The process of normalizing audio isn't the same as using a brickwall limiter on the master bus. In fact, when you normalize audio this will make the loudest part of the audio material as loud as it can be without going over 0 dBFS.

And as for the quieter parts of the same audio file, they will have the same amount of gain increase just like the louder parts and that's basically how the normalizing process works.

N.B. When you normalize an audio file the ratio between the loudest and quietest parts remains the same meaning the dynamic range isn't affected.


The difference between brickwall limiting and audio normalization​

The use of a limiter raises the overall level of the audio such that the loudest bits are squared off and that's done via a brickwall attenuation process.

Furthermore, as soon as the loudest sounds have passed, what follows is a gain increase for the level of the quieter sounds in that specific audio file.

N.B. In layman's terms, a brickwall limiter works by squashing the peaks of audio so that no distortion occurs, and henceforth boosting the overall level of the troughs (quieter sounds).

So we can therefore say audio limiting affects the dynamic range of an audio file because the quieter bits are turned up more than the louder bits whilst normalization lets you increase the amplitude of the signal as far as it can go without clipping.
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