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reddvoid
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how to find whether the system is LTI or not when only its input and output is given . . .
reddvoid said:how to find whether the system is LTI or not when only its input and output is given . . .
KingNothing said:If the input and output are given as functions of s, the complex frequency, then yes.
That's interesting, would the time variation of the system serve as a frequency translation/modulation on the input signal?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?
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.
An LTI (Linear Time-Invariant) system is a type of system in which the output response is directly proportional to the input signal and is not affected by time. This means that the system's behavior remains the same regardless of when the input is applied.
A system can be determined to be LTI by performing an input and output analysis. This involves applying different input signals to the system and observing the corresponding output responses. If the output response is directly proportional to the input signal and is not affected by time, then the system is LTI.
One advantage of an LTI system is that it is easier to analyze and predict the system's behavior. This is because the output response is directly proportional to the input signal and is not affected by time. Additionally, LTI systems have a wide range of applications in various fields such as signal processing and control systems.
Yes, a system can be both linear and time-invariant but not LTI. For a system to be LTI, it must satisfy the conditions of linearity and time-invariance as well as have a proportional output response to the input signal and not be affected by time. If a system does not meet these conditions, it is not considered to be LTI.
Determining if a system is LTI is important because it allows us to accurately predict and analyze the system's behavior. This is especially useful in applications such as signal processing and control systems, where understanding the system's response to different input signals is crucial. Additionally, knowing if a system is LTI can help in designing and optimizing the system for better performance.