Idea for a distortion analyser on a PC

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From what I have seen here and what I've played with (on my simulation) the distortion analyser takes an input signal subtracts a sinusoidal fundamental, and whatever remains must be the distortion component. That is of course very useful and I use it regularly on my circuits.

However I was thinking of another approach. Why not feed the distortion analyser the input signal, the very same one we feed to the amplifier under test, at the same time. Then the analyser will compare the input signal with the output and anything that should not be there is "distortion". In that way analysis can be performed on realistic input, and not simply on perfect sinusoidals at a single fundamental frequency.

An idea as follows:

The analyser takes the input signal and digitizes it and stores it as a waveform in memory. It does the same to the output signal. So now it has two waveforms, say of 1 second length. From now on the analysis is all in software, no electronics involved.

The analysis loop. It amplifies the input signal digitally (in software, no electronics invloved) and tries to do a best match (for phase shifts inside the amp) so that it matches the output signal. On every attempt of (a) phase shift and (b) amplitude, it pivots on those settings and calculates the distortion component. It carries on until it discovers the smallest distortion (ie the best fit).

What do you think of this idea? I suppose it could be done on a PC with a good quality sound card installed, eg something that could use say 32 bits per sample and 200,000 samples per second ought to do the trick? I am not sure how good modern sound cards are, they usually come on the motherboard these days.
 
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