Limiter Spectrum



I decided to look at what audible artifacts could arise from using a limiter or allowing a waveform to clip. Using a limiter is preferred because it uses a controlled gain shaping over a selectable duration. Clipping produces the same spectrum as a limiter in the limit of instantaneous gain ducking.

The spectrum from isolated clipping is just a plain flat spectrum of amplitude equal to the gain excess. So if you allow a track to clip 1 dB, you get a 1 dB flat spectrum – meaning all frequencies are affected equally, and it sounds like a pure impulse.

Whether that 1 dB is significant or not, depends entirely on the rest of the music. During a quiet portion, you’ll probably notice it. But most of the time, a 1 sample clip would be unnoticeable. They become awful when they persist over many consecutive samples, or repeat very frequently.

So let’s look at what a more controlled limiter action produces. It will produce audio artifacts. But the question is, how bad are they?

Here is a graph showing the spectrum due to a limiter acting with a 2 ms lookahead, and a 2 ms release period:

This graph shows the absolute minimum spectrum that can be had – a 0 dB over. For greater amounts of over, simply shift this entire curve upward by the amount of the over. So, for a 3 dB over, the bass region will see a 3 dB click.

But that little secondary peak out at 700 Hz looks interesting. Its contribution will be about -28 dBFS plus however much the over is. That is probably comfortably small, but in quiet passages it might become audible. But it only lasts for 4 ms, so the ear probably wouldn’t notice it. Sounds have to persist longer than about 10 ms before we can really notice them.

Okay, let’s look at a more gentle limiting action over 10 ms:

The little artifact out at 700 Hz has now moved to just under 300 Hz, diminishing the level there by almost 12 dB. And the lower frequencies are now less affected, as you can see the spectrum falling above 70 Hz, whereas before that same degree of decline didn’t happen till closer to 200 Hz.

So yes, a more gentle limiter action produces smaller artifacts, but they also last longer and could therefore become more audible to us during quiet passages. But it is also more concentrated under the bass region and hence more easily hidden during average loudness passages.

On the whole, a 2 ms lookahead and 2 ms release looks like a pretty good compromise between duration and magnitude of artifacts. I don’t think it would be good to use a shorter limiter response. Everything is always a compromise.

  • DM

[ These spectra come from an assumed triangular response, which is what they appear to be on an oscilloscope. Hence these spectra are Sinc^2 functions. ]

Author: dbmcclain

Astrophysicist, spook, musician, Lisp aficionado, deaf guy

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