In most cases, the primary task of a filter is the targeted intervention in the amplitude frequency response
If one tries to determine the filter order from a frequency representation, one must first look for the point on the curve at which the level decreased by 3 dB. From this point the edge steepness is determined.
<aside> 📎 Most filters make an (often unwanted) intervention in the phase frequency response. This always leads to a distortion of the waveform in the passband of the filter. This distortion does not always have to be negative, it is often imperceptible.
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The output amplitude reduces proportional to the frequency.
<aside> 📎 DB/Octave
The most important distinguishing criterion for different filters is the steepness of the falling edge. This edge steepness is always specified in audio engineering with the unit: dB/octave.
For the rough distinction: n * 6dB/octave where n specifies the filter order.
Example: order 1 (6dB/octave), order 2 (12dB/octave), order 3 (18dB/Octave)
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Relative to 10 kHz, the 20 kHz amplitude is halved. The difference between 10 kHz and 20 kHz is one octave and a halving of the signal is 20*log(2) = approximately -6.021 dB but it's easier to say -6 dB.
Cascading two of these filters produces an attenuation of signal with frequency that is twice the amount of one filter so, a 2nd order filter attenuates at ~12.042 dB/octave. A 3rd order attenuates at ~18.06 dB/octave.
Here, different, controllable filters interact with each other, giving the user the ability to precisely affect the frequency response. The frequency curves used here are always the result of a complex circuit and can not be realized with passive filters.
