I hope I'm not imposing by this longish post...? =o)
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Can you hear non linear phase? Yes you can.
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I've always wondered which aspect of non-linear phase (also known as group delay) people mean when they talk about audibility, under which circumstances they apply, and which orders of magnitude are considered to be the threshold level.
1) Signals that fall into the stationary category (meaning superimposed sine waves that don't change rapidly in amplitude over time) of not too high a level shouldn't be an issue, since the averaging principle of the ear applies here. Obviously transients are the signals where the effect gets audible most. If a transient is subject to group delay, a portion of it's frequency band will arrive somewhat before or after the rest. Now the question is, what is the threshold of audibility, or in other words, what is the smallest time delay our ears can resolve?
I have some older textbooks which I still regard as an authoritative standard, and they state that the minimun audible time delay is 2 ms. However, I suppose (but I'm not sure) under which conditions this is valid, if it gets larger for low frequencies, if other nearby frequencies of a delayed freq band are masked, etc. - anyone??
2) With stereo signals, you will surely get cancellation effects and shifting of stereo image to a greater or lesser extent if one channel has a relative group delay, even with stationary signals. but with mono signals, e.g. recording vocals through a microphone which introduces group delay, audibility should be restricted to the transient type.
3)If you consider the stationary case, but at high levels - approaching a device's headroom - you might get secondary audible effects due to non-linear distortion in the frequency domain. Example: Imagine two transients which closely follow each other in the original signal. If enough group delay is applied, a portion of the first transient is superimposed on the second, resulting in an increase of amplitude. In reference e.g. to a publication of Bill Whitlock's (of Jensen Xformers), these changes can be higher than 10dB in some cases, exceeding the device's headroom and resulting in freq distortion.
Regarding transformers: Actually, they are a bit more complex than a simple inductor, aren't they? They inherently also have all sorts of parasitic inductances and capacitances, series and shunt type. Different parts of these take effect at different frequencies, resulting in a band pass characteristic, and ringing at a certain resonant frequency. Which of course also means non-linear phase!! All this can be overcome more or less satisfactory by good construction and appropriate external loading, but it has to be considered.