human
Solve the following python programming problem given the following code:
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.

    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.

    ' 
    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 
else : 
                if (k < 0) : 
                    return (- 1.0) 
return 0.0 
omega = convolve.init_convolution_kernel (n, tmp, d = 1) 
        _cache [n] = omega 
overwrite_x = _datacopied (tmp, x) 
    return convolve.convolve (tmp, omega, swap_real_imag = 1, overwrite_x = overwrite_x) 

    
    

    Fix the buggy line: omega = convolve.init_convolution_kernel (n, tmp, d = 1)
assistant
#Here is Python program to fix the buggy line: omega = convolve.

omega = convolve.init_convolution_kernel (n, def kernel(, d = 1)