Terminology

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You may have seen me rail against how the schools teach that inversion is t
he same thing as 180 degrees out. Out of phase, by definition or etymology  
or whatever the fuck at least strongly implies that THIS signal is THAT sig

  

Now, these two waveforms, say applied to a CRO (and ALWAYS own a CRO as lon
g as you shall live) and syncing, they look the same as long as they are sy
mmetrical. But we have two types of symmetrical.  

Consider:



/\/\/\/\/\/\/\/\/\/\/\/\

And:

/|/|/|/|/|/|/|/|/|/|/|/|/|

Or as my Wavtek will put out:

/|_/|_/|_/|_/|_/|_/|_/|_/|

With a dead time that is half the sawtooth wave.  

Now, we should all know this, it is not that hard of a concept. But how is  
it expressed ?  

If I was the word chooser of the world, a sawtooth wave would be called "Sy
mmetrical in period" but NOT "Symmetrical in polarity".  

What are the proper terms for that ?

Re: Terminology
snipped-for-privacy@gmail.com wrote:

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Inversion symmetry and translation symmetry?

Jeroen Belleman

Re: Terminology
I would say an offset sawtooth.
Or a sawtooth with DC component.



Try the "inversion" with a asymetrical signal and see the result, though  
it is periodic.

Exemple : MMMM.... delayed  by half a period gives MMMM..... ; try to  
invert it ! (something like WWWW).

On a scope, you would see the same trace since it is triggered even with  
a dual-channel.

Sorry for my "French English" !




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Re: Terminology

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Periodic waves all have translational symmetry in the time dimension

The first two have glide reflection symmetry, and also mirror
symmetry (at any peak or trough) and rotatinal symmetery (about any zero-crossing)


the last has, only translational symmetrty in the time dimension
the second last has in addition the rotational symmetry


this (square wave through low-pass filter) has glide reflection (on time and voltage)
but not time refelction. or rotation
  
    _     _     _     _     _     _     _     _     _
   / |   / |   / |   / |   / |   / |   / |   / |   / |
  |   \_|   \_|   \_|   \_|   \_|   \_|   \_|   \_|   \


 This (uneven square wave) has time reflectional symmetry on time but
not glide reflection or rotatiom
    _     _     _     _     _     _     _     _     _    
 __| |___| |___| |___| |___| |___| |___| |___| |___| |__


--  
  When I tried casting out nines I made a hash of it.

Re: Terminology
On Wed, 19 Dec 2018 21:46:29 -0800 (PST), snipped-for-privacy@gmail.com wrote:


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We use "symmetric" to mean flippable on the vertical axis, amplitude.

The concept of "time reversal" is pretty rarely discussed, so we say
that when we mean it.

CRO? Those funny old things with electron guns and deflection plates?
Haven't use one in a decade or two.


--  

John Larkin         Highland Technology, Inc
picosecond timing   precision measurement  

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