I've never had any audible problems converting between 44.1kHz (CD) and 48kHz (video) no matter what software I was using so this isn't something I worry about. Changing microphones or changing microphone position will make a bigger difference than using a different SRC. You can measure lots of things that you can't hear!
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and why some sweeps leave a graph with many lines, and others leave only one visible line.
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"Many lines" are aliases (false/additional frequencies that didn't exist in the original).
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Anyone got any good introductory explanations on sample rate conversion?
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Probably the most important thing (maybe the ONLY important thing) is filtering and the
Nyquist limit. If you don't filter before downsampling you get aliasing.