Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Can someone elaborate on what a moving average system is?

I know that the system is defined as: $$y[n] = \frac{x[n] + x[n-1] + x[n-2]}{3}$$ 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?

share|improve this question
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

1 Answer 1

You need to convolve your data $\mathbf{x}$ with the impluse response of the corresponding FIR filter $\mathbf{h}$. You can learn the details from here.

share|improve this answer
This answer would be better if the relevant source material were summarized, rather than using a non-permanent link to the top level of a 1700-word Wiki page. Alternatively, this is well-suited as a comment. –  Arkamis Jan 9 at 19:55
@Arkamis I would write definitely more if the question would not be asked 3 years ago. I can write alot and it is a loss of time if the OP is already away. It is therefore better to spend less time at the beginning and if the OP is still alive then he/she will definitely contact you for details. –  Seyhmus Güngören Jan 10 at 1:26

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.