Logic Domain Filtering How To Analyze THAT 4301 Circuit

[XixiDudu]

Hi KVRs,
I'm trying to model a digital chip THAT 4301. Inside the 4301 there is a RMS filter using log domain filtering.
It seems that log domain filtering utilizes current-mode circuits, with linear current in/output outside of the circuit and log voltage internal processing state. The filter can be discribed with the form of I_in * I_b = I_out*(I_c + I_b), which can be transformed into wc * I_out = wc_I_in - I'out, where wc is the cut off frequency. Unlike the traditional RC filters, which uses voltage as inputs and outputs, the log domain circuit uses current for inputs and outputs, and are discribed with currents.
But instead of using current, can I describe the circuit with the voltage that directly tells me whats happening inside the internal processing states?
And if possible, can I construct a log domain digital low pass filtering algorithm that mimics the process of the log internal processing state of a log domain filter? So I can take log of the input, and filter the logged input in log domain, and exp it back to linear. And I am not sure will this process affect the sound at all? Will this aproach generate different effects compared to traditional filtering algorithm that builds from traditional RC circuits?