def itilbert(x,h,period=None, _cache=_cache):
    """
    Return inverse h-Tilbert 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)*tanh(j*h*2*pi/period) * x_j
      y_0 = 0

    For more details, see `tilbert`.

    """
    tmp = asarray(x)
    if iscomplexobj(tmp):
        return itilbert(tmp.real,h,period) + \
               1j*itilbert(tmp.imag,h,period)
    if period is not None:
        h = h*2*pi/period
    n = len(x)
    omega = _cache.get((n,h))
    if omega is None:
        if len(_cache) > 20:
            while _cache:
                _cache.popitem()

        def kernel(k,h=h):
            if k:
                return -tanh(h*k)
            return 0
        omega = convolve.init_convolution_kernel(n,kernel,d=1)
        _cache[(n,h)] = omega
    overwrite_x = _datacopied(tmp, x)
    return convolve.convolve(tmp,omega,swap_real_imag=1,overwrite_x=overwrite_x)
dataset/ETHPy150Open scipy/scipy/scipy/fftpack/pseudo_diffs.py/itilbert/original