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-off frequency only, or rather, frequencies beyond the cut-off frequency progressively fade away to the point that they no longer become relevant. High-pass filters do the same as low-pass filters except they only allow the passage of high-frequencies:

Low-pass filters and high-pass filters

High-pass filters are typically used to eliminate low-frequency vibrations such as those generated by musicians' footsteps picked up by microphones onstage, or background noise generated by air conditioners. Low-pass filters are instead used for eliminating hiss 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-off frequency. We can see how after a few octaves, gain is diminished by a dozen dB's or so, which means that these frequencies are no longer worthy of note, their amplitude being far inferior than that of the frequencies below the cut-off frequency.

5.3.1.1. Slope rate

The slope of a filter establishes how rapidly amplitude decays. We have seen how in different situations an almost vertical slope rate is needed. 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 states by how many dB the gain decreases within an octave (remember that one octave corresponds to a doubling in frequency). Let's take a numeric example:

Slope rates of a filter

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

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

Table 5.2. Typical 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 is calculated from the equation which describes the circuit. For our needs it will suffice to be aware that every time the number of poles is increased by 1, the slope rate increases by 6dB/octave.

Digital filters created with software algorithms also exist. Some are used to create sounds through subtractive synthesis simulating 6-pole filters (36 dB/octave).

If we combine a low-pass filter and a high-pass filter we obtain two more types 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's frequencies.