Find Out if System is LTI - Input & Output Analysis

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    Lti System
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Discussion Overview

The discussion revolves around determining whether a system is Linear Time-Invariant (LTI) based solely on its input and output. Participants explore various methods and considerations for analyzing the system's characteristics, including both frequency domain (FD) and time domain (TD) approaches.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that the type of input and output is crucial for determining if a system is LTI, indicating that specific frequency inputs leading to different frequency outputs suggest non-linearity.
  • There is a discussion about whether the input and output need to be expressed as functions of complex frequency (s) to assess linearity, with some arguing that linear transformations can be analyzed in the time domain as well.
  • One participant proposes checking for new spectral components in the output that are not present in the input as a method to identify non-linearity, particularly in the frequency domain.
  • Another participant raises the idea that time-varying systems might produce sideband frequencies, leading to a discussion about whether this constitutes frequency translation or modulation.
  • Clarifications are made regarding the nature of sideband frequencies in relation to LTI systems, specifically in the context of filtering audio signals.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of using complex frequency functions versus time-domain analysis, indicating that multiple competing perspectives exist regarding the methods for determining if a system is LTI.

Contextual Notes

There are unresolved assumptions regarding the definitions of linearity and time-invariance, as well as the implications of spectral components and time variation on system behavior.

reddvoid
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how to find whether the system is LTI or not when only its input and output is given . . .
 
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reddvoid said:
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.
 
If the input and output are given as functions of s, the complex frequency, then yes.
 
KingNothing said:
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.
 
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.
 
Ecthelion said:
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?
 
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.
 
Ecthelion said:
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 :)
 

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