# A sparsifying max filter that is not a dilation. Is there a name for this operation?

I implemented a sparsifying max filter that takes a sliding window of length $$M$$ that runs over a time series of length $$L$$, keeps the maximum value in that window, and put zeros everywhere else at the output. The windowed outputs are lagged and summed to simulate a convolution operation. For example, if the input is

$$[4,5,7,6,4,3,4,2,0,2,4,5,6,7,8],$$

$$M=4$$, and we use a zero-padding of length $$3$$ at both ends of the input, we will get the output

$$[0, 0, 0, 4, 5, 28, 6, 2, 0, 10, 0, 0, 0, 4, 5, 6, 7, 32, 0, 0, 0].$$

At first, I thought that this was a dilation operation, but then I realized that what I did is different since the dilation doesn't sparsify. Is there another math operation, or algorithm, that do something similar to what I did? or maybe closer than the dilation or moving max?