The median, z, of a set of numbers is such that half the values in the set are below
z and the other half are above it. For example, the median of the set of values
{2, 3, 8, 20, 21, 25, 31} is 20.
U. Dreher
The basic definition of linearity is that the output of a function exhibits a proportional response to changes in the input.
Regarding a median filter of length 3 on a sample of length 5, we are able to calculate 3 results (assuming that results off-index are invalid).
Input [1 2 3 4 5] ==> Output [2 3 4]
Input [1 2 3 4 6] ==> Output [2 3 4]
A single example is sufficient to prove that the conditions for linearity are not fulfilled. Even if many other examples might exhibit a response similar to linear functions.
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