A Simple Low-Pass Filter

The simplest low-pass filter (and therefore furthest from ideal) is given by the difference equation

$\displaystyle y(n) = x(n) + x(n-1).$
The corresponding system diagram is given below:

Figure 2: System diagram for the simple low-pass filter .
$\begin{figure}\centerline{% \input{lp_sysdia.pstex_t}}\end{figure}$
This filter is really just a running averager (2-point averager) with a factor of two. That is, it takes the average of two adjacent samples.

**Figure 2:** System diagram for the simple low-pass filter .
$\begin{figure}\centerline{% \input{lp_sysdia.pstex_t}}\end{figure}$

Why is it a Low-Pass Filter?

``Mus 270a: Introduction to Digital Filters'' by Tamara Smyth, Department of Music, University of California, San Diego.