I am currently reading on the topics of image filtering and convolution kernels. While the process of convolution is clear to me, I do not understand, how one arrives at the statement, that a certain filter is a low or a high pass?
How can one derive that? For example, if one averages the value of a pixel respecting its surrounding pixels, does that for all pixels, then each pixel would have a value between the minimum and the maximum value of the previous image. It treads low values and high values equally, however literate often states, that it is a low pass filter.
For that specific case I found the question What is the intuition of "averaging is a low pass filter". Reading it, however didn't help me, as I seem to lack something to see how these arguments are correct and intuitive. Thus I hope, that a more mathematical approach (can be a general one), would benefit me.