Harmonic signature is due to the PHASE ANGLE where the distortion occured

[Dan Bullard]

I've been kicked off of most bulletin board sites trying to make this point, but I discovered some interesting things about Harmonics that nobody else seems to know. In this animated GIF I show how the harmonic signature varies as the result of the phase angle where the distortion occurs in a sine wave. Here I show the spectra of several sine waves that were distorted by clipping (at the positive peak) and I record the phase angle where the clipping first started. It's a linear relationship, and I have worked out the formula for this too. This is not caused by the FFT, as I have proven this behavior on analog instruments as well. This  is real. Who here wants to kick me off of this site for saying unspeakable things?

 

[swansont]

You’re going to have to explain this in more detail. 

[studiot]

19 minutes ago, swansont said:

You’re going to have to explain this in more detail. 

Yes please more detail.

 

2 hours ago, Dan Bullard said:

I show how the harmonic signature varies as the result of the phase angle where the distortion occurs in a sine wave. Here I show the spectra of several sine waves that were distorted by clipping (at the positive peak)

I am suprised by animated graph in relation to you statement that the positive peak is clipped.

I would expect harmonics with negative values at the fundamental positive clip to be shown as they must predominate to reduce the positive peak, which is what clipping is.

[Dan Bullard]

Which peak is clipped cannot be seen in the magnitude portion of the spectrum, it doesn't matter which peak is clipped, the harmonic signature is identical. Only the phases of the EVEN harmonics are different. In this animation, based on real data I extracted from the FFT that I made in Excel shows how the harmonic phases determine which peak is clipped. Notice that when both peaks are clipped, the even harmonics (in RED) don't move at all, but when I clip only the positive peak I get even harmonics (again, in RED) to help the ODD harmonics (in BLUE) to make the same size distortion. So why isn't the distortion bigger? Because both the ODD and EVEN harmonics work together to make the distortion, but the EVEN harmonics now oppose the ODD harmonics trying to replicate the distortion on the negative peak.

[Dan Bullard]

More detail, OK, I can't give you the formula (intellectual property) but I can show how the Bullard Harmonic Solution accurately predicts the harmonic signature in this video.

 

[Bufofrog]

12 hours ago, Dan Bullard said:

I can't give you the formula (intellectual property)

Well that is going to make any meaningful discussion quite difficult.

[Dan Bullard]

I give away everything else, but this one thing is only understandable if you understand 1) Total Distortion Energy (TDE) and 2) the formula for predicting harmonics from the duty cycle of a square wave and triangle wave. I don't have the time to cover them all online and I have to leave some reason for people to read the books. I give you all 5 laws of the Bullard Laws of Harmonics, the formula for the Bullard Harmonic Solution isn't going to make any difference to this discussion, and if you are so smart, derive with it yourself. The video proves that it is valid, and that is all you need to know.

When everyone else is arguing over how many angels can dance on the head of a pin, what's the point in giving you a formula that you won't understand?

Edited November 2, 2021 by Dan Bullard

[swansont]

46 minutes ago, Dan Bullard said:

I don't have the time to cover them all online and I have to leave some reason for people to read the books.

!

Moderator Note

Ah, the other shoe drops.

Coming to a discussion board to not actually discuss your idea was a clue, but as this is admittedly bait to sell books, it violates our rules on advertising and having discussions in good faith