**Spectrum Centralization**From the previous example, we see that in the 2D spectrum array, the DC component is at the upper-left corner, the highest frequency component is in the middle, and the high frequency components are around the middle, while the low frequency components are around the four sides. Sometime it is preferable to centralize the spectrum by shifting the spectrum by M/2 vertically and N/2 horizontally, so that the DC component and the low frequency components are in the middle while the high frequency components are around the four sides.

Similar to 1D DFT, the 2D DFT of a M by N 2D array of spatial samples also has the frequency shift property:

If we change the sign of all spatial sample points if is an odd number, i.e.

then the resulting 2D Fourier spectrum will be centralized with DC component in the middle and high frequency components around the four edges.The 2D DFT of an M by N 2D spatial signal is also an M by N 2D array. After centralization, the element in the middle where , becomes the DC component. The farther a frequency component is from the center, the higher spatial frequency it represents. Specifically, the (k,l)th component represents a spatial sinusoid with

**Examples:****Fourier Filtering**During filtering, The 2D spectrum is multiplied by a 2D filter mask :

so that the frequency components can be modified (enhanced or reduced).