Smoothing Data with Average Calculation

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Discussion Overview

The discussion revolves around the concept of smoothing data through average calculations, particularly in the context of causal systems and transfer functions. Participants explore the implications of indexing and the conditions under which a system can be considered causal or non-causal.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant proposes a formula for smoothing data using a moving average, suggesting that the output y(n) is calculated based on the average of three input values.
  • Another participant discusses the need to adjust the transfer function to ensure it is located in the right half plane, indicating a transformation of the index from n to m.
  • A subsequent post questions the reasoning behind the change in indexing from m-1 to m, highlighting the uncertainty regarding the causality of the system without knowing the specific form of x(n).
  • Another participant asserts that if the system is Linear Time Invariant (LTI), it is causal if the impulse response h(n) equals zero for t less than zero.

Areas of Agreement / Disagreement

Participants express differing views on the conditions for causality and the implications of indexing in the context of transfer functions. The discussion remains unresolved regarding the causal nature of the system based on the provided information.

Contextual Notes

There are limitations regarding the assumptions about the input function x(n) and the definitions of causality and non-causality in the context of the discussed formulas.

rjunior
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How to make it causal:

y (n) = x ((n-1) + x(n) + x(n+1))/3
 
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you need to move the transfer function such that it is located in the right half plane, n>=0

replace n=m-1, this will move the function in time

y(m)=x((m-2)+x(m-1)+x(m))/3
 
Jaynte said:
you need to move the transfer function such that it is located in the right half plane, n>=0

replace n=m-1, this will move the function in time

y(m)=x((m-2)+x(m-1)+x(m))/3

So why does y magically become indexed at m instead of m - 1?

It also seems like you can never know if that system is causal (though you can know it is non-causal) without knowing what x(n) looks like since he is evaluating x at x(n-1) + x(n) + x(n+1).
 
Sorry for the index.

If the system is Linear Time Invariant it is casual if h(n)=0 for t<0
 

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