what's the different between ‘Energy Spectral Density’ and ‘Power Spectral Density’？

[huangxm]

“Energy Spectral Density(PSD)” and “Power Spectral Density(PSD)" are  Commonly features in sound and vibration.

Both B&K and LMS has these Features. But Labview doesn't have the "energy Spectral Density ", It only offer the "Power Spectral Density VI".

I want to know what's the algorithm between  ESD and PSD , and how to achieve ESD in Labview.

thank u  !

[LocalDSP]

Stationary signals (like sine tones) have usually a finite power but integrated over time you will end with infinite energy. This is why Power Spectral Density (PSD) is defined based on power rather than on energy.

For transient signals (like pulses) Energy Spectral Density (ESD) may on the other hand be a  better measurement to do since these signals have finite energy over time.

Simply explained, the main difference is that ESD is integrating your 'PSD' over time while PSD is.. well averaging PSD (so itself) over time.

In LabVIEW the Power Spectral Density VI can optionally perform linear averaging resulting in an averaged value of the PSD. What happens is that it adds (integrates) a number N of consecutive PSD results for then at the end divide by N (average). If you have a transient signal you can run the Power Spectral Density VI over your entire signal (it may or may not require more than one averaging depending on the duration of your transient signal) but then re-create the 'energy' rather than 'power' by multiplying the result by N.

Note: Make sure to:

- Select Linear Averaging

- Select an averaging number N that results in an analysis that covers your entire transient signal duration (1 may or may not be enough)

- Select Rectangular window (no Window)

- Set the dB Boolean = False

I hope this helps!

[huangxm]

Thank you very much, dear LocalDSP

You helps me a lot.

My  data is transient signals in 30ms pulses. As your Instructions, it could be used in PSD VI to calculate and analysis.

But the unit of  ESD is   (EU)*s   (in B&K or LMS system, it  use (mm/s2) *s  in Acceleration) , and the unit of NI-PSD is  (EU)/sqrt(Hz)  or  (EU^2) / Hz.

So after I analysis the "30ms pules signals", do I need to Multiply the result with the Time period（0.03 s）？

[LocalDSP]

No, when you multiply your PSD averaged result by N you are effectively integrating the power to get energy.

Power is Energy per time unit (like kW becomes kWh).

The PSD unit is as you mentioned (EU^2) / Hz or (EU^2) * s which becomes (EU^2) * s^2 when integrated.

For EU = mm/s2 you then get (mm/s2) *s when you take the square root of the resulting ESD.

[huangxm]

Thank you.

But my pulses signals seems doesn't need to averaged. It just get 1024 Amplitude，from 0 s to 40 ms as the attachment"40 ms".

 

When these signals data get into the "SVFA Power Spectral Density .vi" in one time, the PSD vi  could calculate the result  as the  attachment "PSD". I have no more data to let it averaged one more time.

 

As your Guidelines， DO you mean that PSD is Actually "ESD"？ And I don't need to do any more calculate for the PSD result ?

[LocalDSP · Accepted solution]

That is correct, for N = 1 (no averaging) the numerical values of ESD is the same as PSD. The units are still different though since you are still integrating over the 1/1 Hz = 1 s of your PSD.

[huangxm]

Thanks a lot !  

 If that's some time you come to china, Guangzhou , Let me Know.

[LocalDSP]

Thanks for the offer, that is very kind. I've been in Guangzhou a couple of times and I love the city.

Good luck with your project and please feel free to post other questions as needed.

The type of questions like the one you asked is likely relevant and interesting to other members of this forum and discussing work-arounds for features not implemented in LabVIEW is a good way to advance the product too.