## Math behind dynamic compression - help me to understand

fikiz
KVRer

2 posts since 9 Jan, 2014

by fikiz; Mon Apr 02, 2018 5:03 am Math behind dynamic compression - help me to understand

Hi all.

I'm trying to build my own digital dynamic compressor using my pc and usb audio card. I read a lot of code and documentation but there's something that i still don't get.

My target is very simple: a compressor with thresold and compression ratio as parameters. No attack and release. Just for the sake of my understanding of how things work - I'd like to have an easy-but-working compressor rather than a good compressor (fine details will come later).

What I need to know is how to calculate the multiplication factor (excuse my bad jargon) I have to apply to my samples when the compression kicks in.

I'm receiving samples from my audio input, and I apply the RMS formula to the last n samples, where n is my RMS window. I convert the rms value to db:
rms_db = 20 * log10(rms)

if rms_db is higher than my defined thresold (also expressed in db, between -Inf and 0) the compression starts and it will stop when the input rms_db goes below the thresold.
Let's say in a given moment rms_db = -3, thresold_db = -3.5, and the compression ratio is 3:1. What's the math to find the gain to multiply the input sample to get the corresponding output?

Also... am I reasoning right? Or this completely wrong?

stratum
KVRAF

1837 posts since 29 May, 2012

Ratio
The amount of gain reduction is determined by ratio: a ratio of 4:1 means that if input level is 4 dB over the threshold, the output signal level is reduced to 1 dB over the threshold. The gain and output level has been reduced by 3 dB:

The highest ratio of ∞:1 is often known as limiting. It is commonly achieved using a ratio of 60:1, and effectively denotes that any signal above the threshold is brought down to the threshold level once the attack time has expired.
~stratum~
Miles1981
KVRian

1355 posts since 26 Apr, 2004, from UK

by Miles1981; Mon Apr 02, 2018 2:20 pm Re: Math behind dynamic compression - help me to understand

The gain for a simple compressor with a variable knee can be found here: https://github.com/mbrucher/AudioTK/blo ... er.cpp#L49

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