Hello,
I want to ask you definition of Fourier transform used in the fft command.
Does the command perform the FFT with \exp(i\omega t), or \exp(+i\omega t)?
I tried to find it out from the SAC manual, but I could not.
Regards,
Genti Toyokuni
I want to ask you definition of Fourier transform used in the fft command.
Does the command perform the FFT with \exp(i\omega t), or \exp(+i\omega t)?
I tried to find it out from the SAC manual, but I could not.
Regards,
Genti Toyokuni

The forward transform uses your first option: exp(i\omega t).
I thought it was documented but did not see it with a quick check. if it
is there somewhere, please let me know where. If not, we will put it in
the next release  probably in the help file for FFT, if no one has a
better idea.
On Mon, 12 Apr 2010, Genti Toyokuni wrote:
Hello,
I want to ask you definition of Fourier transform used in the fft command.
Does the command perform the FFT with \exp(i\omega t), or \exp(+i\omega t)?
I tried to find it out from the SAC manual, but I could not.
Regards,
Genti Toyokuni
_______________________________________________
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sachelp<at>iris.washington.edu
http://www.iris.washington.edu/mailman/listinfo/sachelp

If the forward fft has a +i, the unwrapped phase will increase with
frequency, for a i (SAC convention) the phase will decrease.
An easy way to check is the following sequence:
SAC> fg seis
SAC> unwrap
DC level after DFT is 0.98547
SAC> plotsp
Waiting
SAC>
The plot displayed after "Waiting" is the unwrapped phase, which clearly
decreases with increasing frequency.
I have not used unwrap, and the HELP file says "The maximum length of data
that can currently be transformed is 4096." The help file was last
updated in January 8, 1983, If that limitation has been relaxed, the
unwrap command might be useful for some: "The data is filled with zeros to
the next power of two before being transformed. You may specify a
larger number of zeros by using the FILL option." My nonSAC program for
working with time series pads time series by a factor of 4 before the FFT.
On Mon, 12 Apr 2010, Arthur Snoke wrote:
The forward transform uses your first option: exp(i\omega t).
I thought it was documented but did not see it with a quick check. if it is
there somewhere, please let me know where. If not, we will put it in the
next release  probably in the help file for FFT, if no one has a better
idea.
On Mon, 12 Apr 2010, Genti Toyokuni wrote:
Hello,
_______________________________________________
I want to ask you definition of Fourier transform used in the fft command.
Does the command perform the FFT with \exp(i\omega t), or \exp(+i\omega
t)?
I tried to find it out from the SAC manual, but I could not.
Regards,
Genti Toyokuni
_______________________________________________
sachelp mailing list
sachelp<at>iris.washington.edu
http://www.iris.washington.edu/mailman/listinfo/sachelp
sachelp mailing list
sachelp<at>iris.washington.edu
http://www.iris.washington.edu/mailman/listinfo/sachelp
