# Phase shift and phase spectrum terms in multidimensional signal

I know about phase of a 1D signal. But when I go into higher dimensions like 2D,3D etc, it becomes headache to grasp the concept.

• What are the terms phase shift and phase spectrum mean in case of multidimensional(2D,3D etc.) signal like an Image or video signal?
• How is the phase term represented mathematically?
• How do we analyze phase spectrum?
• Which information do we get from phase spectrum about the signal?
• Can anybody explain with a plot or figure ?
• Check out this answer - stackoverflow.com/questions/9644708/… – Naveen Apr 16 '15 at 17:52
• That answer demonstrates that phase is important for an image. It does not speak about what exactly is phase. – Manoj Kumar Apr 17 '15 at 3:52

## 2 Answers

For a real signal, the magnitudes of the Fourier transform bins tell what are the amplitudes of the sinusoidal components that an infinite tiling of the signal frame can be decomposed into. The phases of the bins encode translation of the sinusoids along their direction, like so: The translation can be decomposed into a series of component translations one along each of the axes. The axes of an image are spatial axes, and in video the third axis is temporal. The component translations have magnitudes inversely proportional to the frequencies indicated by the multidimensional index of the bin. For example, you can easily spatially translate an image in the frequency domain by adding to all phases (in a polar form representation of the bins) a function of form $af_x + bf_y$ where $a$ and $b$ are constants that give the amount of translation and $f_x$ and $f_y$ are the vertical and horizontal frequencies (bin indexes).

Translation of a sinusoid of zero frequency is a bit of an oxymoron. With real FFT its phase is fixed to zero.

The phase means the shift in the sine gratings components which were used to make the image. Physically the phase of the image tells about the features of the image,suppose you are doing a phase only reconstruction of an image then you can see that the most of the image's texture is obtained except for the contrast of the image.So if you try changing the phase of an image or rotate it by some orientation the feature such as texture of the image can change

for example see this link Image Reconstruction:Phase vs. Magnitude