# Dynamic compressor - ratio in logarithmic scale problem

I want to use decibels to describe compression ratio. So for example ratio 4:1 means that every 4 input decibels above threshold causes raise of output only 1 decibel. And I also want ratio to be constant on whole range above threshold. So for 4:1, if input is 8 decibels above I want output raise 2 decibels.

But decibels are in logarithmic scale, so when I draw linear graphical representation (dB in logarithmic scale) of my compressor characteristic it is clear that my ratio is not constant, and looks like that: So when I convert my graph to be logarithmic (dB on linear scale), then my ratio section is curved like that: • How to make my ratio which is described in decibels, to make it constant?

My ratio function is like that now:

$$o = \left( \frac1r + \frac { t ( r - 1 ) } { g} \right) \cdot {i}$$

where:

• $$r$$ - ratio
• $$t$$ - threshold
• $$g$$ - input gain
• $$i$$ - input
• $$o$$ - output

I suppose I need to modify that equation somehow, but have no idea how?

• First order approach: replace all linear gains quantities in your equation with their logarithmic equivalents. – Hilmar Feb 10 '19 at 13:54
• Hilmar, thanks for your advice. What you say seems to be obvious, but please find out $i$ on the end after brackets is my input which I think I can't replace by logarithmic equivalents, it could to destroy my input signal. I am almost sure I need to modify part in brackets which is my gain reduction multiplicator. But don't have idea how to do that. – pajczur Feb 12 '19 at 21:43