LOWPASS, HIGHPASS
AND BANDPASS

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 and impedance. 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