dft_preprocess_data

odl.trafos.util.ft_utils.dft_preprocess_data(arr, shift=True, axes=None, sign='-', out=None)

Pre-process the real-space data before DFT.

This function multiplies the given data with the separable function:

p(x) = exp(+- 1j * dot(x - x[0], xi[0]))

where x[0] and xi[0] are the minimum coodinates of the real-space and reciprocal grids, respectively. The sign of the exponent depends on the choice of sign. In discretized form, this function becomes an array:

p[k] = exp(+- 1j * k * s * xi[0])

If the reciprocal grid is not shifted, i.e. symmetric around 0, it is xi[0] =  pi/s * (-1 + 1/N), hence:

p[k] = exp(-+ 1j * pi * k * (1 - 1/N))

For a shifted grid, we have :math:xi[0] =  -pi/s, thus the array is given by:

p[k] = (-1)**k

Parameters

arrarray-like

Array to be pre-processed. If its data type is a real non-floating type, it is converted to ‘float64’.

shiftbool or or sequence of bools, optional

If True, the grid is shifted by half a stride in the negative direction. With a sequence, this option is applied separately on each axis.

axesint or sequence of ints, optional

Dimensions in which to calculate the reciprocal. The sequence must have the same length as shift if the latter is given as a sequence. Default: all axes.

sign{‘-‘, ‘+’}, optional

Sign of the complex exponent.

outnumpy.ndarray, optional

Array in which the result is stored. If out is arr, an in-place modification is performed. For real data type, this is only possible for shift=True since the factors are complex otherwise.

Returns

outnumpy.ndarray

Result of the pre-processing. If out was given, the returned object is a reference to it.

Notes

If out is not specified, the data type of the returned array is the same as that of arr except when arr has real data type and shift is not True. In this case, the return type is the complex counterpart of arr.dtype.