human
Complete the below
def hilbert(x, _cache=_cache):

    ''''Return Hilbert transform of a periodic sequence x.
    If x_j and y_j are Fourier coefficients of periodic functions x
    and y, respectively, then::
    y_j = sqrt(-1)*sign(j) * x_j
    y_0 = 0
    Parameters
    x : array_like
    The input array, should be periodic.
    _cache : dict, optional
    Dictionary that contains the kernel used to do a convolution with.
    Returns
    y : ndarray
    The transformed input.
    See Also
    scipy.signal.hilbert : Compute the analytic signal, using the Hilbert
    transform.
    Notes
    If ``sum(x, axis=0) == 0`` then ``hilbert(ihilbert(x)) == x``.
    For even len(x), the Nyquist mode of x is taken zero.
    The sign of the returned transform does not have a factor -1 that is more
    often than not found in the definition of the Hilbert transform.  Note also
    that `scipy.signal.hilbert` does have an extra -1 factor compared to this
    function.'
    '''
 What is a Python code to compute the analytic signal, using the Hilbert?
assistant
#Here is Python code to compute the analytic signal, using the Hilbert
.
    tmp = asarray(x)
    if iscomplexobj(tmp):
        return (hilbert(tmp.real) + (1j * hilbert(tmp.imag)))
    n = len(x)
    omega = _cache.get(n)
    if (omega is None):
        if (len(_cache) > 20):
            while _cache:
                _cache.popitem()
        def kernel(k):
            if (k > 0):
                return 1.0
            elif (k < 0):
                return (-1.0)
            return 0.0
        omega = convolve.init_convolution_kernel(n, kernel, d=1)
        _cache[n] = omega
    overwrite_x = _datacopied(tmp, x)
    return convolve.convolve(tmp, omega, swap_real_imag=1, overwrite_x=overwrite_x)