transform.py 文件源码

def fft(fEM, time, freq, ftarg):
    """Fourier Transform using the Fast Fourier Transform.

    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.

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

    conv : bool
        Only relevant for QWE/QUAD.

    """
    # Get ftarg values
    dfreq, nfreq, ntot, pts_per_dec = ftarg

    # If pts_per_dec, we have first to interpolate fEM to required freqs
    if pts_per_dec:
        sfEMr = iuSpline(np.log10(freq), fEM.real)
        sfEMi = iuSpline(np.log10(freq), fEM.imag)
        freq = np.arange(1, nfreq+1)*dfreq
        fEM = sfEMr(np.log10(freq)) + 1j*sfEMi(np.log10(freq))

    # Pad the frequency result
    fEM = np.pad(fEM, (0, ntot-nfreq), 'linear_ramp')

    # Carry out FFT
    ifftEM = fftpack.ifft(np.r_[fEM[1:], 0, fEM[::-1].conj()]).real
    stEM = 2*ntot*fftpack.fftshift(ifftEM*dfreq, 0)

    # Interpolate in time domain
    dt = 1/(2*ntot*dfreq)
    ifEM = iuSpline(np.linspace(-ntot, ntot-1, 2*ntot)*dt, stEM)
    tEM = ifEM(time)/2*np.pi  # (Multiplication of 2/pi in model.tem)

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


# 3. Utilities