[SAC-HELP] About fft routine in SAC

[Brian Savage]

For an forward FFT (fft) in SAC the output series is scaled by the  
time sampling or delta

For an inverse FFT (ifft) in SAC the output series is scaled by 1/ 
(delta * npts)

See below for a further discussion, but simply

fg sine 5 npts 1024 delta 0.01
# Put the delta back in
div 0.01
# Scale the FFT by the length of the signal
div 1024
fft
psp am
# Maximum should be around 0.5
writesp tmp
read tmp.am
lh depmax
# depmax should be about 4.671955e-01 (not exactly 0.5, but close)

Cheers
Brian Savage

Begin forwarded message:

> Thanks for your reply.
> To meet the Paseval's theorem, SAC multiplies the constant 2/T to  
> the input
> trace, thank you very much.
>
>
> Your sincerely,
> Xu W.
>
> ************************************************
> Dr. WeiWei Xu
> Institute of Geology and Geophysics
> Chinese Academy of Sciences
> P.O.Box 9825
> Beijing 100029
> China
> Tel: 0086-10-62007354(Office)
> Fax: 0086-10-62010846
> ************************************************
>
> Garrett Euler д:
>
> Xu,
>
> SAC scales data in the frequency domain with the time domain sample
> interval rather than the npts.  Not sure why this is.  To correct  
> for this
> multiply amplitudes given in SAC by 2/(npts*delta) where npts and  
> delta are
> the time domain values and the 2 accounts for the energy in the  
> negative
> frequencies.
> You'll have to do the multiplying before the fft since SAC doesn't  
> let you
> use mul on spectral data:
>
> 2/(1024*0.01) = 0.1953125
>
> funcgen sine 5 npts 1024 delta 0.01
> mul 0.1953125
> fft
> psp am loglin
>
>
> Garrett
>
>
>
> "wwxu" <wwxu at mail.iggcas.ac.cn> wrote ..
> Hi ALL,
>
> In SAC, I generate a 5Hz sine wave and do fft transforming as follows:
> sac> funcgen sine 5 npts 1024 delta 0.01
> sac> fft
> sac> psp am loglin
> and I find that the maximum absolute amplitude is greater than 4 near
> frequency 5Hz, but in theory, it should be 0.5 because of amplitude
> spectrum symmetry of real series, so could you tell me why?
>
> B.T.W., I also compute the amplitude spectrum using fft program I  
> wrote
> and
> find that the result is not the same with SAC generated, I checked the
> program carefully and be sure that it's right and conform with the
> theoretical result.
>
> thanks for your attention!
>
>
> Your sincerely,
> Xu W.
>
> ************************************************
> Dr. WeiWei Xu
> Institute of Geology and Geophysics
> Chinese Academy of Sciences
> P.O.Box 9825
> Beijing 100029
> China
> Tel: 0086-10-62007354(Office)
> Fax: 0086-10-62010846
> ************************************************
>
> _______________________________________________
> sac-help mailing list
> sac-help at iris.washington.edu
> http://www.iris.washington.edu/mailman/listinfo/sac-help
>

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://www.iris.washington.edu/pipermail/sac-help/attachments/20080310/619372bd/attachment.html>