2DFouriertransformation
The two-dimensional Fourier transformation is a mathematical operation that converts a function f(x, y) defined on the plane into its frequency components. In the continuous form, the 2D Fourier transform is F(u, v) = ∫∫ f(x, y) e^{-i 2π (u x + v y)} dx dy, and the inverse transform is f(x, y) = ∫∫ F(u, v) e^{i 2π (u x + v y)} du dv. Normalization conventions vary; some definitions place 1/(2π)^2 factors in the inverse. The transform assumes f is integrable (or square-integrable) and is used to analyze spatial frequency content.
For digital data, the discrete 2D Fourier transform applies to an M by N array f[m, n].
Key properties include linearity, and the correspondence between spatial and frequency operations: translation in space results