Cosine Roll-off Filter

Use the Cosine Roll-off option to apply a Fast-Fourier Transform Cosine Roll-off filter to a channel.

The filter option is available with the following extensions and menus:

• Geophysics: 1D FFT > 1D Filtering
• Gravity and Terrain Correction: Moving Platform Gravity  > Apply Single FFT Filter

Cosine Roll-off filter options

Start roll-off wavelength (in ground units)	The cosine roll-off filter (see illustration) spreads the cut-off over a range in a smooth gradual fashion using a cosine function. This range is bound by two user specified wavelengths. Define the short wavelength of the bounding range (Default is 0.1). Script Parameter: FFTCOSN.WSTART
End roll-off wavelength (in ground units)	See above. Define the long wavelength of the bounding range (Default is 1). Script Parameter: FFTCOSN.WEND
Degree of Filter	The higher the degree of the cosine function (see illustration), the sharper the drop-off (Default is 2). Script Parameter: FFTCOSN.DEGREE
Low or High Pass Filter	To filter out the noise or obtain the regional signature of the field, select "Low" pass. To obtain the near surface signature of the field, select the "High" pass option (Default is Low). Script Parameter: FFTCOSN.PASS

Application Notes

The cosine roll-off filter is commonly used for simple high-pass or low-pass operations. This is because an abrupt cut-off filter causes ringing in the resulting output data. The Cosine roll-off mitigates this artifact by introducing a gradual drop over a range. The desired cut-off wavelength resides within this range, but need not be centered on the range. If you observe ringing, you can reduce the artifact by widening the separation between the short and long wavelengths, or decreasing the degree of the filter.

Cosine Roll-off Filter

For ease of use and interpretation, the user is prompted to enter the cutoffs in units of wavelength, starting with the small wavelength. These are internally translated to wavenumbers for processing. In the illustration below the filter is portrayed in the Fourier domain, and as a result the horizontal axis is in units of Wavenumber. Wavenumbers are the inverse of wavelengths.

Parameters:

k₀ Low wavenumber, starting point of the cosine taper: k₀ = Long wavelength-1

k₁ High wavenumber, end point of the cosine taper. K₁= Short wavelength-1

n Degree of the cosine function. The default is a degree of 2 for a cosine squared roll-off.

N Nyquist wavenumber