Equalizers and Filters - Filters

The two most important kinds of filters are low-pass filters (LPF) and high-pass filters (HPF). The first allows the passage of frequencies below the cut frequency only- or rather- frequencies beyond the cut frequency progressively disappear to the point that they no longer become relevant. The second does the same things as the first except it only allows the passage of high-frequencies:

Low-pass filters and high-pass filters

Typical uses of high-pass filters are the elimination of low-frequency vibrations such as those generated by musicians' footsteps on the stage floor where microphone have been placed, or background noise generated by an air-conditioner. Low-pass filters are instead used for eliminating whirring noise or high-frequency noises.

The following is a figure comparing a low-pass filter and a shelf equalizer:

Comparison between a low-pass filter and a shelf equalizer

Notice how the shelf equalizer amplifies a frequency-range and leaves the rest of the frequency-spectrum unaltered, whereas the low-pass filter has no influence on the low frequencies and attenuates the frequencies beyond the cut frequency. We can see how after a few octaves, gain is diminished by a dozen dB's or so and this means that those frequencies are no longer noteworthy, their amplitude being far inferior compared to the amplitude of frequencies below the cut frequency.

5.3.1.1. Slope Rate

The slope of a filter establishes how rapidly amplitude decays. We have seen how in different situations (yet not all situations) an almost vertical slope rate is necessary. In reality this cannot take place, but we can only try and get as close as possible to such a slope rate. The slope rate is measured in dB/octave, in other words, it tells us the measurement of by how many dB the gain of an octave decreases (we already know that to this term corresponds a doubling in frequency). Let's take a numeric example to fix our ideas with regards to the following diagram:

Slope rate of filters

We can see how the gain of the first filter, going from f_c to 2f_c, decreases by 12 dB, whilst the second, going from 2f_c to 4f_c (still an octave) decreases by 6dB, therefore the first filter shall have a slope rate of 12dB/octave, the second 6dB/octave

In analog filters we have 4 standard slope rates, which are the following:

Table 5.2. Values for slope rates of filters 

Slope rate (dB/octave) Order of filter Number of poles 6 First 1 12 Second 2 18 Third 3 24 Fourth 4

The number of poles refers to the equation of the circuit which creates the filter. For our needs it suffices to notice that every time the number of poles increases by 1, the slope rate increases by 6dB/octave. Digital filters also exist, created through the use of software algorithms; some of these are used to create sounds through subtractive synthesis and simulate 6-pole filters (36 dB/octave).

If we overlap a low pass filter and a high pass filter we obtain another two kinds of filters: the band-pass filter and the band-rejection filter. The first allows for the passage of certain frequency-bands to take place and blocks the passage of the rest of the signal (the same comparisons previously made between the bell-equalizer and the band-pass filter are valid here). The second blocks the passage of a certain band and consents the passage of the rest of the signal frequencies.