First time asking a question here so hopefully I can provide enough information to you guys without explaining more than necessary.
I'm doing some amateurish numerical analysis in MATLAB on some digital signals I'm generating with certain parameters.
I plotted the two parameters and their response below in a contour plot and a surface plot. I'm seeing this rotating staircase pattern. Is there any mathematical significance to this pattern? Or anyway I can estimate some functions that would predict the response based on these two variables? I'm at a loss as to how to make sense of this.
It's hard to see in the linked picture, but the response looks almost like choppy water at the lower end of the staircase, and becomes more defined on the higher steps.
It appears that:
the response depends only on the ratio "slope"/"aperture level", not on the individual quantities themselves. This suggests reorganizing the data by grouping the measurements by this ratio. You'll get a single-variable function, easier to visualize and analyze.
The response is somehow quantized. After making the aforementioned single-variable plot, you should take note of (a) amplitude of peaks; (b) position of peaks. Say, enumerate peaks $1,2,3\dots$ starting with the tallest. Then the amplitudes form a nicely decreasing sequence $a_n$. Try to fit a function of the form $cn^{-\alpha}$ to this sequence (Matlab has some curve-fitting tools). Similar for position of peaks.