Consider the contour plot below, of a function f(x,y) - which is calculated numerically by solving some equations. If one looks carefully, one can observe two types of waves, to the left and right of the depression at (0,0). To the right we see waves of long wavelength (only two crests are visible actually). The waves to the left, on the other hand, are much more closely spaced and much less intense, but one can still distinguish them. Let us ignore the vertical stripes, which are of no interest.
Now if we take the 2D Fourier transform of the data, we get a picture like this:
The very small circle in the center corresponds to the waves of large separation, and the other 2 circles correspond to the washed out, closely-spaced waves.
My question is, what type of manipulation can I do (some filtering/convolution comes to mind) in order to give more weight to the washed-out waves to the left (make them more visible)?
Just to clarify the above. I am not interested in any of the parallel vertical lines in the real-space plot, either to the right or to the left. What I am interested in are the very small parabolic waves very close to the center of the image, on the left side. I try to point them out in the zoom below, because they might be hard to spot in the original plot.
I would prefer a way of selecting just the waves which correspond to a certain ring in the Fourier transformed image, something like a band pass filter which selects one ring. That is because I suspect that the close-spaced waves on the left of the center correspond to one particular ring only (the one pointed to by the blue arrow in the fourier plot).
The main motivation for doing things like this is that then I want to apply the same method to the problem below:
data = Import["http://pastebin.com/raw.php?i=ieiLy8AD"]; img = Image[Rescale[data], ImageSize -> 400]
In this image, the washed out waves to the left of the dark central point are even weaker. My gut feeling is that they can be best brought out by filtering in Fourier space.
However, I am willing to accept any answer that can transform this last image to one where the small ripples are seen clearly and then make a cut of that 2D plot to calculate their wavelength (along the y=0 axis for instance).