transform.py 文件源码

def ffht(fEM, time, freq, ftarg):
    """Fourier Transform using a Cosine- or a Sine-filter.

    It follows the Filter methodology [Anderson_1975]_, see `fht` for more
    information.

    The function is called from one of the modelling routines in :mod:`model`.
    Consult these modelling routines for a description of the input and output
    parameters.

    This function is based on `get_CSEM1D_TD_FHT.m` from the source code
    distributed with [Key_2012]_.

    Returns
    -------
    tEM : array
        Returns time-domain EM response of `fEM` for given `time`.

    conv : bool
        Only relevant for QWE/QUAD.

    """
    # Get ftarg values
    fftfilt, pts_per_dec, ftkind = ftarg

    # Settings depending if cos/sin plus scaling
    if ftkind == 'sin':
        fEM = -fEM.imag
    else:
        fEM = fEM.real

    if pts_per_dec:  # Use pts_per_dec frequencies per decade
        # 1. Interpolate in frequency domain
        sfEM = iuSpline(np.log10(2*np.pi*freq), fEM)
        ifEM = sfEM(np.log10(fftfilt.base/time[:, None]))

        # 2. Filter
        tEM = np.dot(ifEM, getattr(fftfilt, ftkind))

    else:  # Standard FHT procedure
        # Get new times in frequency domain
        _, itime = get_spline_values(fftfilt, time)

        # Re-arranged fEM with shape (ntime, nfreq).  Each row starts one
        # 'freq' higher.
        fEM = np.concatenate((np.tile(fEM, itime.size).squeeze(),
                             np.zeros(itime.size)))
        fEM = fEM.reshape(itime.size, -1)[:, :fftfilt.base.size]

        # 1. Filter
        stEM = np.dot(fEM, getattr(fftfilt, ftkind))

        # 2. Interpolate in time domain
        itEM = iuSpline(np.log10((itime)[::-1]), stEM[::-1])
        tEM = itEM(np.log10(time))

    # Return the electromagnetic time domain field
    # (Second argument is only for QWE)
    return tEM/time, True