Yes, correction of the linear part of the total system error, actually the A to B difference. Only small errors, the 1% max regime.

Think applications like capacitor testing, two caps of same nominal value but different construction, say input coupling capacitors.

This will introduce an (additional) highpass in the loopback chain but the corner frequencies will slightly differ (even a after selection and/or analog fine trim) and the resulting phase shift spoils coherence at low frequencies, decreasing null depth. The influence of the linear differences could be brought down one order of magnitude easily if most of it were factored out by applying a well-estimated or measured transfer function. For the capacitor example we know that the correction function would have the shape of an analog (min-phase) shelving filter. In general, any slightly moving pole or zero in the analog transfer function will result in a correction shelving filter (with a fraction of a dB level change).

I'm aware of the problems of processing noise. A way to mitigate this is curve-fitting an analytical transfer function to the reasonably smoothed empirical one, if we know the correction function is min-phase then this can be a bunch of simple IIR filters which can be applied directly (or used to obtain a "clean" convolution kernel from that by sampling a dirac response).

I feel I need to try your program first before making any further comments ;-)

Think applications like capacitor testing, two caps of same nominal value but different construction, say input coupling capacitors.

This will introduce an (additional) highpass in the loopback chain but the corner frequencies will slightly differ (even a after selection and/or analog fine trim) and the resulting phase shift spoils coherence at low frequencies, decreasing null depth. The influence of the linear differences could be brought down one order of magnitude easily if most of it were factored out by applying a well-estimated or measured transfer function. For the capacitor example we know that the correction function would have the shape of an analog (min-phase) shelving filter. In general, any slightly moving pole or zero in the analog transfer function will result in a correction shelving filter (with a fraction of a dB level change).

I'm aware of the problems of processing noise. A way to mitigate this is curve-fitting an analytical transfer function to the reasonably smoothed empirical one, if we know the correction function is min-phase then this can be a bunch of simple IIR filters which can be applied directly (or used to obtain a "clean" convolution kernel from that by sampling a dirac response).

I feel I need to try your program first before making any further comments ;-)