🚀 go-pugleaf

:I am using a 12-bit DSP system to do real time processing on full frequency
:range audio signals.  Because of the dynamic range in volume, however, 12 bits
:is very inadequate at low signal levels.  The solution for my application,
:since I do not need to know the actual volume, is to use an analog circuit
:similar to an AGC:
:
:     INPUT--->AMP 1--->DSP--->AMP 2--->OUTPUT
:       |        ^               ^
:       v        |               |
:     POWER-----------------------
:
:Here POWER calculates the power of the input signal, which is filtered at
:something like 10Hz.  AMP 1 takes the input signal and amplifies/de-amplifies
:the output to be about 1v.  AMP 2 takes the output from the DSP, also about
:1v, and amplifies/de-amplifies back to the original volume level.  If both
:amplifiers are linear to 12 bits over the entire power and frequency range,
:then the entire configuration should have no audible distortion.
:
:Since my circuit design knowledge is not up to this level, I have no idea
:how to actually implement this application.  I cannot believe that someone
:out there hasn't already done this, or doesn't have something better.

What you are describing is a companding DAC. These are widely used in 
the communication industry to achieve a constant SNR over a wide
range of inputs. In this way the quantizing noise for a
loud talker (-18dBm) is thae same as that of a quiet talker (-35dBm).

Any complete text on communications will have a description of
the transfer functions used in the compressor and expander.
Approximations to logarithmic curves are often used.
Common ones are the A Law and mu255 Law curves. These are
described in CCITT documents.

Common telephoney codecs will supply 13 bit resolution with 8 bit
accuracy. Since these are $3 chips, they may be suitable for you.