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The function of the compressor is to reduce dynamic range.
That is, to reduce the different in level between loud parts of the signal and quiet parts. It does this by reducing the level of the loud sections.
The natural sounds of life have an extremely wide dynamic range, from the rustle of a falling leaf to the roar of a jet engine on take off.
The human ear has an automatic gain control which enables it to accommodate all of these sounds from the threshold of hearing to close to the threshold of pain, a dynamic range of approximately 120 decibels.
Even the most modern audio equipment is incapable of handling the full range that the ear can cope with.
Analog tape without noise reduction can manage almost 70 decibels dynamic range between its noise floor and the 3% distortion point. 16 bit digital audio equipment can achieve over 90 dB. Still almost 30 dB less than the ear's range.
Even with a theoretical dynamic range of 144 dB (which would be possible in 24-bit digital equipment, given perfect analog to digital convertors), would it be desirable - and useful?
A listener in a domestic setting might enjoy the exhilarating effects of levels up to 100 dB SPL (Sound Pressure Level) and more, but what annoyance or distress might that be causing to his neighbor?
At the other end of the dynamic scale, a typical ambient noise level of at least 40 dB SPL precludes the use of very quiet levels in recorded or broadcast sound media.
Almost always, it is necessary to compress the dynamic range of natural sounds to fit them into a window suitable for comfortable listening.