Cosine Roll-off (COSN)

Use the Cosine Roll-off option to apply a cosine roll-off filter.

Cosine Roll-off Filter dialog options

Long wavelength cutoff	The starting wavelength roll-off in ground unit. See illustration, this parameter is equivalent to k₀^-1.
Short wavelength cutoff	The ending wavelength roll-off in ground unit. See illustration, this parameter is equivalent to k₁^-1.
Degree of cosine function:	The degree n of the cosine function. The higher the degree, the sharper the roll-off. The default is 2.
Low pass or High pass	To generate the regional field, select Low pass. This is the default. The High pass is the reciprocal filter and produces the residual field.

Application Notes

Because this filter has a smooth shape, and it does not alter the energy spectrum below the start of roll-off (or after the end of roll-off in high-pass mode), it is commonly used for simple high-pass or low-pass operations. To reduce ringing, the separation between k₁ and k₀ can be increased.

Cosine roll-off filter

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Where,

k₀	The starting wavelength roll-off.
k₁	The ending wavelength roll-off.
n	Positive integer value determining the degree of sharpness of the cutoff.

Wavenumber domain variable definition


k	Wavenumber domain increment, used to depict a radially symmetrical variable.	where: np is the number of points cs is the cell size
u	X component in the wavenumber domain.	k = 2π ( i μ+j ν )
v	Y component in the wavenumber domain.
r	Radial component in the wavenumber domain.	also 2πk
θ	Polar component in the wavenumber domain.

Ground_unit is the survey ground units as defined in your grid (e.g. metre or feet). Ground units may be left undefined.