The concept of frequency spectrum exists because it is possible to sum sines and cosines of various frequencies together to make any periodic signal. The frequencies of these individual sinusoids make up the spectrum of the final signal. Now when it comes to image processing we treat image as a signal similar to sound for example in that it has a bandwidth and it is possible to filter certain frequencies it to achieve various results.
What I am not clear about is, how did people get concept of frequency in 2D? Sinusiods are 1D signals, how can we extend this concept of frequency into 2D? Is it possible to do the same in 3D and do filtering in 3D? Does anyone do that in any application?
I fully understand low pass, high pass, band pass and band stop filters. Their frequency respons curves are quite straight forward. What I do not understand is, how is this extended into 2D?