# Fourier domain: temporal versus spatial

I am little bit confused over these two. As per my understanding, spatial domain is the usual method we did in matlab by using the function fft2, which will return a complex value for each pixel. What about temporal? If it is a sequence of images, how do I obtain the 'temporal Fourier domain'?

If you looking at the image, is it true that the temporal Fourier domain shall have the same shape as the spatial domain image (shown in figure is the amplitude of Fourier domain)?

• "temporal", "spatial", "frequency" domain (and a lot others, like "impuls space" in solid state physics) are just terms that describe one's "intellectual" interpretation of some data/signal. So, if you sample a signal in consecutive points in time, you get a "digital time domain signal". In any case, the DFT (fft) doesn't care at all. It's just a mathematical operation applicable to vectors (or matrices (fft2) or tensors (higher-dimensional transforms)) of numbers. – Marcus Müller Jul 9 '17 at 8:11

I have done very little work using 2-dimensional FFTs. Most of my work deals with speech, so the short-term Fourier transform applied to a 1-dimensional speech signal is what I understand.

I do not know of a "canned" function, particularly in Matlab, that would realize the time-varying "temporal Fourier domain" characterization that you require. However, I would suspect you could apply a 2-dimensional FFT to a set of time-slices extracted from the original video sequence that you are working with. The time resolution of when the slices are extracted would depend on the nature of the events captured by the video. The magnitude and phase response of each 2-dimensional FFT computation could then be determined and examined to see how the Fourier domain response changes across time.

From what I understand, viewing images in the Fourier domain is not readily intuitive. I believe the Fourier domain is used to realize efficient image filtering.

I hope this helps.

If it is a sequence of images, how do I obtain the 'temporal Fourier domain'?

You would have temporal variation for each pixel. So, Fourier spectrum for each pixel, considering time variation.

If you looking at the image, is it true that the temporal Fourier domain shall have the same shape as the spatial domain image (shown in figure is the amplitude of Fourier domain)?

Temporal Fourier spectrum has just one axis, time. So, lets say image size is (N x N), you would have $N^2$ Fourier spectra for each pixel. How come your output has two axis, as an image? And there's no reason for temporal spectrum to be similar spectrum in spatial domain.