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21.4 Fourier domain filters

# 21.4 Fourier domain filters

The functions described in this section perform filtering operations in the Fourier domain. Thus, the input array of such a function should be compatible with an inverse Fourier transform function, such as the functions from the numarray.fft module. We therefore have to deal with arrays that may be the result of a real or a complex Fourier transform. In the case of a real Fourier transform only half of the of the symmetric complex transform is stored. Additionally, it needs to be known what the length of the axis was that was transformed by the real fft. The functions described here provide a parameter n that in the case of a real transform must be equal to the length of the real transform axis before transformation. If this parameter is less than zero, it is assumed that the input array was the result of a complex Fourier transform. The parameter axis can be used to indicate along which axis the real transform was executed.

 fourier_shift( input, shift, n=-1, axis=-1, output=None)
The fourier_shift function multiplies the input array with the multi-dimensional Fourier transform of a shift operation for the given shift. The shift parameter is a sequences of shifts for each dimension, or a single value for all dimensions.

 fourier_gaussian( input, sigma, n=-1, axis=-1, output=None)
The fourier_gaussian function multiplies the input array with the multi-dimensional Fourier transform of a Gaussian filter with given standard-deviations sigma. The sigma parameter is a sequences of values for each dimension, or a single value for all dimensions.

 fourier_uniform( input, size, n=-1, axis=-1, output=None)
The fourier_uniform function multiplies the input array with the multi-dimensional Fourier transform of a uniform filter with given sizes size. The size parameter is a sequences of values for each dimension, or a single value for all dimensions.

 fourier_ellipsoid( input, size, n=-1, axis=-1, output=None)
The fourier_ellipsoid function multiplies the input array with the multi-dimensional Fourier transform of a elliptically shaped filter with given sizes size. The size parameter is a sequences of values for each dimension, or a single value for all dimensions. Note: This function is only implemented for dimensions 1, 2, and 3.

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