.de BR
.in 0
.in +8n
.ti -3n
..
.Th                                      FFT
.S2 SUMMARY:
Obtain the discrete Fourier transform of traces in memory

FFT  [Length 1|2|4|8] [Default]
.S2 INPUT
Length Nvalue - pad the time series with zeros to increase the FFT by a factor or 1, 2, 4 or 8. The purpose of this is to ensure greater frequency resolution.
.sp
.BR
Default - resent Length to 1
.sp
Note that the use must ensure there is no offset between the time series and the appended zeros by some combination of RMEAN, RTR or TAPER. The default is Length = 1. 
.sp
Note also that zeros are always added since the FFT requires a power of 2 length.


.S2 DESCRIPTION:
This estimates the discrete Fourier transform of the traces in 
by using a version of Brenner's original FOUR1 routine. The definition
of the DFT is
.nf
.na
                      N\-1       j {2 pi n k/N}
      H( n DF ) = DT  SUM h(k) e              
                      k=0                     
.fi
.ad
where DF = 1/(N DT), DT = sampling interval, DELTA, and N is a power of
2. Note that this is an extension to the definition  of a DFT in that
physical dimension are introduced
.S2 NOTE
This DFT is with respec to the first data point. this decision controls the phase.
The WRITESP has the option to set the phase with respect the O (origin marker)
.S2 DEFAULT
FFT L 1

.S2 "SEE ALSO":
PLOTSP, WRITESP, RMEAN, RTR, TAPER

