Linear and non-linear processes - Signals, Processes, and Systems - page 204

The behaviour of filters refers to a process in the frequency domain. Thus a „lowpass“
filter allows the low frequencies to pass, the high ones are largely blocked out etc. The
type of filter always indicates what range is filtered out.
Note:
The word „filter“ is reserved in signal processing for the frequency domain.
The equivalent process in the time domain is the „window“.
Radio and television are at present (still) technologies which are inseparably linked with
filtering. Every station operates within a specific frequency band. Above and below this
frequency band there are other stations. The aerial receives all the broadcasters, the task
of the „tuner“ is above all to filter out this station accurately. Accordingly, a tuner func-
tions in principle like a tracking filter .
The history of (analog) filter technology is an example of the basically futile attempt to
develop filters using analog components - coils, capacitors which come as near as possi-
ble to the ideal of a rectangular filter. In Chapter 3 - „The Uncertainty Principle“ - it was
shown that rectangular filters are basically impossible to realise because they would con-
tradict the laws of nature.
Digital filters represent a quantum leap in filter technology. They come close to the rect-
angular ideal although they can never achieve it. As will be shown in Chapter 10 - see
also Illustration 126 - they can without exception be realised by means of three extremely
straightforward linear processes: delay, addition and multiplication of a signal by a
constant. All this in the time domain.
First, a number of traditional filter types used in analog technology will be described
briefly and examined from a measurement technology point of view using DASY Lab . We
will confine ourselves to three types which can be realised as lowpass, highpass, bandpass
filters and band elimination filters. Bandpass and band elimination filters can in principle
be put together from lowpass and highpass filters.
These three types were named after scientists who created the mathematical basis for
calculating the circuits:
1. BESSEL filter
2. BUTTERWORTH filter
3. CHEBYCHEFF filter
These filter types are important within the framework of analog filter technology. They
can, however, also be realised digitally. However, there are much better filters available
in digital signal processing.
In Illustration 141 these three filter types are contrasted using the example of the lowpass
filter. Their behaviour in the context of transmission technology demonstrates their
different advantages and disadvantages and points to possible areas of application.