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Computes the two-dimensional discrete Fourier transform.
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#### Parameters
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-**a**: _<array>_
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- Input array.
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-**s**: _Union\[ Sequence\[ int ], Tuple\[ int, ... ]]_
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- Size of each transformed axis of the output. If given, each axis will be either zero-padded or trimmed to the length `s[i]` before computing the Fourier transform. Otherwise, no padding will be performed in each dimension. Default: `None`.
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-**axes**: _Union\[ Sequence\[ int ], Tuple\[ int, ... ]]_
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- Axes over which to compute the Fourier transform. If it is not specified, the last two axes are used. Default: `(-2, -1)`.
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-**norm**: _str_
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- Specify the normalization mode. Should be one of the following modes:
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-`'backward'`: No normalization.
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-`'ortho'`: Normalize by `1/sqrt(n)`
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-`'forward'`: Normalize by `1/n`.
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Default: `'backward'`
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#### Returns
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-**out**: _<array>_
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- An array transformed along the axes indicated by the `axes` keyword.
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#### Raises
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- If `s` and `axes` have a different length.
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- If `axes` is not given and the length of `s` is different from 2.
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- If an element of `axes` is larger than the number of axes of `a`.
Computes the two-dimensional inverse discrete Fourier transform.
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#### Parameters
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-**a**: _<array>_
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- Input array.
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-**s**: _Union\[ Sequence\[ int ], Tuple\[ int, ... ]]_
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- Size of each transformed axis of the output. If given, each axis will be either zero-padded or trimmed to the length `s[i]` before computing the Fourier transform. Otherwise, no padding will be performed in each dimension. Default: `None`.
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-**axes**: _Union\[ Sequence\[ int ], Tuple\[ int, ... ]]_
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- Axes over which to compute the inverse Fourier transform. If it is not specified, the last two axes are used. Default: `(-2, -1)`.
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-**norm**: _str_
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- Specify the normalization mode. Should be one of the following modes:
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-`'backward'`: Normalize by `1/n`.
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-`'ortho'`: Normalize by `1/sqrt(n)`
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-`'forward'`: No normalization.
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Default: `'backward'`
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#### Returns
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-**out**: _<array>_
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- An array transformed along the axes indicated by the `axes` keyword.
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#### Raises
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- If `s` and `axes` have a different length.
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- If `axes` is not given and the length of `s` is different from 2.
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- If an element of `axes` is larger than the number of axes of `a`.
Computes the two-dimensional inverse discrete Fourier transform for real-valued input.
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#### Parameters
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-**a**: _<array>_
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- Input array.
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-**s**: _Union\[ Sequence\[ int ], Tuple\[ int, ... ]]_
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- Length of the transformed axis of the output. If given, the input will be either zero-padded or trimmed to this length before computing the real Fourier transform. Otherwise, it will default to `2 * (m - 1)` where `m` is the length of the input along the axis given by the `axes` keyword. Default: `None`.
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-**axes**: _Union\[ Sequence\[ int ], Tuple\[ int, ... ]]_
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- Axes used to compute the real Fourier transform. If it is not specified, the last two axes are used. Default: `(-2, -1)`.
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-**norm**: _str_
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- Specify the normalization mode. Should be one of the following modes:
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-`'backward'`: Normalize by `1/n`.
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-`'ortho'`: Normalize by `1/sqrt(n)`
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-`'forward'`: No normalization.
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Default: `'backward'`
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#### Returns
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-**out**: _<array>_
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- An array transformed along the axes indicated by the `axes` keyword.
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#### Raises
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- If `s` and `axes` have a different length.
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- If `axes` is not given and the length of `s` is different from 2.
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- If an element of `axes` is larger than the number of axes of `a`.
Computes the two-dimensional discrete Fourier transform for real-valued input.
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#### Parameters
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-**a**: _<array>_
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- Input array.
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-**s**: _Union\[ Sequence\[ int ], Tuple\[ int, ... ]]_
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- Size of each transformed axis of the output. If given, each axis will be either zero-padded or trimmed to the length `s[i]` before computing the Fourier transform. Otherwise, no padding will be performed in each dimension. Default: `None`.
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-**axes**: _Union\[ Sequence\[ int ], Tuple\[ int, ... ]]_
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- Axes over which to compute the Fourier transform. If it is not specified, the last two axes are used. Default: `(-2, -1)`.
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-**norm**: _str_
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- Specify the normalization mode. Should be one of the following modes:
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-`'backward'`: No normalization.
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-`'ortho'`: Normalize by `1/sqrt(n)`
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-`'forward'`: Normalize by `1/n`.
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Default: `'backward'`
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#### Returns
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-**out**: _<array>_
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- An array transformed along the axes indicated by the `axes` keyword.
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#### Raises
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- If `s` and `axes` have a different length.
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- If `axes` is not given and the length of `s` is different from 2.
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- If an element of `axes` is larger than the number of axes of `a`.
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