Ivey,

When fitting transfer functions for the OSEM estimator, I tested several transfer function fitting programs to find one that is both accurate and efficient.

A brief side note: In the 6/24 M1-to-M1 dataset that Oli took, we observed an unexpected right-hand zero near 1.2 Hz (see attached plot), where we had expected a left-hand zero. After comparing with the 4/15 and 4/18 datasets, we found no corresponding right-hand zero, suggesting the 6/24 zero is likely due to noise.

I wrote a document highlighting the pros and cons of each of the fitting programs here:
TF Fitting Comparison (Google Doc)

The programs include:

Vectfit3 (I recommend using this with strong inverse weighting): Uses vector fitting. Created by Bjorn Gustavsen. Not built into MATLAB. Performs nearly identically to Vectfit4, but has more documentation.

Rational: Built-in MATLAB function. Uses the AAA algorithm.

Spectrumest: Built-in MATLAB function. Chooses an internal algorithm based on the data.

Rationalfit: Built-in MATLAB function. Uses vector fitting.

Generally, these programs fit poles and end behavior well, but often compromise the accuracy of the fit in the zero regions. In these cases, we often have to manually refine the fit in the zero regions. However, Vectfit3 performs very well on the 6/24 M1-to-M1 and SusPoint-to-M1 datasets when used with strong inverse weighting. We were able to produce better fits than manual methods, and expect this approach to be more efficient for future use.

Example plots are available here:
Plot Comparison Slides (Google Slides)

Attached is the MATLAB code used for the M1-to-M1 fits.
To use vectfit3, you must download the package
here.
All other functions used are built into MATLAB's toolboxes.

Measurement file paths:

 /ligo/svncommon/SusSVN/sus/trunk/HLTS/H1/SR3/Common/Data/2025-06-24_1700_H1ISIHAM5_ST1_WhiteNoise_SR3SusPoint_L_to_Y_0p02to50Hz.xml 
 
 /ligo/svncommon/SusSVN/sus/trunk/HLTS/H1/SR3/SAGM1/Data/2025-06-24_1900_H1SUSSR3_M1_WhiteNoise_L_to_Y_0p02to50Hz.xml