Thread: About definition of Fourier transform

Started: 2010-04-13 03:00:18
Last activity: 2010-04-13 03:09:51
Topics: SAC Help
Genti Toyokuni
2010-04-13 03:00:18
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

  • Arthur Snoke
    2010-04-12 16:18:31
    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
    _______________________________________________
    sac-help mailing list
    sac-help<at>iris.washington.edu
    http://www.iris.washington.edu/mailman/listinfo/sac-help


    • Arthur Snoke
      2010-04-13 03:09:51
      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 non-SAC 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
      _______________________________________________
      sac-help mailing list
      sac-help<at>iris.washington.edu
      http://www.iris.washington.edu/mailman/listinfo/sac-help

      _______________________________________________
      sac-help mailing list
      sac-help<at>iris.washington.edu
      http://www.iris.washington.edu/mailman/listinfo/sac-help


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