Extended Hilbert transform for the multidimensional signals

In this paper, we yielded one novel Hilbert transform for multidimensional signal and it not only provides the analytic signal which has the general properties of complex signal, but also has the properties as the 1D Hilbert transform has, including π/2 phase shifting property and etc. Since for higher dimensional signals the mechanism of our Hilbert transform is the same except for the dimension, we will take 2D signal as our main discussed example in this paper. The relationship between frequency domain and time domain are discussed.