About your J-test results here:
It could be the speed difference in clocks of the QA vs DUT. When you view close in even 100 ppm difference (common to be this large or larger) will spread the base of your Jtest signal. I suppose noise might obscure the missing small signal spikes. All that is happening in such cases is the actual frequency as seen by the QA is not 12 khz, but some fraction that fits off-center in the FFT bin so low levels spread to adjacent bins. Once you start looking at close in jitter you need to fix the relative speeds or your results will mislead on close in jitter.
So to start looking close in you need to correct for the clock rate differences. I sometimes correct the speed with a speed change function in Audacity. Current Audacity only corrects to the nearest 10 ppm. Earlier versions would correct to the nearest 3 ppb. Another option is do the first Jtest then use it to see what speed change is needed. For instance if you found the recorded signal was 100 ppm slow you could repeat the test with 12,001.2 hz for the Jtest which is 100 ppm faster. The ADC will see it as 12,000 rather precisely.
Here is the digital J-test, vs the same signal sped up by 100 ppm. The sped up version is in hot pink. There actually is no close in jitter spreading the base of the tone. The tone is simply the wrong frequency. The difference is too small to notice in the full 20 khz graph.
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