# Describing a time delay at a maximum for maxima and minima but tends to 0 elsewhere

I have two force-time signals obtained from a couple of force plates, corresponding to input/output signals for some system. Plotting the two together one of the first things I noticed was a time delay. Initially I used cross correlation to gain some approximation for this feature however now I look a little closer I realize things are little more complex.

Basically the output trails behind the input with a time delay that is maximum at the maxima/minima on the two signals and in between the delay tends towards 0.

I literally have no idea how to express this. Can anyone suggest anything?

EDIT: Rough plot below. Genuinely apologize for the MSPaint... I don't have access to anything better or my plots right now! Also the absolute integral of both signals is approximately equal.

I'm thinking of making the time delay dependent on amplitude but sadly my mathematical skills at the moment restrict me to something as basic as pulling off maxima/minima with basic differentiation and recording the separation of corresponding features as a function of amplitude. Far too crude!

• Your systems is non-linear and has memory. There is no expression for the delay as a function of amplitude, because for the same amplitude you can get different delays, e.g. to the left and to the right of the maximum of the input signal. I'm not sure what it is that you're looking for, but a simple amplitude-dependent formula for the delay does not seem to exist. Mar 30, 2014 at 15:18
• What kind of measurement are you actually doing? Probably this phenomena is described in literature and solution can be deduced from there. To me it looks like some kind of hysteresis. And more important - can you provide us with real plot and preferably some data?
– jojeck
Mar 30, 2014 at 18:11
• Can you provide the same plot for 3 different amplitudes? Mar 30, 2014 at 20:46
• I'll tr and sort out some actual data sets tomorrow afternoon. I'm measuring the transfer function of the human body in the vertical plane... input signal defined as the force experienced by an accelerometer held in my hand (with a load) and the output is the force experienced by a force plate. Mar 30, 2014 at 23:27
• I agree with Matt L. / jojek: something nonlinear or involving hysteresis (or both :-) is happening, from what you describe. Either that, or you're only measuring one axes of a three axis (two of six) system, and the object is rotating in 3D while you're measuring.
– Peter K.
Mar 31, 2014 at 1:14