harmonica.filters.gaussian_highpass_kernel#

harmonica.filters.gaussian_highpass_kernel(fft_grid, wavelength)[source]#

Filter for Gaussian high-pass in frequency domain

Return a xarray.DataArray with the values of a Gaussian high-pass filter the frequency domain. The filter is built upon the frequency coordinates of the passed fft_grid and is defined as follows:

$$g(\mathbf{k})=1-e^{-\frac{1}{2}{\left(\frac{|\mathbf{k}|}{k_c}\right)}^2}$$

where $\mathbf{k}$ is the wavenumber vector ($\mathbf{k}=2\pi \mathbf{f}$ where $\mathbf{f}$ is the frequency vector) and $k_c$ is the cutoff wavenumber: $k_c=\frac{2\pi }{{\lambda }_c}$, where ${\lambda }_c$ is the cutoff wavelength.

Parameters:

fft_gridxarray.DataArray

Array with the Fourier transform of the original grid. Its dimensions should be in the following order: freq_northing, freq_easting. Use xrft.xrft.fft and xrft.xrft.ifft functions to compute the Fourier Transform and its inverse, respectively.

wavelengthfloat

The cutoff wavelength for the high-pass filter. Its units should be the inverse units of the coordinates in fft_grid.

Returns:

da_filterxarray.DataArray

Array with the kernel for the Gaussian high-pass filter in frequency domain.

See also

harmonica.gaussian_highpass

References

[Geosoft1999]