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Why are some audio waveforms TOTALLY asymmetrical to the zero crossing?
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Simonator
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26th June 2010
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Why are some audio waveforms TOTALLY asymmetrical to the zero crossing?

Hey All,

Why are some waveforms SO different above their zero crossing than from below?

I stumbled upon this question here:

A thread for asking the things you should know by now but don't

... But I'm not satisfied with any of the responses there.


I wouldn't expect perfect symmetry obviously... but approximate.

From what I was taught, anything above the line is positive amplitude, anything below is negative. I would expect that before any wave repeats a cycle of one it would go through roughly the same of the other... this is essentially the 'back & forth' of a vibration that we are seeing represented visually.
... But some waveforms are REALLY off kilter. One that springs to mind is an 808 hi-hat; often appears to be PURELY positive (or negative) amplitude- bouncing back as soon as it hits the center to create a dorsal fin shape on the horizontal zero crossing.

Here is an image of a mono 808 closed hi-hat waveform loaded into Battery:



... Which appears to be nearly all negative amplitude. I've put this through an oscilloscope & it's still the same; very negative dominant.


The respondents in that linked post offer the following answers:

a.) 'A single frequency would be symmetrical, but harmonics/timbre cause this offset.'

This could have something to do with it AFAIK... but that explanation alone does not cut it in my book... harmonics to my understanding would be other smaller (higher frequency) waves 'riding' on the longer wavelength... and would do this over the positive & the negative stretches of that wave.

b.) 'Volume.'

I'm not buying it: surely louder sounds would result in BOTH positive AND negative peaks of the wave to be further from the zero crossing.


So can someone please either point out where I'm going wrong with these assertions... or offer a better explanation of why this happens??

Many thanks :-)
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DC Offset.
Quote
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Quote:
Originally Posted by Robobaby View Post
DC Offset.
Excellent!!

Thanks a lot for clearing that up!!!


I just had a scan around t'interwebs to find out what that means. The wikipedia page hurt my head, so if anyone else is interested I suggest you read this page:

************************* - Understanding DC-Offset
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According to wiki if you apply a high pass filter it will greatly reduce DC Offset so that should be a quick and easy way to verify it.

I've seen similar "lopsided" waveforms but usually the offset is in the positive spectrum and not the negative like in the pic you've got there.
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some of my favourite waveforms are asymmetrical
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Quote:
Originally Posted by timbreman View Post
I've seen similar "lopsided" waveforms but usually the offset is in the positive spectrum and not the negative like in the pic you've got there.
I doubt it would make much difference; you could invert the phase & it would then be positive... but I imagine it would sound pretty much the same... wouldn't it??
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Quote:
Originally Posted by rasseru View Post
some of my favourite waveforms are asymmetrical
With DC offset?

Sounds like something best avoided from what I've just read.

... But then it seems like 808 closed hi-hats I have from from several different production companies have this same waveform... so I guess it is common to 808 hats.

Any chance you could share examples of what it is you like??
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Quote:
Originally Posted by simonator View Post
I doubt it would make much difference; you could invert the phase & it would then be positive... but I imagine it would sound pretty much the same... wouldn't it??
Looks like even physics students are applying the same concept to remove dc offset.

Removing DC Offset
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I know this can come about for many reasons, generally stuff in hardware I've found although I could be wrong.


What i did want to add was that this is still a very valid waveform in the speaker will still move in a positive and negative way, BUT because its lopsided you can imagine you will lose potential volume as the heavy side will hit 0 long before it would if its centre had been in the middle. this may or may not be an issue but is a reason to mildly avoid this...mildly

dont be concerned tho theres nothing to worry about...its usually a voltage issue in some hardware it was recorded from.

Dc Offset can be fixed in most wave editors also.
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Yep this is DC offset!
Can be introduced by:

1. Analog Circuits (in real world) OR Analog Simulation (when driven hard) in Plug-In world. (your 808 sample looks normal cause TR 808 is analog maschine and DC components are always there if you not HIGH pass them with filter + if you record via PRE AMP like API or Neve you get even more offset because of additional even/odd harmonics content & voltage fluctuations (TRY Soundtoys Decapitator on sample without any offset and you will see offset produced by some settings))

2. Unusual audio rate modulation settings on a synths when you programm some fresh & cool sound on my nord modular G2 this is quite normal with some crazy FM & PM sounds (again caused by creative EVEN/ODD harmonics combination & voltage fluctuations in simulated analog invironment) so in the end of the Patch i ALWAYS insert 6db High Pass filter for some Waveform Phase stability.
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No, it's not just DC offset and there is an audible effect beyond amplitude. I agree some of the best sounding waveforms are asymmetrical. It's what makes certain sounds special. The male voice or brass instruments are often highly asymmetrical. Certain synths sounds (probably due to some sort of half-wave distortion) are also very asymmetrical. It won't be removed by high pass filtering everything below 50 Hz or so.
And interestingly enough, asymmetrical waveforms sound different when inverted. There is such a thing as the correct polarity for many signals.

I've got an ancient broadcast phase scrambler (basically an all pass filter flanked by two giant UTC transformers) meant to symmetrify the waveform, which makes for a very interesting effect: Vocals send through the thing get an instant Larry-King-sound. And it allows for the signal to be compressed a lot more and achieve a higher amplitude. It adds a certain punch to many signals (however, this last thing might be due to the transformers).

I think certain aspects we like about analog sound have to do with phase and symmetry.
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Quote:
Originally Posted by living sounds View Post
No, it's not just DC offset and there is an audible effect beyond amplitude. I agree some of the best sounding waveforms are asymmetrical. It's what makes certain sounds special. The male voice or brass instruments are often highly asymmetrical. Certain synths sounds (probably due to some sort of half-wave distortion) are also very asymmetrical. It won't be removed by high pass filtering everything below 50 Hz or so.
And interestingly enough, asymmetrical waveforms sound different when inverted. There is such a thing as the correct polarity for many signals.

I've got an ancient broadcast phase scrambler (basically an all pass filter flanked by two giant UTC transformers) meant to symmetrify the waveform, which makes for a very interesting effect: Vocals send through the thing get an instant Larry-King-sound. And it allows for the signal to be compressed a lot more and achieve a higher amplitude. It adds a certain punch to many signals (however, this last thing might be due to the transformers).

I think certain aspects we like about analog sound have to do with phase and symmetry.
Thanks! Intriguing stuff thumbsup
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Quote:
Originally Posted by living sounds View Post
No, it's not just DC offset and there is an audible effect beyond amplitude. I agree some of the best sounding waveforms are asymmetrical. It's what makes certain sounds special. The male voice or brass instruments are often highly asymmetrical. Certain synths sounds (probably due to some sort of half-wave distortion) are also very asymmetrical. It won't be removed by high pass filtering everything below 50 Hz or so.
And interestingly enough, asymmetrical waveforms sound different when inverted. There is such a thing as the correct polarity for many signals.

I've got an ancient broadcast phase scrambler (basically an all pass filter flanked by two giant UTC transformers) meant to symmetrify the waveform, which makes for a very interesting effect: Vocals send through the thing get an instant Larry-King-sound. And it allows for the signal to be compressed a lot more and achieve a higher amplitude. It adds a certain punch to many signals (however, this last thing might be due to the transformers).

I think certain aspects we like about analog sound have to do with phase and symmetry.
Yep this not SIMPLE DC offset here and MAGIC DC REMOVE button don't work here because FULL SPECTRUM WAVE PHASE was shifter too much in one direction so only one more PHASE shift in other direction will CURE this offset so you need some phase shifting process to do this sometimes PS EQ with High Pass work sometimes some distortion like your transformers.
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DC offset and Wave Phase offset is not the same thing for sure.
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Yeah its true that you can have a vibrating mechanism that has unequal excursion on one side of its rest state than the other. You won't typically see it with synthesizers because the basis of most of it are linear periodic waves (sine wave). So that has equal amplitude above and below -infinity with 0 DC offset and its cyclical and expressible mathematically.

To get those assymetrical shapes with no DC offset I'm guessing you need to electrically combine or sample some very non linear, non periodic wave shapes. I doubt you could do it with an oscillator or by mixing oscillators which are by definition periodic.
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Quote:
Originally Posted by simonator View Post
With DC offset?

Sounds like something best avoided from what I've just read.

... But then it seems like 808 closed hi-hats I have from from several different production companies have this same waveform... so I guess it is common to 808 hats.

Any chance you could share examples of what it is you like??

im at my lappie, but my jp-8000 frequently makes good reeces that are asymmetrical, 2 detuned waves, filter & cross mod the usual suspects.


real 'pyawwwwwwwww' type, 303 sounding, phat bass
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Sonar will optionaly remove dc offset upon record.
Your DAW may also.

FYI: Capacitors block DC.
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Quote:
Originally Posted by Robobaby View Post
Yeah its true that you can have a vibrating mechanism that has unequal excursion on one side of its rest state than the other.
I'm having a lot of difficulty in getting my brain to compute this information...

I'm picturing a sheet of metal vibrating normally.

Then that same sheet of metal vibrating the same yet ONLY positively from its centre rest position... To my mind that would just moves the zero crossing to wherever half way between the extremities of the vibration.

Weird stuff.

Quote:
Originally Posted by Robobaby View Post
To get those assymetrical shapes with no DC offset I'm guessing you need to electrically combine or sample some very non linear, non periodic wave shapes. I doubt you could do it with an oscillator or by mixing oscillators which are by definition periodic.
... and I doubt speakers enjoy reproducing these off centre waveforms.
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BTW, do a search in this very forum, asymmetrical waveforms and theiir psychoacoustic properties have been discussed previously here, including the relevant scientific research.
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Quote:
Originally Posted by living sounds View Post
BTW, do a search in this very forum, asymmetrical waveforms and theiir psychoacoustic properties have been discussed previously here, including the relevant scientific research.
Thanks.

I obviously tried this before posting... can you tell me what search terms to use, or better still provide some links?

Cheers.
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Quote:
Originally Posted by simonator View Post
I'm having a lot of difficulty in getting my brain to compute this information...

I'm picturing a sheet of metal vibrating normally.

Then that same sheet of metal vibrating the same yet ONLY positively from its centre rest position... To my mind that would just moves the zero crossing to wherever half way between the extremities of the vibration.

Weird stuff.
... I guess an easier way to picture it would be thinking of the speaker diaphragm with a fixed center that is by definition the zero crossing (at least electrically)... Its easier to picture that projecting outwards, returning to center & then repeating.

Wouldn't fancy doing that too much with a nice set of Bang & Olufsens though!
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Quote:
Originally Posted by simonator View Post
... and I doubt speakers enjoy reproducing these off centre waveforms.
In Nord Modular G2 you can cut positive on negative side of waveform produced by OSC so in the end you have only one sided waveform phase sound BUT how musical this sound is? not so musical i can say and headroom is too low (low volume in the end) because of one sided phase structure which tend to crackle fuzzy overdrive AND IF YOU TRY TOO PLAY LOUD 20Hz you have big woofer blowing chance! (i blow onestike)
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Natural musical waveforms are not symmetric in terms of polarity. This has to do with the phase relationship between harmonics that is part of the natural timbre of acoustic instruments, including the the voice. Some instruments appear more symmetric than others, and even this is dependent on the particular notes and how it is being played.
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Here's an article on DC Offset by Craig Anderton (I think it first appeared in EQ mag):

Recording & Production: DC Offset: The Case of the Missing Headroom | Harmony Central

This is interesting:
"In addition to reduced headroom, there are two other major problems associated with DC offset in digitally-based systems.

When transitioning between two pieces of digital audio, one with an offset and one without (or with a different amount of offset), there will be a pop or click at the transition point.

Effects or processes requiring a signal that's symmetrical about ground will not work as effectively. For example, a distortion plug-in that clips positive and negative peaks will clip them unevenly if there's a DC offset. More seriously, a noise gate or "strip silence" function will need a higher (or lower) threshold than normal in order to be higher than not just the noise, but the noise plus the offset value."
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Quote:
Originally Posted by tremo View Post
Here's an article on DC Offset by Craig Anderton (I think it first appeared in EQ mag):

Recording & Production: DC Offset: The Case of the Missing Headroom | Harmony Central

This is interesting:
"In addition to reduced headroom, there are two other major problems associated with DC offset in digitally-based systems.

When transitioning between two pieces of digital audio, one with an offset and one without (or with a different amount of offset), there will be a pop or click at the transition point.

Effects or processes requiring a signal that's symmetrical about ground will not work as effectively. For example, a distortion plug-in that clips positive and negative peaks will clip them unevenly if there's a DC offset. More seriously, a noise gate or "strip silence" function will need a higher (or lower) threshold than normal in order to be higher than not just the noise, but the noise plus the offset value."
One single pole HPF @20 Hz, is enough to remove everything said above.

That is expected from you to perform to audio recording anyway.

Unless you have an engineer who will take care of it.
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has nothing to do with dc offset.. on dc offset the wave stays symetrical.. when its unsymetrucal we deal with unsymetrical distortion..
quite logical.. and that unsymetrical distortion does has a sound.. opposite to dc offset, that in itself is not altering the sound.. just it´s side fx might lead to reduced headroom or clicks...
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DC offset will shift the entire wave form up or down, but by itself, DC offset won't change the shape of the wave and it does not account for why some waves are shaped differently above and below the zero crossing line. There are lots of other factors that CAN account for this.
In the physical world, this is due to all sorts of mechanical and physical properties in the instrument. Keep in mind that not all instruments produce sound by some method like a plucked string, or certain other methods which are more likely to produce a somewhat symetrical waveform. Think about things like an oboe, which produces a very asymetrical wave that can be similar to a very narrow pulse wave. Blowing air through a device will produce sound in a completely different way than a vibrating string. Even the hi-hat example that was mentioned at the start of the thread - the object is not mechanically symetrical in the vertical axis, which affects mechanical stresses on the object as it vibrates up and down, and may contribute to the asymetrical wave (of course, struck metal objects tend to have rather complex wave forms anyway due to a whole list of contributing factors).
In a synth, there are many things that will lead to asymetrical waveforms. There's the obvious stuff like some sort of non-linear distortion processor, but there are more, like self-FM. Picture what happens when you modulate the frequency of a sine wave with itself. The waveform 'bunches up' as it approaches the positive peak and 'pulls apart' when it approaches the negative peak, resulting in a shape that looks like a suspension bridge, with pointy peaks on top and wide round curves on the bottom. Just one example, there are lots more.
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Quote:
Originally Posted by Dave Peck View Post
There are lots of other factors that CAN account for this.
There certainly are - fundamentally:

Fourier series applet
Attached Thumbnails
Why are some audio waveforms TOTALLY asymmetrical to the zero crossing?-waveform-asymmetry.gif  
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Ever heard of a "rectifier" circuit being used to introduce distortion? Most guitarists probably have heard that term. Rectification will essentially take whatever is on one side of the zero crossing and flip it to the other side. There's also asymmetrical clipping type distortion:

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Quote:
Originally Posted by Robobaby View Post
DC Offset.
Not DC offset. As the signal decays it settles towards ground not DC.

This asymmetrical waveshape is know to be caused by overdriving tubes, similar to the diode clipping technique above. It appears to be DC offset but it is not.
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