Definition of "Model fit" value in RT60 Decay

[Tdep11]

Hi,

I've been using REW for acoustic measurements, particularly the RT60 Decay graph. I am trying to understand precisely how the Model fit value is calculated.

I understand that it quantifies how well the fitted exponential decay matches the measured Schroeder integral — the lower the value, the better the fit. However, I need the exact mathematical definition in order to use it as a basis for uncertainty propagation in a research context (specifically, propagating the fit quality into an uncertainty on the decay rate).

If there is any documentation that describes this calculation or if anyone knows how it's done, I'd be bery interested to know.
Thanks !

 

[John Mulcahy]

It's the mean squared error between the measured response (the slices of the waterfall) and the model response after the model response has been convolved with the left window to account for its effect on the measurement. The error is the difference in the dB values, with uniform weighting from the fit start (green dot) to fit end (red dot) for points on the curve that are within 30 dB of the fit start level and weighted by pow(2, (level - (fitStartLevel - 30))/10) below that to attenuate the contribution of parts of the response that are more than 30 dB below the fit start.

The model is based on frequency domain data, the Schroeder integral is not used at all.

 

[Tdep11]

Thanks for the quick reply ! I am trying to use it to derive a rigorous uncertainty on the RT60 value for a research project, but the values I'm getting are quite low, so I'd like to check my method is correct.

From what you said, the Model fit F is the weighted mean squared error (in dB²) between the measured decay slices and the fitted model, with uniform weighting over the first 30 dB below the fit start and attenuated weighting below that. Starting from this, I derived the following formula for the 1σ uncertainty on T60:

sigma_T60 = (T60² / 60) × (1 / 8.686) × sqrt( 12 × F / (N_eff × Delta_t²) )
where:

• Delta_t = t_red − t_green (fit window duration in seconds)
• N_eff = Delta_t / (slice_step + rise_time), accounting for slice correlation due to the rise window
• 8.686 = 20×log10(e), converting dB/s to e-foldings/s

Is this the correct way to propagate F into an uncertainty on T60, or is there something in the way REW computes F that would require a different approach?
Thank you very much !

 

[John Mulcahy]

REW is using UNCMIN to minimise the error function (model fit) across the range of the data between the green and red dots by adjusting the parameter vector consisting of the starting level in dB, T60 in seconds and noise in dB. I'm not qualified to say how that should define an uncertainty, sorry.