# harmonica.filters.gaussian_lowpass_kernel¶

harmonica.filters.gaussian_lowpass_kernel(fft_grid, wavelength)[source]

Filter for Gaussian low-pass in frequency domain

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

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

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_grid (xarray.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.

• wavelength (float) – The cutoff wavelength for the low-pass filter. Its units should be the inverse units of the coordinates in fft_grid.

Returns

da_filter (xarray.DataArray) – Array with the kernel for the Gaussian low-pass filter in frequency domain.

References

[Geosoft1999]