Fundamental Flaws in Distortion Audibility Perception Studies
Lately I've been wondering about various studies that claim to quantify the audibility of distortion. These studies are linked below.
How Much Distortion Can We Hear With Music?
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Associated explanation on the above.
Both studies evaluate the audibility by introducing distortion into a 'clean' signal. Both studies highlight how much distortion can be introduced before it becomes audible, with the point being that we can tolerant very high levels of distortion before they become audible.
However!
Distortion artifacts are biproducts of lost energy from the fundamental tones. In other words, energy from the fundamental tone is stolen and distributed across the frequency spectrum as side band artifacts. The above studies are flawed in that they introduce the distortion artifacts as noise without altering the fundamental tone's energy.
The concept of stolen energy is explained by Gregory in the All Electronics Channel video here starting at 6.21 location in the video.
I've pasted the transcript of the video below starting at 7:37
"take a look at this when the amplitude is very small we almost don't have harmonic content but as the signal Clips the power starts to be shifted to the second harmonic third harmonic..."
Gregory clearly demonstrates how the power is shifted from the fundamental tone to second and third harmonics etc.
You cannot introduce the the harshness of clipping distortion by simply mixing in harmonics with the original signal.
For example, tape hiss distortion is noise that has been imposed onto a linear signal. There are many beautiful recordings with tape hiss that we simply tolerate.
However this is exactly what the studies mentioned above have attempted to do, simply add noise to an already linear signal. It still sounds good!
However if the device is brought near clipping and consequentially harmonic distortion shows up, the device will sound harsh because of the device's nonlinearity, with harmonic distortion being a symptom, not the cause of said harshness.
In another one of Gregory's videos he goes on to explain the difference between harmonic distortion and noise which can be found here.
For the above study to be valid, the device would have to be pushed into nonlinear behavior by some means, such as increased signal, and then compared against the sound of the same device in a more linear operation. Level matching may be required depending on the method.
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For an example study where the signal nonlinearity is altered using MathCAD click here.