Physical significance of RMS of acceleration

[EngForm78]

What is the physical significance of the RMS of acceleration data. I have read that it is a measure of energy. What would the units be? Is there an integral function to describe this? Can anyone expand on this a little?

Thanks in advance

 

[electricpete]

I think was wrong about that.

The reason I was confused was by by comparison with the continuos Fourier transform.
X(w) = Integral{x(t)*exp(-j*w*t)dt
x(t) = 1/(2Pi)*Integral{X(w)*exp(j*w*t)dw

Those are tricky units. X(w) has an extra unit of time compared to x(t). I don't think that same complication applies to discrete fourier transforms that we work with (FFT's).

(I'm interested to hear if anyone has other comments to clear that up).

Thanks for the correction.



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[electricpete]

My previous response was to Steve.

IRStuff - I was objecting to your statement "He has a PSD and an RMS value of that PSD."

I think he has a spectrum, not a PSD. I agree he could calculate a PSD if he wanted. (but that's only another complication not needed here in my opinion).

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[IRstuff]

Extra?

Time series has units of seconds for the independent variable. FT has units of radians/second for the independent variable. That's a direct consequence of the j*w*t in the exponent of the transform kernel.

TTFN

 

[electricpete]

I'm not sure what you're point is.

I'm not talking about the independent variable but about the units we apply to waveform x(t) and continuous spectrum X(w).

If x(t) were g's, then X(w) would be g*sec as can be seen from the definition above.

We can apply Parseval's theorem:
Int(x(t)^2 dt = Int(X(w)^2 dt (integral -inf to +inf both cases)
g^2 * sec = (g*sec)^2 * (1/sec)
Parseval is happy.

I personally view FFT as an approximation to the fourier transform of the underlying continuous signal. I think many others do as well. That's why the funky units of continuous fourier transform seem a little bit tricky to me.

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[electricpete]

My last sentence should have been: "That's why I brought up the funky units of continuous fourier transform even though the discussion is presumably about discrete spectra".

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