis) and n₂ - in vertical direction (y axis).