[SAC-HELP] About definition of Fourier transform

[Arthur Snoke]

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
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>> 
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