fourier_transform.py 文件源码

def frft(x, alpha):
    """
    Implementation of the Fractional Fourier Transform (FRFT)
    :param x: array of data to be transformed
    :param alpha: parameter of FRFT
    :return: FRFT(x)
    """
    k = np.arange(x.size)

    y = np.hstack([
        x * np.exp(-np.pi * 1j * k**2 * alpha),
        np.zeros(x.size, dtype=np.complex)
    ])
    z = np.hstack([
        np.exp(np.pi * 1j * k**2 * alpha),
        np.exp(np.pi * 1j * (k - x.size)**2 * alpha)
    ])

    G =  fftpack.ifft(
        fftpack.fft(y, overwrite_x=True) * fftpack.fft(z, overwrite_x=True),
        overwrite_x=True
    )

    return np.exp(-np.pi * 1j * k**2 * alpha) * G[:x.size]

# generate the desired momentum grid