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)

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:

:class:`ConvolutionFilter`

namedtuple containing filter attributes

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

collections.namedtuple containing attributes defining a 2D Convolution Filter. A namedtuple is used because they’re easier to use when using nopython mode in numba.

africanus.filters.full_sup

Full support

africanus.filters.full_sup_wo_padding

Full support without padding

africanus.filters.half_sup

Half support

africanus.filters.oversample

Oversampling factor

africanus.filters.no_taps

Number of taps

africanus.filters.filter_taps

2D filter taps with shape (v, u)

Kaiser Bessel

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)

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

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)

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)

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)

Estimate the kaiser bessel beta using the following heuristic:

\[\beta = 2.34 \times W\]

Derived from Nonuniform fast Fourier transforms using min-max interpolation.

Parameters:

W : int

Width of the filter

Returns:

float

Kaiser Bessel beta shape parameter

Sinc

The Sinc function.