Time Domain measurements?

Joachim Gerhard

Active Member
Industry Insider
Every thing else is a terrific misconfiguration and there are many.

Joachim Gerhard

Active Member
Industry Insider
We do not fly to the moon because it is easy, Kennedy.

Joachim Gerhard

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This one costs 45.000,-€ in Germany.

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RayDunzl

Major Contributor
Central Scrutinizer
The display is Audacity (free).

and my math skills are much too rusty.
Mine never had a chance to bloom.

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.
Yes. It shows in the spectrum, but at -31dB for 200Hz, where the square spectrum registers 0dB for 200Hz:

Tweeter:

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.

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.

And I haven't figured out how to interpret the second graph.
The second graph is the decibel representation of the sample points in the tweeter wave.

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KeithPhantom

Senior Member
Forum Donor
how is it possible that an all-pass filter of the type used in some crossovers are able to introduce phase shift without attenuation?
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:

http://www.ecircuitcenter.com/Circuits/op_allpass1/op_allpass1.htm
https://www.analog.com/media/en/training-seminars/tutorials/MT-202.pdf

Don Hills

... 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). ...
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...

Joachim Gerhard

Active Member
Industry Insider
This is kind of true. It is a wave phenomenon on the cochlea.

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Joachim Gerhard

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Some processing in the brain too.

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dc655321

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?
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?

Joachim Gerhard

Active Member
Industry Insider
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?

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KeithPhantom

Senior Member
Forum Donor
Not sure it's possible to explain all-pass filters without resorting to math, which you seem shy of...
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...

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KaiserSoze

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.
There is some good stuff here:

https://en.wikipedia.org/wiki/Fourier_series

It bothers me immensely that at one point in time all the math on this page would have been easy to me and that I did not work to keep those skills honed over the years.

Anyway, there are several animations on this page that are informative. The graphic very close to the top of the page, on the right, goes through several transformations, one of which shows the relative amplitudes of the first several terms in the Fourier expansion of a square wave. What is apparently happening is that even though the 200 Hz fundamental is greatly attenuated by the filter, it is still a dominant spectral component in the tweeter output, as your graphics imply.

KaiserSoze

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...
Yes, but dare I ask how this helps to answer the question of why it isn't reasonable to expect audio components to reproduce square waves?

KaiserSoze

Some processing in the brain too.
I believe this phenomenon is fairly well known, but where I don't quite make the connection is with how this helps to explain why it isn't reasonable to expect audio components to accurately reproduce square waves.

KaiserSoze

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?
Correctly or incorrectly, I inferred a relationship between phase and attenuation from another comment made here, which does not warrant any further elaboration.

Why would I mean amplitude instead of attenuation? Given that at the most superficial level of understanding passive filters introduce frequency-dependent attenuation and also frequency-dependent change in the phase angle between voltage and current, it seems perfectly reasonable and obvious to me to relate each primary effect to the other. I have no idea what your second question is asking. Magnitude/amplitude as opposed to what? Attenuation, perhaps? Is this what you mean to say? That instead of "attenuation" I should have been meant to say "amplitude" or "magnitude"? Why, exactly? At the most superficial level of understanding a passive filter element introduces both frequency-dependent attenuation and frequency-dependent alteration of the phase angle between voltage and current. As such it would seem perfectly natural to inquire as to how these two effects are related to each other.

Now what on earth would motivate you to say, " ... math, which you seem shy of ..."

I asked the question here, directed to KeithPhantom, because a couple of his comments touched on the subject. But if you have good knowledge of this subject and are good at explaining things, then please share your knowledge. And if you want to start a new thread for the purpose, then please do that and point me to the new thread.

KeithPhantom

Senior Member
Forum Donor
I will only add that I provided the best answer that my knowledge can generate. If there is something I get wrong, you may correct me.

KaiserSoze

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?
Wow, 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.

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UliBru

Member
Technical Expert
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.)
"It will somewhat resemble a square wave, but one where the fundamental frequency is the 45 Hz "
So if you take away the fundamental 15 Hz of your example the result clearly does not resemble a square wave.

Joachim Gerhard

Active Member
Industry Insider
Wow, 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.
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 times

on Threads like this that people do not have basic understanding. When that basic understanding is not there it is mostly impossible to discuss advanced issues.

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DonH56

Major Contributor
Technical Expert
Forum Donor
All-pass transfer function: H(s) = (1-sRC)/(1+sRC) where s = jw = j2*pi*f and RC = product of resistor and capacitor values in the circuit (or equivalent if in Z-domain -- the time constant). The magnitude is 1 over all frequencies and phase is determined by RC.

There are a number of ways to implement all-pass filters. I have used simple passive and op-amp implementations for audio stuff, lattice (or trellis) and T-section circuits for RF, and of course standard digital (DSP) implementations. In practice there are bandwidth limitations and such with different schemes having narrow (octave or less) to multiple octave (e.g. audio op-amps or digital domain) bandwidth.

I imagine there are a bazillion or so articles on the web with much better and more detailed explanations along with pictures and such.

Edit: Square wave in Wikipedia -- shows the Fourier series: https://en.wikipedia.org/wiki/Square_wave#:~:text=Fourier analysis,-The six arrows&text=The ideal square wave contains,wave is the Gibbs phenomenon.

Edit 2: Forgot I wrote this, building a square wave: https://www.audiosciencereview.com/.../composition-of-a-square-wave-important.1921/

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