Introduction

It is often necessary to filter data from sensors or audio streams in order to suppress unwanted noise. And, most of the time, a simple first order filter is all that is required. The technique discussed below describes a quick design solution that will allow you to design and implement a first order using fixed-point math.

Background

In the z-domain, the equation for a first order filter looks like:

Where:

• T: sampling period
• a: the cutoff frequency in units of radians/second

In the time domain, the above transforms into:

The Meat of the Matter

If we replace:

with k and solve the above to get unity gain, then our difference equation can be simplified to:

The trick now is to determine what those k values need to be. First, let’s translate a to our cutoff frequency and T to our sampling rate:

a=2πf_c

T=1/f_s

k can now be readily derived given our desired cutoff frequency and sampling rate: