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Fonction convolve - module numpy.matlib

Signature de la fonction convolve

def convolve(a, v, mode='full') 

Description

convolve.__doc__

    Returns the discrete, linear convolution of two one-dimensional sequences.

    The convolution operator is often seen in signal processing, where it
    models the effect of a linear time-invariant system on a signal [1]_.  In
    probability theory, the sum of two independent random variables is
    distributed according to the convolution of their individual
    distributions.

    If `v` is longer than `a`, the arrays are swapped before computation.

    Parameters
    ----------
    a : (N,) array_like
        First one-dimensional input array.
    v : (M,) array_like
        Second one-dimensional input array.
    mode : {'full', 'valid', 'same'}, optional
        'full':
          By default, mode is 'full'.  This returns the convolution
          at each point of overlap, with an output shape of (N+M-1,). At
          the end-points of the convolution, the signals do not overlap
          completely, and boundary effects may be seen.

        'same':
          Mode 'same' returns output of length ``max(M, N)``.  Boundary
          effects are still visible.

        'valid':
          Mode 'valid' returns output of length
          ``max(M, N) - min(M, N) + 1``.  The convolution product is only given
          for points where the signals overlap completely.  Values outside
          the signal boundary have no effect.

    Returns
    -------
    out : ndarray
        Discrete, linear convolution of `a` and `v`.

    See Also
    --------
    scipy.signal.fftconvolve : Convolve two arrays using the Fast Fourier
                               Transform.
    scipy.linalg.toeplitz : Used to construct the convolution operator.
    polymul : Polynomial multiplication. Same output as convolve, but also
              accepts poly1d objects as input.

    Notes
    -----
    The discrete convolution operation is defined as

    .. math:: (a * v)[n] = \sum_{m = -\infty}^{\infty} a[m] v[n - m]

    It can be shown that a convolution :math:`x(t) * y(t)` in time/space
    is equivalent to the multiplication :math:`X(f) Y(f)` in the Fourier
    domain, after appropriate padding (padding is necessary to prevent
    circular convolution).  Since multiplication is more efficient (faster)
    than convolution, the function `scipy.signal.fftconvolve` exploits the
    FFT to calculate the convolution of large data-sets.

    References
    ----------
    .. [1] Wikipedia, "Convolution",
        https://en.wikipedia.org/wiki/Convolution

    Examples
    --------
    Note how the convolution operator flips the second array
    before "sliding" the two across one another:

    >>> np.convolve([1, 2, 3], [0, 1, 0.5])
    array([0. , 1. , 2.5, 4. , 1.5])

    Only return the middle values of the convolution.
    Contains boundary effects, where zeros are taken
    into account:

    >>> np.convolve([1,2,3],[0,1,0.5], 'same')
    array([1. ,  2.5,  4. ])

    The two arrays are of the same length, so there
    is only one position where they completely overlap:

    >>> np.convolve([1,2,3],[0,1,0.5], 'valid')
    array([2.5])