check if a system is linear?

[gnappo]

Hi,

I have a problem that I even don't know if it has a solution. I have 2 set of experimental data: Xi(t) (input) and Yi(t) (output). Is there any Labview toolkit that can help me to understand if the physical system giving Y as output if X is the input is a linear system or has some degrees of non-linearities? 

I am not at all an expert in signal theory. Further, I have not control on input data (that is I cannot play like I could play with electric circuits changing the input voltage for example). My data are what they are, and I would like to understand if there is some degree of nonlinearity into them. 

If you know if there is any toolkit in labview that could help, I would be glad if you could say to me its name. 

Thank you

[Bob_Schor]

Linear systems are defined by having the following property:  If you know the output F(A) to input A, and know the output F(B) to input B, then if the system is linear, the output to A+B will be F(A) + F(B).  In particular, the output to F(kA) will be kF(A).

Usually when I think about linear systems, I think about systems taking time-varying signals.  For example, a perfectly good linear operator is differentiation, since the derivative d(A+B)/dt = dA/dt + dB/dt.  For this sort of linear system, a property that pops out of the definition is that if you put a sine wave of a certain frequency in, you get out only a sine wave of the same frequency, but possibly with different amplitude and phase.  Thus many such linear systems are characterized by how they handle sine waves of multiple frequencies.

 

I guess the bottom answer is that you may need to understand a little more about signal theory, and the nature of your data.  Once you have this information, you can probably figure out how to design a test to see if your system is, indeed, linear.

 

One final note -- almost no system is "linear" -- they all typically "saturate" if you give them too much input, and on the low end, will either have a threshold or an inherent "noise" level that buries the signal when small enough.  So you need to think about how "linear" you need it to be.

 

BS

[billko]

Bob, the kudo is because you are s SUPER teacher!!!