Struggling to Understand Causality in Input-Output Relationship

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SUMMARY

The discussion centers on the concept of causality in the input-output relationship defined by the equation y(t) = x(|t|). Participants clarify that a system is considered causal if the output at any time t relies solely on current or past inputs, not future ones. The equation presented indicates that when t is negative, the output y depends on future input values, thus confirming that the system is non-causal. The confusion arises from interpreting the relationship between x and y, particularly when considering the integral x=∫y, which incorporates past values.

PREREQUISITES
  • Understanding of causal systems in signal processing
  • Familiarity with input-output relationships in mathematical modeling
  • Knowledge of the absolute value function and its implications
  • Basic concepts of integrals and their role in determining past values
NEXT STEPS
  • Study the definition and examples of causal vs. non-causal systems in signal processing
  • Explore the implications of the absolute value function in input-output relationships
  • Learn about the properties of integrals and their applications in system analysis
  • Investigate the concept of time-invariance in relation to causality
USEFUL FOR

Students and professionals in engineering, particularly those focused on signal processing, control systems, and mathematical modeling, will benefit from this discussion.

cybernoodles
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Hi All,

So I'm at the point where my brain is numb. I've been struggling for the past few hours trying to understand causality. Specifically, I have an input-output relationship y(t) = x(|t|). Determining if this is causal has been very difficult. Causal means that the output at any given time t is dependent on either the current input (present) or past input. So, if I plug in 5 to my output equation, I just get 5. How is that dependent on the past? I'm being told that this system is NOT causal, I.E. dependent on the past, which is really killing me.
 
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Consider the value of y when the parameter of y is negative. The value would be equal to the value of x with a positive parameter, which you may interpret as the output of the system depending on the future value of the system input.
 
x=y seems present tense.

x=∫y would include past?
 

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