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Every thing else is a terrific misconfiguration and there are many.
Interesting. I don't have access to this kind of tool
and my math skills are much too rusty.
But, the mere fact that the overall periodicity of the tweeter output that you show is 200 Hz, it seems like the tweeter must be carrying a lot of energy at that low frequency.
But I'm probably not thinking about this correctly.
And I haven't figured out how to interpret the second graph.
For what I know, all practical filters (even linear-phase) introduce phase shift because we cannot replicate ideal conditions in electronics due to constraints in physics. For what I've seen in schematics, the phase shift in Op-Amp based all-pass filters is a relationship between the capacitance and the resistance in the feedback connection going back to the op-amp. To create an all-pass filter, many usually rely on rearranging the components of a high-pass filter and making sure to place the capacitor in series with the non-inverting output. and placing an extra resistor in the feedback connection. The capacitor will introduce a phase shift depending on the cutoff frequency and the signal frequency. I will leave you with two sources that can explain it better than I could:how is it possible that an all-pass filter of the type used in some crossovers are able to introduce phase shift without attenuation?
... What I was trying to say (and believe that I did say in an adequately clear manner) is that if the low-pass filter that is applied is sufficiently steep, that there will be no remnant of the original 15 Hz fundamental in the output waveform, and that the overall periodicity evident in the output waveform will be that of the 3rd harmonic (45 Hz). ...
If phase change is a function of attenuation (and of frequency when attenuation is directly related to frequency), how is it possible that an all-pass filter of the type used in some crossovers are able to introduce phase shift without attenuation?
That's what I didn't want to use to explain that to him, but I'm not an expert in the math as well...Not sure it's possible to explain all-pass filters without resorting to math, which you seem shy of...
The display is Audacity (free).
Mine never had a chance to bloom.
Yes. It shows in the spectrum, but at -31dB for 200Hz, where the square spectrum registers 0dB for 200Hz:
Tweeter:
View attachment 73199
I didn't explain my view correctly, either.
Start with a sine of f1, it has no flat, and no edges.
The higher odd harmonics add to create the "attack", and partially add to fill above the slope of the F1 sine, and cancel at the peak of the F1 sine, is how I think of it now.
The math proof? I dunno. Here is a sine and the first two odd harmonics at 1/3 and 1/5 amplitude building toward a square wave.
View attachment 73203
At the first zero crossing all three components are going positive (adding) so their sum is more positive than the F1 sine at those points, at the peak of F1 they alternate phase (cancellation), and the sum (mix) reveals that.
The higher harmonics continue with a similar pattern, filling the gap between sine (F1) and square in a similar manner.
The second graph is the decibel representation of the sample points in the tweeter wave.
An observation from this is that we still perceive the fundamental. Our auditory system analyses the relationship and amplitudes of the harmonics and determines the missing fundamental. It's a trick well used by organists, and there are commercial products that employ the technique to give the impression of deep bass from small speakers.
A 15 Hz (originally) square wave with the fundamental filtered out:
45 Hz, 75 Hz, 105 Hz...
has a different harmonic makeup than a 45 Hz square wave:
45 Hz, 135 Hz, 225 Hz...
Some processing in the brain too.
How did you arrive at the first part (phase a function of attenuation)?
Do you perhaps mean magnitude/amplitude?
Not sure it's possible to explain all-pass filters without resorting to math, which you seem shy of...
Perhaps these questions belong in a new thread?
Is this electronics for dummies ? I start to loose the interest in this thread. I have precious little time to explain basics. How can we ever proceed?
I have simply tried to give an answer to your statement:Okay, but how is it not obvious that if you remove any major harmonic component from a square wave that what you're left with isn't a square wave?
In retrospect the point I was making was probably too obvious. The point was that in order for there to be any realistic expectation for a piece of audio equipment to preserve a square wave, the fundamental frequency of the square wave must be within the normal passband for audio equipment. This is a very basic observation, but the question of square waves and audio came up as it often does, and since this implicit requirement with respect to the fundamental frequency of the square wave is rarely mentioned, I thought it appropriate on this occasion to include it among the reasons why it is not generally realistic to expect audio equipment to preserve square waves.
I had thought that the fundamental frequency of periodicity of the modified waveform should be 45 Hz, the lowest odd-numbered harmonic of the suppressed 15 Hz. But now you've got me wondering whether this is correct. Is this what you are implying? If it isn't 45 Hz, what will it be?
(I'm hoping that you won't reply by saying that since it isn't a square wave or a sine wave that periodicity isn't meaningful, or something along these lines. On a typical day and on a typical web forum, a reply of this sort is what I would most likely get.)
I am sorry that my post offended you. That will not happen again. And I had not especially you in mind. That was only a reaction that I see many timesWow, that was patently rude, and obviously directed at me. "Electronics for dummies?" You actually said that? Wow, that's so patently rude. Haven't you ever heard that "Manners make the man?" When you write something like, "I start to loose the interest in this thread. I have precious little time to explain basics", what this does is send the message loudly and clearly that you're arrogant and a sort of a, well, let's just say not a very nice person. Note also also that I've looked back over the thread and did not find a single post where anyone asked you to explain all-pass filters. Whatever.