# Room Impulse Response Inverse Problem

This article here talks about a room impulse response generator which takes the source and destination coordinates, sound speed, sampling rate, room dimension and wall reflection coefficients as input and outputs the impulse response from source to destination.

The equation (36) for the same calculation is given below.

My question is if we know different room impulse responses for different source-destination combinations and other constant parameters like room dimension, sound speed etc. except the wall reflection coefficients($\beta_1,\beta_2,..,\beta_6$). Then is it possible to find the $\beta$ values from the Room Impulse Responses(RIRs) and source destination coordinates?.

What I am essentially trying to do is measure some real RIR of a given room of which dimension and source-destination coordinates are known to me. I want to build a model out this real room measurements with minimal model mismatch. How can I do the same?.

Thanks & Regards,

• Most probably there is no generally plausible solution to this problem. Unless you are able to track first order reflections and extract the absorption coefficients from them I believe it would be quite complex to achieve what you seek. On the other hand though, if one could assemble a matrix with the reflections and multiply that with the absorption coefficients ending up with a linear system a possible inversion could provide some approximation to the absorption coefficients (if the system is invertible). Please keep us posted on your "quest" as it seems quite interesting. Aug 18, 2020 at 10:04