Looking at busbar's link reminds me that there are two basic types of frequency response tests.
One applies an impulse in the time domain, measures a time response, and computes the FFT which represents the frequency response.
The other (as introduced by the Doble article) applies a swept sinusoid input, and measures the magnitude and phase of the response for each frequency.
Theoretically results of both tests are the same. In the real world the time-domain method will never recreate the true frequency response since only an approximation of an impulse can be created, and high frequency signals are a little trickier to measure. I really don't know how any of that translates to ability to diagnose transformers.