def phase_correct_first(spec, freq, k):
    """
    First order phase correction.

    Parameters
    ----------
    spec : float array
        The spectrum to be corrected.

    freq : float array
        The frequency axis.

    k : float
        The slope of the phase correction as a function of frequency.

    Returns
    -------
    The phase-corrected spectrum.

    Notes
    -----
    [Keeler2005] Keeler, J (2005). Understanding NMR Spectroscopy, 2nd
        edition. Wiley. Page 88

    """
    c_factor = np.exp(-1j * k * freq)
    c_factor = c_factor.reshape((len(spec.shape) -1) * (1,) + c_factor.shape)
    return spec * c_factor