units pmtm

Hi,

I'm having trouble making some conversions because after looking through things I've realized I don't quite understand the output of pmtm. I have a time series I am feeding into pmtm with units of m on the y-axis and units of seconds on the x axis. I'm wondering what the units on the y-axis would be after being output from pmtm?

I know the manual says they are units of Power/frequency-but how does this really work out explicitly if I'm starting with units of m? I'm confused, can someone please explain this to me? Inevitably I am trying to get displacement amplitude spectra.

Cheers,

K

Answer 1

[Wayne King]

The output from pmtm() the power spectral density will be in m^2/Hz (if you are using the sampling frequency). You want to make sure you square the units (this comes from the power). So if you had an acceleration recording in time that would be in m/sec^2, the output of pmtm() for that data would be in (m/sec^2)^2/Hz (again if you are using the sampling frequency in pmtm()).

Keep in mind for statistical reasons, it is very common to plot PSD estimates in dB (in your case 10*log10(m^2/Hz))

[Katherine]

Okay thank you very much, this is what I expected it to be in. One could also plot it in amplitude right by using 20*log10(Pxx), if Pxx were the output.

What did you mean it would be m^2/Hz if I'm using the sampling frequency? Fs is 100 Hz, i.e., sampling rate and I use this within the call for pmtm.

Also here's another question, why when I put values of amplitude in that are say on the order of e-6 do I get out ones on the order of e-16?

[Wayne King]

I wouldn't use 20*log10() because the output of pmtm() is squared already, so you want 10*log10(), remember that 10*log10(z^2)=20*log10(z)

I mean if you input the sampling frequency into pmtm(), then the output is per Hz, if you do not input the sampling frequency, then it's m^2/rad/sample

are you saying that the output is on the order of 10^(-16) everywhere or just at most frequencies? What happens if the signal has dominant mode of oscillation is the the power is concentrated at a few frequencies and most of the frequencies are close to zero as opposed to the picture you get in the time domain.

[Katherine]

10*log10() would put it in dB. I thought that 20*log10() would then transfer it into amplitude. Eventually what I want on the y-axis is amplitude.

Yes I'm saying for the most part the y-axis values are on the order of e-6 when I input these amplitude values into pmtm the output is on the order of 10^(-16) or less for the majority of the frequencies. So this would suggest the dominant mode of oscillation is concentrated near zero then?

I'm just trying to make sense of what physically comes out of pmtm and how to interpret these results.