Convolution Filters¶

Convolution filters suitable for use in gridding and degridding.

API¶

convolution_filter(half_support, …) Create a 2D Convolution Filter suitable for use with gridding and degridding functions.

africanus.filters.convolution_filter(half_support, oversampling_factor, filter_type, **kwargs)[source]¶

Create a 2D Convolution Filter suitable for use with gridding and degridding functions.

Parameters:

half_support : integer: Half support (N) of the filter. The filter has a full support of N*2 + 3 taps. Two of the taps exist as padding.
oversampling_factor : integer: Number of spaces in-between grid-steps (improves gridding/degridding accuracy)
filter_type : {‘kaiser-bessel’, ‘sinc’}: Filter type. See Convolution Filters for further information.
beta : float, optional: Beta shape parameter for Kaiser Bessel filters.
normalise : {True, False}: Normalise the filter by the it’s volume. Defaults to True.

Returns:

africanus.filters.ConvolutionFilter = <class 'africanus.filters.conv_filters.ConvolutionFilter'>¶

The Kaiser Bessel function.

`kaiser_bessel`(u, W, beta)	Compute a 1D Kaiser Bessel filter as defined in Selection of a Convolution Function for Fourier Inversion Using Gridding.
`kaiser_bessel_with_sinc`(u, W, oversample, beta)	Produces a filter composed of Kaiser Bessel multiplied by a sinc.
`kaiser_bessel_fourier`(x, W, beta)	Computes the Fourier Transform of a 1D Kaiser Bessel filter.
`estimate_kaiser_bessel_beta`(W)	Estimate the kaiser bessel beta using the following heuristic:

africanus.filters.kaiser_bessel_filter.kaiser_bessel(u, W, beta)[source]¶

Parameters:	u : `numpy.ndarray` Filter positions W : int Width of the filter beta : float, optional Kaiser Bessel shape parameter
Returns:	:class:`numpy.ndarray` Kaiser Bessel filter with the same shape as u

africanus.filters.kaiser_bessel_filter.kaiser_bessel_with_sinc(u, W, oversample, beta, normalise=True)[source]¶

Produces a filter composed of Kaiser Bessel multiplied by a sinc.

Accounts for the oversampling factor, as well as normalising the filter.

Parameters:	u : `numpy.ndarray` Filter positions W : int Width of the filter oversample : int Oversampling factor beta : float Kaiser Bessel shape parameter normalise : optional, {True, False} True if the filter should be normalised
Returns:	:class:`numpy.ndarray` Filter with the same shape as u

africanus.filters.kaiser_bessel_filter.kaiser_bessel_fourier(x, W, beta)[source]¶

Computes the Fourier Transform of a 1D Kaiser Bessel filter. as defined in Selection of a Convolution Function for Fourier Inversion Using Gridding.

Parameters:	x : `numpy.ndarray` Filter positions W : int Width of the filter. beta : float Kaiser bessel shape parameter
Returns:	:class:`numpy.ndarray` Fourier Transform of the Kaiser Bessel, with the same shape as x.

africanus.filters.kaiser_bessel_filter.estimate_kaiser_bessel_beta(W)[source]¶

Estimate the kaiser bessel beta using the following heuristic:

\[\beta = 2.34 \times W\]

Parameters:	W : int Width of the filter
Returns:	float Kaiser Bessel beta shape parameter

The Sinc function.