# A Case for Linear Compression

I often criticize linear compression for its failings when applied to hearing restoration. When used in that manner it will invariably over-correct across some portion of the dynamic range, and under-correct elsewhere. At best, it can only be correct at two loudness levels, where its straight line representation intersects the concave upward curve of the proper anti-recruitment compression curve.

But there are various ways of thinking about linear compression, and a valid case could be made for using it ahead of Crescendo correction. Compression upon compression, you say?

Yes. One way of viewing compression is to see it as reducing the dynamic range of its input material. That’s often how it used in broadcasting applications, where very wide dynamic range material must fit into a more restricted range as permitted by the modulation applied to radio and television signals during transmission.

That’s how I want to view it for the moment. A linear compressor with a compression ratio greater than 1 will reduce the dynamic range by the inverse of that compression ratio. For example, a compressor with ratio = 1.5 would cut the dynamic range to 2/3 of its former span. This is a gentler degree of compression than often seen. Compression this mild is almost unnoticeable. But it could be quite useful to us.

When your degree of hearing impairment is severe, it becomes very tricky to dial in the right amount of vTuning so that you get the weak reverb tails and the higher harmonics of pitched sounds. Sounds at levels near the extreme faint limits are more difficult to capture properly. Too much vTuning, and the lower frequencies become overcorrected at faint levels. Too little, and you lose those faint high frequency portions.

Fortunately, the extreme correction levels happen only at the very highest frequencies, where sounds become unpitched. A musical 3rd at 6 kHz is not particularly discernible. Those frequencies are the domain of shaped noise, and supporting harmonics.

By preceding Crescendo with a mild dynamic range reduction compression, we could more easily capture those fainter sounds. We wouldn’t be using the linear compression as a corrective gain, and so we won’t suffer distortion among harmonic ratios, nor damage the musical timbre of instruments. We simply squeeze the wide dynamic range of sound into a narrower range, making it easier to correct at the faintest levels.

But we need RMS compression, not the more customary peak compression. And not every compressor offers RMS compression.

And this is a 1 band compressor, applied globally to the whole musical spectrum. We don’t want to differentially compress distinct frequency bands. But rather, we want to compress the whole musical content all together.

You want to arrange for the compression to be neutral at the 0 dBVU level, which takes a simple bit of algebra to compute the required makeup gain at some lower threshold.

For example, with EBU R128 calibration, 0 dBVU = -23 dBLUFS. A typical compressor threshold could be -50 dBFS. That’s 27 dB below the 0 dBVU level. But remember we have to work in RMS units, so that is really only 24 dB below. At a ratio of 1.5, we need a makeup gain of 8 dB to become neutral at the 0 dBVU level:

$G = (T + 26)(1/R - 1)$

That downward range of 24 dB now becomes only 16 dB. This should also ease the tendency for some kinds of music to crowd the clipping limit.

You barely notice the difference overall in the music playback, except for the fact that the faintest levels are now more apparent than before. Maybe you didn’t even get to notice them before.

• DM

[ If you find that a compression ratio of 1.5 is a bit more than you like, you could try 1.2. That requires a makeup gain of only 4 dB at threshold -50 dBFS RMS, and squeezes the dynamic range into 5/6 of its original, instead of 2/3.

Or, between those two, you have a compression ratio of 1.33 with makeup gain of 6 dB, for a squeeze of 3/4.  And ratio 1.25 with makeup gain 4.8 dB, for a squeeze of 4/5. ]

## Author: dbmcclain

Astrophysicist, spook, musician, Lisp aficionado, deaf guy