Beside the envelope design for the control signal the compressors transfer curve is the most influencing part speaking in terms of the resulting sound impression. If we ignore any time dependend behaviour of the compressor for the moment then it basically works like this: Signals at a level below a certain threshold are passing through the device unaltered. Reaching the threshold level the input signal gets lowered by a certain ratio. The result is a so called “hard-knee” transfer curve.
Given some math (or some circuit in the hardware domain) this curve can be designed in a way that there is no level to which the compression suddenly starts but rather starts smooth and increases while the signal level continues to raise. Plot 1 shows a 1:1 transfer curve (for reference) and below that a hard-knee curve which starts compression around the 0dB level with a 2:1 ratio. Below that curve two basic soft-knee variations are shown all working with 2:1 ratio.
Given a rather wide soft-knee range the resulting curves can look (and sound) really smooth and some examples at different ratio settings are shown in plot 2.
Sometimes such soft-knee curve behaviour is referred to as “over easy” compression since dbx introduced this term (and trademark) once. In an actual compressor this transfer curve shape can depend on other parameters or even behave program dependend. This is often the case in so called “Vari-Mu” compressors such as Fairchild or Manley gear. Plot 3 shows an example of a specific implementation where the selected ratio affects the shape of the curve.
Since this looks somehow similar to some smooth waveshaper/softlimiter curves (omitting their below zero part) one might ask if there is a difference at all. In fact we could describe both using the same math and just have to handle logarithmic conversions as well as signal rectifying which both typically are used in digital compressors but not on waveshapers. Given that, we can use some waveshaping algorithm for compression purposes as well or looking the other way around apply envelope behaviour to waveshaping which opens the door to some interesting applications.