# Thread: signal analysis - step function

1. ## signal analysis - step function

Hi there,

I have a problem about the characterization of a step function:

I analyze a discrete time discrete valued slow signal over the time.
The signal corresponds to the conductivity measurement of a water solution during the time, the conductivity value in the water solution is controlled by a slow feed-back system, the reference value is change let's suppose an increase in one unit, and some actuators increase the solution conductivity until the new reference value is achieved. So I guess that the function could be described as a step function with a high amortiguation.

I need to detect when the signal arrives to the new value, however the signal is subject to some noise, I mean that even when raising is it possible to find values which are a bit lower when compared with the previous one.

Thanks,
Caste

I have programmed an algorithm which iterates through each value comparing it with the previous one, when the increase respect the previous one is not big enough, the algorithm considers it has arrived to a plateau.

I am not sure is my approach is reliable enough or I should try to characterize the function using some mathematical model. If so could you give me some directions to leatn how to do so?

2. Originally Posted by caste
Hi there,

I have a problem about the characterization of a step function:

I analyze a discrete time discrete valued slow signal over the time.
The signal corresponds to the conductivity measurement of a water solution during the time, the conductivity value in the water solution is controlled by a slow feed-back system, the reference value is change let's suppose an increase in one unit, and some actuators increase the solution conductivity until the new reference value is achieved. So I guess that the function could be described as a step function with a high amortiguation.

I need to detect when the signal arrives to the new value, however the signal is subject to some noise, I mean that even when raising is it possible to find values which are a bit lower when compared with the previous one.

Thanks,
Caste

I have programmed an algorithm which iterates through each value comparing it with the previous one, when the increase respect the previous one is not big enough, the algorithm considers it has arrived to a plateau.

I am not sure is my approach is reliable enough or I should try to characterize the function using some mathematical model. If so could you give me some directions to leatn how to do so?

There is no right or wrong answer to this problem, it all depends on what you
want to do and how much you know.

If you know the demands and the systems transfer function or whatever
is appropriate to your case, and the times when the demand is changed
you can calculate from the system model when the new set point will be
achieved (to a given tolerance).

Otherwise will need some other method.

RonL

3. Hi Captain,

That's exactly the point, I know the transfer functions, but not the times at all, and there's quite a lot of factors that might influence the evolution of the function producing a delay (increase of the amortiguation) of the step.

That's why so far I recognize plateaus and peaks based on a loop that compares the value with the previous one, and a set of tunning factors. However this factors are difficult to understand intuitively.
One of the most important things is that I have some noise, I mean, let's suppose that the conducitivity is at a baseline of 1, and I set a step to 2, a typical value set would be: 1, 1, 1.2, 1.3, 1.25, 1.4, 1.6, 1.53, 1.5, 1.59, 1.6,1.8,2, ....
It happens that even during the raise I can find values lower than the previous one, so my algorithm besides of the comparison tracks any possible increase start, and requires a given number of raising or decreasing values without noise in order to change the statte to raise or decrease.

Another approach I've been thinking lately is base the recognition on the variance of some range of values, as long as the system arrives to a plateau the variance will be lower.

As you said there's no right or wrong answer... I want to collect some impressions of math people to wonder if my approach is acceptable or if I should go for another method.

Thanks,
Caste