# Moving Average Filters

A **moving average** filter is an LTI system *MovingAverage*:
[*Integers* → *Reals*] →
[*Integers* → *Reals*] where the output
*y* = *MovingAverage*(*x*) is given by

*y*(*n*) = (1/*L*) ∑_{(m
= 0 to L − 1)} *x*(*n*
− *m*)

The output at *n* is the average of the most recent *L * inputs.
Such a filter is widely used on Wall Street to try to detect trends in stock
market prices. We can study its properties. First, it is easy to see that it
is an LTI system. In fact, it is an FIR system with impulse response

*h*(*n*) = 1/*L* when 0
≤
*n* < *L*

*h*(*n*) = 0 otherwise