FFT Space -> Fourier

Use the 1D FFT > Advanced Settings > FFT Space -> Fourier menu option (FFTIN GX) to transform a channel from the space domain to the frequency domain.

FFT Space -> Fourier dialog options

Channel to transform	Name of the channel to transform. Script Parameter: FFTIN.IN
[Trend Removal>]	Click to set the trend parameters.
[Expansion>]	Click to set the grid expand parameters.

FFT Space -> Fourier - Trend Removal dialog options

Type of trend line to remove

Trend line removal options: 3: remove mean value 2: remove trend line based on all data points (default) 1: remove trend line based on two edge points 0: do not remove trend Script Parameter: FFTIN.DETRD

FFT Space -> Fourier - Expansion dialog options

Minimum expansion (%)

Minimum data expansion (%) before FFT process The default: 10%. Script Parameter: FFTIN.EXP

Application Notes

Three output channels are created; the real and imaginary components of the transform as well as the wavenumber channel.  All three of these channels acquire the base name of the input channel and are respectively appended by "_r", "_i" and “_w”.  The fiducials are in cycles/fiducial.  The wavenumber channel is in radians/fiducial

In space domain an observed signal has only a real component and no imaginary component thus the transform of the signal in wavenumber domain is symmetrical and the negative part of the spectrum is the conjugate of the corresponding positive part, i.e H(-f) = [H(f)]*.  This leads to the fact that in wavenumber domain we need only be concerned with saving the positive signal.   An additional FFT stipulation is that the space domain sampling should be at a constant increment.  To ensure this requirement,  prrior to performing the transformation, the data is re-fided to a constant space interval.

Furthermore, to adhere to the fundamental assumption of signal periodicity, the 1^st order trend is removed from the data prior to the FFT process.  The intent is to ensure that the signal is cyclical and there are no discontinuities at the edges.  The removed trend will be placed back into the processed data by the FFTOUT GX.

Lastly, the data is padded by at least 10% (the default) before the FFT process. This buffer zone paired with the trend removal allows for an extrapolation that ensures continuity between the two ends of the data. The extended size of the array is rounded up to the smallest power of 2 larger than the % specified by the user. For instance, if the original data contains 60 points, and the user has chosen a 10% extension the final size of the data array will be 128, the smallest power of 2 larger than 60.

The padded segment will be interpolated by either the Maximum Entropy Prediction (MEP) method or the Constrained Linear Prediction (LP) method. MEP determines the spectral content or the preceding real data segment. It then predicts a data function that has the same spectral signature as the original data. As a result, the predicted data will not significantly alter the energy spectrum of the original data.

The Constrained Linear Prediction (LP) method, calculates a series of linear prediction coefficients based on a segment of real data, and then uses these coefficients to recursively extrapolate the data. The nature of geophysical data with its wide range of distribution, generally yields coefficients that produce a reasonable extrapolation.  However if the data contains undamped oscillations, such as superimposed aircraft systematic noise, then LP may produce an unstable outcome.  An additional constrain on the calculation of the coefficients pushes the results back into the stable zone.  The details of the constrained LP are outside the scope of this document.  The avid reader can find further information in the reference below:

Reference