Wow! Where to start...
According to a whitepaper I read by Cyril Hammer at Soulution Audio, he states following:
- an amplifier with a bandwidth of 20 KHz (-3dB) has a phaseshift of 45 ° at 20 KHz, very audible.....
In his whitepaper he gives an example of sine waves with 1kHz and 2kHz and the resulting signal. Then the phase of one sine signal is changed by an unknown amount and again the resulting signal is shown (red curve):
Apart from the fact that the human ear/brain does not hear in this way, let us assume that his statement has some relevance.
Then the result would look really bad - the "character" of the original signal has changed significantly due to the phase shift. But he did not tell us how big the phase shift was and if it was realistic.
To check this we take a look at the data given by Cyril Hammer himself (and what
@haraldo quoted) about the phase-shift when using a low-pass (for bandwidth limitation):
Let's take the worst case, as quoted by
@haraldo with a first order lowpass at 20kHz.
The phase shift at 1kHz, 2kHz and 20kHz is represented by the purple circles.
Now we can judge whether the above example of phase shifting is realistic. According to his diagram the phase shift is about 3 degrees between 1kHz and 2kHz.
So let's turn on the oscilloscope and see what happens at 3 degrees phase shift.
The "character" of the signal changes (with 3deg phase-shift) practically not at all. The example shown above has nothing to do with reality.
Okay, at 1kHz and 2kHz the bandwidth limitation may not matter, but if we look at 2kHz and 20kHz, it certainly does!
Between 2kHz and 20kHz the phase-shift is about 40 degrees, which is quite a lot - but does it also change the "character" of the combined signal?
Also here practically no change, the 20kHz signal is only slightly shifted in time on the "carrier wave".
The 1 KHz tone is the difference between 23 Khz and 24KHz. The sum 47 KHz is another sideband. Such sum and difference sidebands are generated whenever two pure tones are mixed in a nonlinear environment. The nonlinear environment in this case is the middle and inner ear. In addition to intermodulation products, the nonlinearity of the ear generates new harmonics that are not present in the sound falling on the eardrum.....
F Alton Everest claim that signals above 20KHz is audible through the subharmonics... if you cut these high frequencies through brickwall filter, the subharmonics that you can hear will also disappear; which means you lose audible artifacts within the music... That's not my claim. It's the way to understand the writings of F. Alton Everest, author of Master Handbook of Acoustics.
A music signal does not correspond to "white noise", but the sound pressure decreases steadily at high frequencies on average. Signals above 15kHz are in mostly 10-20dB below RMS (my guess, does anyone know more?).
The "perceived sound pressure" of the quadratic distortion produced in the hearing system in the example quoted by
@haraldo was determined by Zwicker. This distortion is about -40dB when the frequencies f1 and f2 are at 90dB.
But if you consider how much the super high frequency is lowered in sound pressure compared to the average music signal, the quadratic distortion produced in the hearing system should fall below the threshold of audibility.
Source: Zwicker, Fastl - Psychoacoustiks, Chapter 14 "The Ear’s Own Nonlinear Distortion"
This means that the effect of quadratic distortion produced in the hearing system of this subject (and many other subjects) follows approximately the relatively simple rule that is indicated by the broken lines. This rule corresponds to what is expected for a transmission system, that acts with an ideal quadratic distortion. The characteristic, expressed by the broken lines, follows the equation
L (f 2 − f 1 ) = L 1 + L 2 − 130 dB . (14.4)
The fact that the two parts of Fig. 14.2 can be described well by the same set of dashed lines indicates that, in this case, the nonlinearity is independent of frequency distance. This means that the transmission characteristic of the hearing system of such a subject differs relatively little from regularity.
For lower values of the primaries, the difference tone remains inaudible. For L 1 ≈ L 2 = 70 dB, the cancellation level remains at about 10 dB. This means that it is 60 dB below the level of the primaries, corresponding to an amplitude of the sound pressure of the cancellation tone of about one thousandth that of the primaries. This difference becomes smaller for increasing level of the primaries and reaches about 40 dB (corresponding to 1%) for L 1 ≈ L 2 = 90 dB.