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phase spectrum

Where, spatially, each frequency component is positioned.

The phase spectrum \angle F(u,v) = \operatorname{atan2}(\operatorname{Im}(F(u,v)), \operatorname{Re}(F(u,v))) reports each frequency component's position -- shifting a pattern sideways changes phase at every frequency it appears in while leaving magnitude completely unchanged. Both spectra together are needed to reconstruct an image exactly.

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