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Module « numpy.fft »

Fonction fft2 - module numpy.fft

Signature de la fonction fft2

def fft2(a, s=None, axes=(-2, -1), norm=None, out=None) 

Description

help(numpy.fft.fft2)

Compute the 2-dimensional discrete Fourier Transform.

This function computes the *n*-dimensional discrete Fourier Transform
over any axes in an *M*-dimensional array by means of the
Fast Fourier Transform (FFT).  By default, the transform is computed over
the last two axes of the input array, i.e., a 2-dimensional FFT.

Parameters
----------
a : array_like
    Input array, can be complex
s : sequence of ints, optional
    Shape (length of each transformed axis) of the output
    (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.).
    This corresponds to ``n`` for ``fft(x, n)``.
    Along each axis, if the given shape is smaller than that of the input,
    the input is cropped. If it is larger, the input is padded with zeros.

    .. versionchanged:: 2.0

        If it is ``-1``, the whole input is used (no padding/trimming).

    If `s` is not given, the shape of the input along the axes specified
    by `axes` is used.

    .. deprecated:: 2.0

        If `s` is not ``None``, `axes` must not be ``None`` either.

    .. deprecated:: 2.0

        `s` must contain only ``int`` s, not ``None`` values. ``None``
        values currently mean that the default value for ``n`` is used
        in the corresponding 1-D transform, but this behaviour is
        deprecated.

axes : sequence of ints, optional
    Axes over which to compute the FFT.  If not given, the last two
    axes are used.  A repeated index in `axes` means the transform over
    that axis is performed multiple times.  A one-element sequence means
    that a one-dimensional FFT is performed. Default: ``(-2, -1)``.

    .. deprecated:: 2.0

        If `s` is specified, the corresponding `axes` to be transformed
        must not be ``None``.

norm : {"backward", "ortho", "forward"}, optional
    Normalization mode (see `numpy.fft`). Default is "backward".
    Indicates which direction of the forward/backward pair of transforms
    is scaled and with what normalization factor.

    .. versionadded:: 1.20.0

        The "backward", "forward" values were added.

out : complex ndarray, optional
    If provided, the result will be placed in this array. It should be
    of the appropriate shape and dtype for all axes (and hence only the
    last axis can have ``s`` not equal to the shape at that axis).

    .. versionadded:: 2.0.0

Returns
-------
out : complex ndarray
    The truncated or zero-padded input, transformed along the axes
    indicated by `axes`, or the last two axes if `axes` is not given.

Raises
------
ValueError
    If `s` and `axes` have different length, or `axes` not given and
    ``len(s) != 2``.
IndexError
    If an element of `axes` is larger than than the number of axes of `a`.

See Also
--------
numpy.fft : Overall view of discrete Fourier transforms, with definitions
     and conventions used.
ifft2 : The inverse two-dimensional FFT.
fft : The one-dimensional FFT.
fftn : The *n*-dimensional FFT.
fftshift : Shifts zero-frequency terms to the center of the array.
    For two-dimensional input, swaps first and third quadrants, and second
    and fourth quadrants.

Notes
-----
`fft2` is just `fftn` with a different default for `axes`.

The output, analogously to `fft`, contains the term for zero frequency in
the low-order corner of the transformed axes, the positive frequency terms
in the first half of these axes, the term for the Nyquist frequency in the
middle of the axes and the negative frequency terms in the second half of
the axes, in order of decreasingly negative frequency.

See `fftn` for details and a plotting example, and `numpy.fft` for
definitions and conventions used.


Examples
--------
>>> import numpy as np
>>> a = np.mgrid[:5, :5][0]
>>> np.fft.fft2(a)
array([[ 50.  +0.j        ,   0.  +0.j        ,   0.  +0.j        , # may vary
          0.  +0.j        ,   0.  +0.j        ],
       [-12.5+17.20477401j,   0.  +0.j        ,   0.  +0.j        ,
          0.  +0.j        ,   0.  +0.j        ],
       [-12.5 +4.0614962j ,   0.  +0.j        ,   0.  +0.j        ,
          0.  +0.j        ,   0.  +0.j        ],
       [-12.5 -4.0614962j ,   0.  +0.j        ,   0.  +0.j        ,
          0.  +0.j        ,   0.  +0.j        ],
       [-12.5-17.20477401j,   0.  +0.j        ,   0.  +0.j        ,
          0.  +0.j        ,   0.  +0.j        ]])

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