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Frequency Sections: How can I have the same energetic content of a time trace?

Siemens Experimenter Siemens Experimenter
Siemens Experimenter

Hi,

 

I'm processing a time signal (10s - Fs=2000Hz) in order to obatin frequency sections (frequency: 100Hz, 200Hz, and so on). The spectrum frequency resolution is 100 Hz.

My aim is to sum all these frequency sections and obtain the same energetic content of the time trace.

 

Even if I changed parameters like frequency bands of the frequency section, I didn't reach the target. And I'm far away from the target.

 

Anyone is able to explain me how the process work regardless to the numbers I used?

 

Thanks

Roberto

 

7 REPLIES

Re: Frequency Sections: How can I have the same energetic content of a time trace?

Siemens Legend Siemens Legend
Siemens Legend

Hi Roberto,

Can you check the processing setting in Acquisition Parameters->Tracking & Triggering as shown in the image below:

Picture1.jpg

What's your measurment mode, tracking method?  Like the example above the measurement mode is track, and tracking method is time, with 0.5 second increment.  What's that mean is I'm processing FFT every 0.5 second.  Like you said, if your frequency resolution is set to 100 hertz, the frame size is 0.01 second.  That mean you're only processing 0.01 second of your time data, not all data.  Your first FFT start at time 0 to .01 second, then second FFT start from 0.5 to 0.51, third FFT from 1 to 1.01...so on till then end of time recording.  In this case, you're missing time from 0.01 to 0.49, 0.51 to 0.99, 1.01 to 1.49...so on, 99% of the data is not process.  You might need to adjust the frequncy resolution, so the frame size is equal to the increment or smaller than the increment.  You can change the resolution to 2 hertz with 0.5 second increment.  If the resolution is smaller than 2 hertz, let's try 1 hertz then frame size is 1 second, now you'll have 50% of overlapping.  Please adjust the setting accordingly and reprocess the data.

 

If you're trying to sum up all frequency content, why don't you try the overall level feature?  It's in Time data processing->Sections->Change Settings->Overall level.

 

Hong

Re: Frequency Sections: How can I have the same energetic content of a time trace?

Siemens Experimenter Siemens Experimenter
Siemens Experimenter

Hi,

 

thanks for your reply.

 

Evenf if I used tracking time with time increment 0,01 second (1/0.01s=100Hz) and I crate frequency section  in order to cover all the frequency bandwidth, we are completely out of the target. I attached some pictures with settings and results. 

 

Unfortunately overall cannot be useful in this case cause I need a "global" RMS value; overall gives us a set of values time dependent. My final target is not to calculate the RMS value but undestranding how frequency section works and how it can give me results with a reliable energetic content Smiley Happy

 


1.jpg2.png3.png4.png

 

 

 

Re: Frequency Sections: How can I have the same energetic content of a time trace?

Siemens Legend Siemens Legend
Siemens Legend

When you set frequency resolution to 100 hertz, that you only have spectral content every 100 hertz, that's 100, 200, 300, 400, 500, 600, 700, 800, 900 & 1000 hertz, and only one data point.  No frequency content in 12.5, 50, 150, 250, 350,450... etc that's why I'm suggesting to change the resolution to much finer like 2 hertz, don't change the increment to 0.01 second.  Please try my suggestion...

 

Hong

Re: Frequency Sections: How can I have the same energetic content of a time trace?

Siemens Experimenter Siemens Experimenter
Siemens Experimenter

Hi Hong,

 

 

I tried with different frequency (0,5 hz, 1 hz, 2 hz) and teh results are attached.

As you can see we have always a sum value that is bigger than RMS time value. There is something in frequency section algorithm or rms calculation I'm not taking into account.

5.png

Roberto

Re: Frequency Sections: How can I have the same energetic content of a time trace?

Siemens Legend Siemens Legend
Siemens Legend

Since the frequncy section is RMS calculation, you cannot just simply add values for each frequency section to match the overall level.  I'll need further investigation to answer your question.  Also, you can try to perform a total frequency band section with lower frequency at 0 hertz, higher at 1000 hertz which it's the same as overall level calculation sum up all freqency bands.

 

Hong

Re: Frequency Sections: How can I have the same energetic content of a time trace?

Siemens Phenom Siemens Phenom
Siemens Phenom

Hello Roberto,

 

Let me give you some suggestions in addition to Hong's.  One quick thing, if you calculate the RMS of the Overall Level you will get the single number you desire and it should match the RMS of the time domain signal.  I like to check things out with a known signal, so I used the Time Signal Calculator to generate a ten second time history with an RMS value of 1 Pa.

 

GENERATE_RANDOM(0.0[Pa];1;0;1;0;10;2000;0)

 

I then processed using Stationary averaging with energetic averaging with a lot of averages (it will stop when it runs out of data).  I would use 67-75% overlap depending on what you want to recover from the Hanning window shape missing some data.   I used 1 Hz resolution which has a frame size of 1 second, but others will work as well.  I calculate Autopower Linear with Peak amplitude (if you stay in Test.Lab we manage Peak versus RMS well but you can calculate RMS if  amplitude if you want).  I also calculated these frequency sections and the Overall Level.  I did not want to miss any data in the frequency sections so I made sure the frequency sections cover the entire 0-1000 Hz range.

 

1.jpg2.jpg4.jpg5.jpg

 

In this plot I am showing the Overal Level with RMS = 1, the Averaged Autopower Linear in an Octave display showing the RMS for each octave band and the Overall Level = 1 (with Linear weighting), the time history with RMS=1 and then each frequency section and it's RMS calculation.  

 

6.jpgIf you take the RMS calculations for the frequency sections to Excel, square them, sum them and square root them that should also = 1 RMS.

 

 7.jpg

I also tried with this in the Time signal calculator which had an RMS = 4.98 in the time domain and the same process resulted in similar results.

 

8.jpg

 

 

Re: Frequency Sections: How can I have the same energetic content of a time trace?

Siemens Experimenter Siemens Experimenter
Siemens Experimenter

Hi Kevin & Hong,

 

all is clear now! Thanks for your support!

 

Roberto