# Delta-limiting filter

Consider a filter which tracks $x_i$, clipping $|x_i - x_{i-1}| >$ some limit, say 1:

in:  0 1 2  10 0 0  10 10 10  0 0 0 0
out: 0 1 2   3 2 1   2  3  4  3 2 1 0  -- |delta| <= 1

(in Python with Numpy:  cumsum( clip( diff( x ), - limit, limit ))


Can anyone point me to a description of such filters, either in theory or in practice ?
Or is there no theory -- for the task of smoothing concrete $x$, just vary the limit and see what happens ?

(Added: "This tutorial was written for normal engineers, who do not have nonlinear filters for breakfast." -- F.Daum, Nonlinear filters: beyond the Kalman filter. Is this online anywhere ?)