Smoothing Data with Average Calculation

[rjunior]

How to make it causal:

y (n) = x ((n-1) + x(n) + x(n+1))/3

 

[Jaynte]

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

 

[tedbradly]

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).

 

[Jaynte]

Sorry for the index.

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

 

[DeeNos]

Smoothing data with average calculation is a common method used to reduce noise and variability in a dataset. However, it is important to note that this technique does not necessarily make the data causal. Causality refers to the relationship between cause and effect, meaning that one variable directly affects another.

In the equation provided, the output variable (y) is determined by taking the average of the input variables (x) from the current and surrounding time points. This can help to reduce the impact of any outliers or random fluctuations in the data, making it appear more consistent and predictable. However, it does not establish a causal relationship between the input and output variables.

To make the data causal, further analysis and experimentation would be necessary. This could involve manipulating the input variables and observing the effects on the output variable, or conducting a controlled experiment to establish a cause and effect relationship. Simply smoothing the data with average calculation does not guarantee causality.