posted 22 April 2002 14:02            

Audio compression can be viewed from two common vantage points, and both are useful, depending on your application. This note will attempt to exhibit the properties of the Kyma compressors from both views.

The Kyma compressors have the property that signal output level is independent of the compression threshold, so long as the sidechain input level is above that threshold. In other words, for a given makeup gain, all compression curves of output level versus input side chain level intersect at the same point at high side-chain levels. However, this makes the gain at threshold dependent on the threshold setting.

The other view of compression speaks about the signal being gain controlled so that increases of x dB above threshold become x/R dB increases, where R is the compression ratio. Under this view, many compressors offer gain reduction meters showing how the gain diminishes as the signal grows stronger above the threshold level. The gain at threshold is independent of the threshold setting, and without makeup gain, the output vs input side chain level curves all intersect at the threshold and fall away from the unity gain curve as the signals get louder. Strong compression causes the output curve to fall away from the unity gain line at faster rates than for slight compression.

The compression gain equation for Kyma compressors, when the side chain level is above threshold, is

Gcmpr dB = Gmakeup dB - 9.5 dB - (Side dB * (1 - 1/R))

where Side dB is the dBFS level of the side chain signal (always negative dB), and R is the compression ratio (>= 1).

Below threshold the equation represents a constant gain equal to

Gcmpr dB = Gmakeup dB - 9.5 dB - (Thresh dB * (1 - 1/R))

Under the first interpretation mentioned above, when the input signal is its own side chain signal, and this level is above threshold, the output signal level will be

Lout dB = (Lin dB / R) + Gmakeup dB - 9.5 dB

where all signal levels are measured as negative dBFS from zero. In other words, the output signal level is 1/R times the input signal level plus some constant gain offset. Changing the threshold setting has no effect on this level. The signal is always amplified relative to a unity gain signal, and this amplification increases with diminishing signal level until threshold levels are reached. Thereafter a constant gain is applied to the input signal.

The second viewpoint of compression can be expressed by writing the gain equation, for sidechain levels above threshold, as

Gcmpr dB = Gmakeup dB - 9.5 dB - (Side dB - Thresh dB)*(1 - 1/R) - (Thresh dB * (1 - 1/R)

Here the gain is shown as some constant minus an increasing attenuation with increases in signal side chain level above threshold. That third term is the value generally shown as gain reduction on meters. Under this interpretation, the amount of signal increase above threshold is diminished by the compression ratio. For example, when R = 3, then for every 3 dB increase above threshold, the output level increases by only 1 dB.

However, with Kyma, there is that fourth term involving only the threshold level. That causes the effective gain at threshold to change with threshold, unlike many other compressors. So if you want the Kyma compressor to behave like many other compressors you need to take into account that fourth term. You can incorporate it in the expression for your post-gain.

Nothing is fundamentally different in the compressive behavior of these two views. Both of them provide 1/R dB changes in output for each dB of side chain signal change. The difference is mainly one of post gain expectations. The post gain needed at threshold varies, in the second interpretation, by that threshold fourth term, while it is fixed in the first.

So now, armed with these equations we can readily translate between the different kinds of compressors found in a typical studio. From an informal survey in my own studio, I would say that most compressors offer the second viewpoint, but they usually don't have makeup gains that are affected by changes in the threshold setting. Kyma is a little different, but it can be viewed in the same light with a threshold dependent adjustment to the post-gain.

posted 22 April 2002 15:11            

After much pondering over the way that it should be done, we decided that 0 dB should be mapped to a fixed amplitude value (-10 dB). In this way, changes to either the threshold or the compression ratio have no effect on signals reaching the peak input amplitude level. If it wasn't this way, decreasing the threshold or increasing the ratio would cause the output amplitude to drop.

If you want to make the threshold the fixed point, you can place the following expression into the Gain parameter:

posted 22 April 2002 15:15            

I will definitely read your description! You mention 10 dB, but my measurements here show the transfer function at 9.5 dB. Only a half dB difference, but which is correct?

Cheers,

- DM

BTW... shouldn't that expression read
(10 + ((1 - R inverse) * ThreshDB)
?

posted 22 April 2002 15:21            

The corrected formula should be:

(3 inDB + ( (1 - !Ratio inverse) * !ThreshDB ) ) dB

posted 22 April 2002 15:24            

Cheers,

- DM

[Thinking about what you said regarding the peak input levels not changing under ratio and threshold changes... That is certainly true, but the RMS levels will grow louder as a result of ratio changes. Threshold will not affect that except for how far down the gain is increased. Six of one, half dozen of another. All that matters is that we understand how things work so I can translate from one device to another...]