Moving Average

An M-point moving average is a discrete-time system with input

x: Integers ® Reals

and output

y: Integers ® Reals

where " n Î Integers,

y(n) = S _{(k = 0 to M-1)} (1/M) x(n - k)

Recall convolution:

y(n) = S _{(k = 0 to n)} h(k) x(n- k)

Comparing these two, we see that the moving average is an LTI system with impulse response

h(n) = 1/M; if 0 <= n < M
h(n) = 0; otherwise

See more details about the moving average example.