Module « numpy.fft »

Fonction rfft - module numpy.fft

Signature de la fonction rfft

def rfft(a, n=None, axis=-1, norm=None) 

Description

rfft.__doc__

    Compute the one-dimensional discrete Fourier Transform for real input.

    This function computes the one-dimensional *n*-point discrete Fourier
    Transform (DFT) of a real-valued array by means of an efficient algorithm
    called the Fast Fourier Transform (FFT).

    Parameters
    ----------
    a : array_like
        Input array
    n : int, optional
        Number of points along transformation axis in the input to use.
        If `n` is smaller than the length of the input, the input is cropped.
        If it is larger, the input is padded with zeros. If `n` is not given,
        the length of the input along the axis specified by `axis` is used.
    axis : int, optional
        Axis over which to compute the FFT. If not given, the last axis is
        used.
    norm : {"backward", "ortho", "forward"}, optional
        .. versionadded:: 1.10.0

        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.

    Returns
    -------
    out : complex ndarray
        The truncated or zero-padded input, transformed along the axis
        indicated by `axis`, or the last one if `axis` is not specified.
        If `n` is even, the length of the transformed axis is ``(n/2)+1``.
        If `n` is odd, the length is ``(n+1)/2``.

    Raises
    ------
    IndexError
        If `axis` is larger than the last axis of `a`.

    See Also
    --------
    numpy.fft : For definition of the DFT and conventions used.
    irfft : The inverse of `rfft`.
    fft : The one-dimensional FFT of general (complex) input.
    fftn : The *n*-dimensional FFT.
    rfftn : The *n*-dimensional FFT of real input.

    Notes
    -----
    When the DFT is computed for purely real input, the output is
    Hermitian-symmetric, i.e. the negative frequency terms are just the complex
    conjugates of the corresponding positive-frequency terms, and the
    negative-frequency terms are therefore redundant.  This function does not
    compute the negative frequency terms, and the length of the transformed
    axis of the output is therefore ``n//2 + 1``.

    When ``A = rfft(a)`` and fs is the sampling frequency, ``A[0]`` contains
    the zero-frequency term 0*fs, which is real due to Hermitian symmetry.

    If `n` is even, ``A[-1]`` contains the term representing both positive
    and negative Nyquist frequency (+fs/2 and -fs/2), and must also be purely
    real. If `n` is odd, there is no term at fs/2; ``A[-1]`` contains
    the largest positive frequency (fs/2*(n-1)/n), and is complex in the
    general case.

    If the input `a` contains an imaginary part, it is silently discarded.

    Examples
    --------
    >>> np.fft.fft([0, 1, 0, 0])
    array([ 1.+0.j,  0.-1.j, -1.+0.j,  0.+1.j]) # may vary
    >>> np.fft.rfft([0, 1, 0, 0])
    array([ 1.+0.j,  0.-1.j, -1.+0.j]) # may vary

    Notice how the final element of the `fft` output is the complex conjugate
    of the second element, for real input. For `rfft`, this symmetry is
    exploited to compute only the non-negative frequency terms.