Autopower Crosspower nomnclature 2

[SomptingGuy]

So we are all happy with the terms Gxx, Gyy, Gxy in our signal processing world. But does anyone know where the letter G came from? I was trying to explain these things to a colleague today, but all I could point to were definitions of Gxx,Gxy,Gyy. Not why we use the letter G

Steve

 

[hacksaw]

You're dealing with matices, the various subscripts refer to Fourier transforms of cross correlations of different signals.

 

[GregLocock]

Could it be as simple as

F... spectrum
G... spectrum^2
H... transfer function

?

Cheers

Greg Locock


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[IRstuff]

As with many things, there's history and tradition. Oft times, it's simply the nomenclature used by a seminal paper or book, and rather than introducing your own nomenclature and then have to explain that zzXX is the same as Gxx in "the" text, it's easier to use the same notation.

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[GregLocock]

I notice some people use C for cross power (what do they use for coherence?) and others use S. I've definitely seen A for autospectrum. Didn't there used to be an amazing web based maths website? Did it get eaten by Wolfram?



Cheers

Greg Locock


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[SomptingGuy]

I've nearly given up looking. Even some of my favourite references just introduce Gxy as a function.

I thought Appenix A in HP Application note 243, The Fundamentals of Signal Analysis might give some background as it's such a good general read.

Steve

 

[hacksaw]

Never give up, your just starting.

The HP doc refers only to single input point monitoring of simple systems.

When you have complex systems with multiple sensors, you'll likely need to identify the various interactions even with single point excitation.

With multi-point excitations, it gets more interesting.

The Gij's are matrix elements, or in Einstin notation

Yi = Gij Fj for i={x,y,z}, j={x,y,z}, where Yi is the response, Fj excitations

meaning Yx = Gxx Fx + Gxy Fy + Gzz Fz and so on

 

[SomptingGuy]

Yes hacksaw. All of what you say is true and completely familiar (apart from the bit about the HP doc only dealing with single inputs, which is not true). I only asked if anyone knew why G was the letter universally used in the notation.

I wondered if there was a mathematician being honoured or some Greek influence. Like this nice explanation of why we always use S for entropy, but never question it.


Steve

 

[GregLocock]

I've only ever done signal analysis at the application level, mostly using the B&K green book as a reference. I did one back derive coherence to see what was going on as I has a boss who seemed to regard it as the be all and end all of QC for transfer functions measurements... and then some years later found exactly the same explanation in one of the books, probably B&K.

So I haven't got any feel for the history of it.

Cheers

Greg Locock


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[SomptingGuy]

More...

I see some online resources stating that H1(f)=Gxy(f)/Gxx(f) and others that H1(f)=Gyx(f)/Gxx(f). The former being more common. The latter (IMO) giving the phase relationship I'd expect (y, a pure delayed version of x causes a decreasing phase ramp in H1).

Steve