# 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 ?)

I guess that would be a slew rate limiter. This is concept is mostly used an amplifier design as a practical constraint of the circuit. I haven't seen it applied as a digital filter. It is certainly very non-linear and it would make a poor "smoothing filter" as it's highly dependent on the absolute amplitude. Could you shed some light on the specific application and explain what a regular low pass filter can't do the desired smoothing job?

• Briefly, I want to limit slew rate / derivative / large swings in splines. – denis May 1 '13 at 8:41