specfunc.py 文件源码

def kernel_fredriksen(n):
    """
    Generates kernel for Hilbert transform using FFT.

    Parameters
    ----------
    n : int
        Number of equidistant grid points.

    Returns
    -------
    array
        Kernel used when performing Hilbert transform using FFT.
    """
    aux = np.zeros(n+1, dtype=doublenp)
    for i in range(1,n+1):
        aux[i] = i*log(i)
    m = 2*n
    ker = np.zeros(m, dtype=doublenp)
    for i in range(1,n):
        ker[i] = aux[i+1]-2*aux[i]+aux[i-1]
        ker[m-i] = -ker[i]
    return fft(ker)/pi