Find Out if System is LTI - Input & Output Analysis

[reddvoid]

how to find whether the system is LTI or not when only its input and output is given . . .

 

[DragonPetter]

how to find whether the system is LTI or not when only its input and output is given . . .

I think you need to specify what kind of input and what kind of output are given in order to be able to describe the system.

For example, if you apply a specific frequency to an input, and get a different frequency at the output, you will know the system is non-linear.

Time-invariant implies that the transfer function of the system remains the same over time, and so you need a time series signal would let you see if it is changing over time.

 

[KingNothing]

If the input and output are given as functions of s, the complex frequency, then yes.

 

[DragonPetter]

If the input and output are given as functions of s, the complex frequency, then yes.

Is being a function of s even a requirement? I think any linear transformation will yield the characteristics of whether a system is linear. The input and output can be given in the time-domain as well.

 

[Ecthelion]

Well if we want to approach this question in the FD (although can definitely be done in TD...), a couple ways you could check (without a given system) would be to see if there are any new spectral components in the output that aren't in the input. And if the system is time-varying, sometimes it can produce sideband frequencies of the input signal.

Although if you want a more TD approach I'd suggest looking at scaling and superposition properties to see if you could perhaps intuit the system from the input and output given.

 

[DragonPetter]

And if the system is time-varying, sometimes it can produce sideband frequencies of the input signal.

That's interesting, would the time variation of the system serve as a frequency translation/modulation on the input signal?

 

[Ecthelion]

That's interesting, would the time variation of the system serve as a frequency translation/modulation on the input signal?

No, I don't believe so. When I mentioned the sideband frequencies I was referring to spectral copies. So if, when considering LTI systems, you're dealing with filters and you're filtering say an audio file, spectral copies can be made when the filter changes at audio rates. It was just what came to mind when approaching the LTI question from a FD point of view.

 

[reddvoid]

Well if we want to approach this question in the FD (although can definitely be done in TD...), a couple ways you could check (without a given system) would be to see if there are any new spectral components in the output that aren't in the input. And if the system is time-varying, sometimes it can produce sideband frequencies of the input signal.

Although if you want a more TD approach I'd suggest looking at scaling and superposition properties to see if you could perhaps intuit the system from the input and output given.

okay :)