A filter is called lowpass
when it lets pass unchanged the inferior portion of a signal,
rejecting the superior one — the terms inferior and superior are
intended in the domain of frequency. Imagine appropriately connecting
the inductor of the previous lesson to a speaker.
Referring to its behavior it's easy to understand how offering a high
impedance to the highest frequencies, it actually obstructs them the
way; instead offering no impedance to the lowest frequencies, it
allows their transit toward the speaker. This way the speaker will
utter only grave sounds and you won't have done anything else than
make a simple lowpass filtration.
A filter is called highpass
when it lets pass unchanged the superior portion of a signal,
rejecting the inferior one. Replace the inductor with the capacitor
— always that of the previous lesson — and as if by magic
the speaker will stop speaking threateningly and will turn into a
lambkin. What has happened? Simple, the capacitor has opened the door
to the highest frequencies only, obstructing the path to the lower
ones owing to the increase of its inner impedance. There is made a
simple highpass filter.
It's worth making a brief aside
here, in order to clarify the difference between resistance
Generalizing a great deal — a very great deal — we can say
that both are measured in ohms and they express a similar concept,
but we'll refer to resistance when talking about direct current while
we'll speak of impedance in presence of alternate currents, such as
musical signals are.
Forget now about connecting
inductor and capacitor in turn on the same speaker. Instead imagine
connecting them simultaneously on two different speakers: we would
get then both highs and lows — that's the whole signal — but
played by two different transducers. Moreover if we imagine these two
transducers each one dedicated in reproduction of the frequency band
delivered to it, then we'll have made a simple two-way system,
composed — as the whole two-ways — by a lowpass and a highpass.
A filter is called bandpass
when it lets pass unchanged the middle portion of a signal, rejecting
the contiguous ones. It consists of the opportune combination of a
highpass filter with a lowpass filter. Preceding this filter with an
additional lowpass and following it with an additional highpass,
we'll get nothing but a three-way crossover, composed — as the
whole three-ways — by a lowpass, a bandpass and a highpass.
Putting in the middle another bandpass we'll get a four-way crossover
and so on.
[Despite the common term crossover
being used as a synonym of filter, we prefer to observe a certain
strictness and will refer to it as a coupling of filters —
complementary among them, as in the cases just described — that
produces intersections among adjacent ways. The various types of
filter constituting a crossover will then be named rows
and a crossover will be formed by at least a lowpass row and a
highpass row, to include one or more bandpass rows in multiway configurations.]
A fourth kind of filter also
exists. This is the notch-filter,
with inverse function in comparison to bandpass. It can be tuned on a
particular frequency and reject it completely. It's useless for our
purposes and we won't dwell over. However it's nice to know it exists.
The story's not ended here. A
filter has many more distinctive parameters. It's marked by an order
— to which is associated an attenuation slope — a cut
frequency and a merit factor. Nevertheless it's better not to have
too many irons in the fire, so we'll proceed by degrees with
the cut frequency