A mathematical model is presented, which reproduces typical dynamic range compression, when given the nominal input envelope of the signal and the compression constants. The model is derived geometrically in a qualitative approach and the governing differential equation for an arbitrary input and an arbitrary compressor is found. Step responses compare well to commercial compressors tested. The compression effect on speech using the general equation in its discrete version is also demonstrated. This model applicability is especially appealing to hearing aids, where the input-output curve and time constants of the non-linear instrument are frequently consulted and the qualitative theoretical effect of compression may be crucial for speech perception.
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