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.