I stumbled upon this question and I can't seem to solve it correctly "Given a signal $x(n,m) = a +b{\cdot}m + c{\cdot}n $ and a filter, find the processing system response defined in a finite symmetric range." Let's say our filter is the median filter. $M(n,m) = median\{x(m,n)(m,n) \in W\}$ with W the neighborhood centered around location $[m,n]$. My solution till now is:
- I transformed with DFT the initial signal.
- I used median filter on the initial signal.
- I used DFT on the result from the median $M(n,m)$.
- I applied this formula to find the H. $H(u, v) = \frac {M(u,v)}{X(u,v)} $
- I was planning to apply IDFT on H but I'm not quite sure about the process so far.
Could anyone show me this or a similar example with a non linear or morphological filter, or even a linear (e.g. Gaussian)? I really want to understand where I'm going.