Fourier Tranform and Power specral Density

[kennyai]

Dear all,

I am wondering about the units of the Fourier Transform and Power Spectrum. I wish to get my results in radians and not a normalised power spectrum.
Presently they are (with input in m/s^2):
Fourier Amplitude: m^2/s^4 plotted against Hz
Power spectrum: 1/Hz plotted against Hz

I wish to plot:
Fourier Amplitude: m^2/s^4 plotted against w (rad)
Power spectrum: m^2/s^4/rad plotted against w (rad)

How do I convert these values?

Thank you!

[seismosoft]

Hi kennyai,

As we suspect you are implying/expecting already, such post-processing needs to be done outside of SeismoSignal. In other words, if we are not mistaken, your question is not really on SeismoSignal but rather on the issue of units conversion, in which case we, as usual, invite also others to respond.

Seismosoft Support

[inversesugar]

quote:Originally posted by kennyai

Dear all,

I am wondering about the units of the Fourier Transform and Power Spectrum. I wish to get my results in radians and not a normalised power spectrum.
Presently they are (with input in m/s^2):
Fourier Amplitude: m^2/s^4 plotted against Hz
Power spectrum: 1/Hz plotted against Hz

I wish to plot:
Fourier Amplitude: m^2/s^4 plotted against w (rad)
Power spectrum: m^2/s^4/rad plotted against w (rad)

How do I convert these values?

Thank you!



would you please check my post? actually i'm thinking about the same question with you.

http://www.seismosoft.com/forum/topic.asp?TOPIC_ID=736

so, here is my opinion.
the original power spectrum is 1/Hz plotted against Hz
while we want the power spectrum is 1/rad plotted against w (rad)
i think we can do like this:

since the area of the curve with the x-axis should be a constant, we can change the unit of the x-axis from hz to rad by multiply by 2PI, while the uit of y-axis from 1/HZ to 1/rad by divide by 2PI, which can make sure that the energy of the two curve with different unit be a constant.

Am i correct? your judgement and review is greatly appreciated.

[inversesugar]

quote:Originally posted by seismosoft

Hi kennyai,

As we suspect you are implying/expecting already, such post-processing needs to be done outside of SeismoSignal. In other words, if we are not mistaken, your question is not really on SeismoSignal but rather on the issue of units conversion, in which case we, as usual, invite also others to respond.

Seismosoft Support


actually this is not a mistaken of the software, but i think it is also ok for us, the users, to consult to you, just as a discussion.