5616 Analog and Digital Filters
The world we have created today has problems which cannot be solved by thinking the
way we thought when we created them.
Albert Einstein6.1 Introduction ...............................................................................................................
Since the discovery of the electric waves by Campbell and Wagner (1915), fi lters have
gained importance in almost every phase of electrical engineering.
The term fi lter describes a variety of different systems. They all have as the main objec-
tive the removal of unwanted parts of a given signal such as noise, or extract useful parts
of the signal such as information.
Filter theory was fi rst studied in the 1920s (based on the image parameters) primarily by
Zobel. In the 1930s, fi lter theory evolved into what is known today as modern fi lter theory,
based on well-defi ned mathematical equations, models, and specs.
Over time the concept of system transfer or gain function became the foundations of fi lter
theory, and a systematic approach was developed through the efforts of a number of math-
ematicians, scientists, and engineers, to name just a few: Cauer, Foster, Bode, Darlington,
and many others.
Filters can be classifi ed based on different criteria such as
Circuit confi guration (lattice/ladder/etc.)
Element s u s ed (ac t ive/pa ssive/d ig it a l/a n a log/etc.)
Physical characteristics of the element used (electrical/electronics/optical/mechan-
ical/electromechanical/etc.)
Frequency response (pass band/low pass [LP]/high pass [HP]/etc.)
Impulse response (infi nite/fi nite)In this chapter, the criteria used is based on the system frequency response, meaning that
these devices (fi lters) allow certain bands of frequencies to pass while attenuating others,
by using a variety of elements and confi gurations in their implementation.
In most cases, fi lters are specifi ed by the frequency response characteristics in the pass
and stop bands. In its simplest version, the fi lter specs must include a nonzero amplitude
associated with the pass band, a region with a zero amplitude associated with the stop
band, and a transition region between the pass and stop bands.
An ideal fi lter presents only two states in its output, either it allows to pass or to stop a
range of frequencies present in its input.