the units for power spectrum and fourier spectrum
Posted: 30 Jun 2012, 05:31
Dear all,I would like to ask what is the unit for power spectrum and fourier spectrum respectively.
1.For fourier spectrum.
I do read all the posts related to the fourier spectrum and found that,in this post(http://www.seismosoft.com/forum/topic.asp?TOPIC_ID=506),the seismosoft support confirmed that if the user define time history in 'g',the unit for fourier spectrum is also 'g',which is same with the input data.However, in another post(http://www.seismosoft.com/forum/topic.asp?TOPIC_ID=235),the unit for fourier spectrum is m/s^2/Hz,when the input data is in m/s^2,while Hz is 1/s, thus the unit for fourier spectrum is m/s?Do this correct?
2.For power spectrum.
In the software help posts,the power spectrum is calculated by the formula[ FFT(a(t))]^2/[T*PI*aRms^2],and the unit for it is 1/Hz(http://www.seismosoft.com/forum/topic.a ... r,spectrum) which mean that the power spectrum has been normalized?But in my calculation I could not obtain such a unit.Would you please show me how could I deduce such a unit?Or what is wrong with my deduction?
Deduction:(Define the input data in m/s^2)
1).The unit of the data after FFT is the same with the original data,thus the unit for [FFT(a(t))]^2 is m^2/s^4.
2).I think the unit for aRms is the same with the input data,m/s^2,which was deduced by the formula of it,right?
3).T, the unit is s, PI, the unit is rad.
Thus the unit for PSD would be like this:
(m^2/s^4)/[(s)*(rad)*(m/s^2)^2]=1/[rad*s] which is not equal to 1/Hz,or s.
In my some other references, the unit for the PSD should be( m^2/s^4)/Hz,how could I obtain such a series of data?
1.For fourier spectrum.
I do read all the posts related to the fourier spectrum and found that,in this post(http://www.seismosoft.com/forum/topic.asp?TOPIC_ID=506),the seismosoft support confirmed that if the user define time history in 'g',the unit for fourier spectrum is also 'g',which is same with the input data.However, in another post(http://www.seismosoft.com/forum/topic.asp?TOPIC_ID=235),the unit for fourier spectrum is m/s^2/Hz,when the input data is in m/s^2,while Hz is 1/s, thus the unit for fourier spectrum is m/s?Do this correct?
2.For power spectrum.
In the software help posts,the power spectrum is calculated by the formula[ FFT(a(t))]^2/[T*PI*aRms^2],and the unit for it is 1/Hz(http://www.seismosoft.com/forum/topic.a ... r,spectrum) which mean that the power spectrum has been normalized?But in my calculation I could not obtain such a unit.Would you please show me how could I deduce such a unit?Or what is wrong with my deduction?
Deduction:(Define the input data in m/s^2)
1).The unit of the data after FFT is the same with the original data,thus the unit for [FFT(a(t))]^2 is m^2/s^4.
2).I think the unit for aRms is the same with the input data,m/s^2,which was deduced by the formula of it,right?
3).T, the unit is s, PI, the unit is rad.
Thus the unit for PSD would be like this:
(m^2/s^4)/[(s)*(rad)*(m/s^2)^2]=1/[rad*s] which is not equal to 1/Hz,or s.
In my some other references, the unit for the PSD should be( m^2/s^4)/Hz,how could I obtain such a series of data?