With this month's column we will take an introductory look into a topic that many find to be intimidating - digital filters. What digital filters provide is a means to condition a digital signal in order to achieve a variety of purposes. Depending upon the problem that one is confronted with, a filter may be needed to solve one or more signal conditioning requirements: reduce unwanted noise, isolate or reject a piece of the signal, enhance certain components of a signal (either increasing its amplitude or temporal resolution). What makes digital filtering hard to master is that in order to create a filter to achieve your goals takes a bit of calculus (usually in the complex plane) to properly do it. What makes digital filtering intimidating is the degree to which various authors handle the calculus. If they hide the calculus, then digital filters take on the air of a black art. If they just do the calculus then they throw their readers into the deep end, and risk losing a few in the process. I will try to strike a balance and give you the math but start at the shallow end of the pool.
I learned digital filtering from exploration seismologists (the people that inject signals into the ground with various kinds of mechanical vibrators, thumpers and explosives, in search of mineral and oil deposits). Other than notation, the mathematics behind the seismologists version of digital filters is the same as the electrical engineers version. What is different is that the two groups approach the subject somewhat differently. We will use the seismology approach; to the electrical engineers reading this it will look odd at first (but not unfamiliar) but ultimately we get to the same end.