# Moving Average System?

Can someone elaborate on what a moving average system is?

I know that the system is defined as:

y[n] = (1/3) [x[n] + x[n-1] + x[n-2]]

How would we draw y[n] given that we have a graph with discrete values for x[n]? Can someone actually draw a sample discrete time x[n] graph and show how the corresponding y[n] graph is generated?

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Huh, wait. The form I'm accustomed to goes like $\dfrac{x_{n-1}+x_n+x_{n+1}}{3}$. The form you gave is the one usually used for endpoints... could you check your source again? –  Ｊ. Ｍ. Sep 23 '11 at 1:22
this is for a discrete time signal.... I am sure this is correct... –  rrazd Sep 23 '11 at 1:23
Anyway... you're already aware of the "sliding window" analogy, right? Say you have the sequence $(x_1,x_2,x_3,x_4,x_5,x_6,x_7)$. The first pass replaces $x_3$ with the mean of $x_1,x_2,x_3$. Then, you shift by one place, replacing $x_4$ with the mean of $x_2,x_3,x_4$, and so on, up until you're replacing $x_7$ with the mean of $x_5,x_6,x_7$. Note that the group of points being taken always has overlap with the previous one. –  Ｊ. Ｍ. Sep 23 '11 at 1:31