Cosine Roll-off Filter

Use the Cosine Roll-off option to apply a Fast Fourier Transform (FFT) cosine roll-off filter to a channel.

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

• 1D FFT > 1D Filtering
• Moving Platform Gravity  > Filters > Apply Single FFT Filter

Cosine Roll-off filter options

Start roll-off wavelength (in ground units)	Short wavelength of the bounding range for the cosine taper. Default = 0.1 Script Parameter: FFTCOSN.WSTART
End roll-off wavelength (in ground units)	Long wavelength of the bounding range for the cosine taper. Default = 1 Script Parameter: FFTCOSN.WEND
Degree of filter	Controls the sharpness of the roll-off. Higher degree = sharper drop-off. Default = 2 Script Parameter: FFTCOSN.DEGREE
Low or high pass filter	Low-pass: Removes noise or isolates regional field signature. High-pass: Highlights near-surface field signature. Default = Low Script Parameter: FFTCOSN.PASS

Application Notes

The cosine roll-off filter is commonly used for high-pass or low-pass operations because it avoids ringing artifacts caused by abrupt cut-off filters.

• The filter applies a smooth taper between two wavelengths using a cosine function.

• The desired cut-off wavelength lies within this range but does not need to be centered.

• To reduce ringing:

  • Increase the separation between short and long wavelengths.

  • Decrease the degree of the filter.

Cosine Roll-off Filter

The cosine roll-off filter spreads the cutoff over a range in a smooth, gradual manner using a cosine function. This range is defined by two user-specified wavelengths.

For ease of use and interpretation, the user enters cutoff values in units of wavelength, starting with the shorter wavelength. These values are internally converted to wavenumbers for processing. In the illustration below, the filter is shown in the Fourier domain, where the horizontal axis represents wavenumber (the inverse of wavelength).

Key Parameters

k₀: Low wavenumber (start of taper) = Long wavelength^-1

k₁ : High wavenumber (end of taper) = Short wavelength^-1

n: Degree of cosine function (default = 2 for cosine-squared roll-off)

N: Nyquist wavenumber