about the calculation of phase spectrum for a set of coordinates

I want to implement an approach for calculating Phase spectrum of a set of coordinates. In the paper, it is described as 3 equations. However, I have no idea about the function variables (x,y) in the equation. I want to implement it via Matlab. Perhaps, it is easier for someone who knows pure signal processing well.

In (1), the 2D signal series (the coordinates) is represented as a 2D dirac delta function. Varialbe, theta_i, is the direction of each coordinate. The fourier transform of (1) is in the form of (2). Then (3) is the phase spectrum. So, maybe it can be implemented via a few lines in Matlab. But I just don't know it. Could anyone here give any help? Thanks.

Answer 1

[Honglei Chen]

This looks to me is essentially

angle(fft2(theta))

where

theta is the function exp(j\theta_i) defined at each (xi,yi) position

Of course, it depends on how xi, yi, u, and v are defined.

[ZhG]

Honglei, thanks for reply.

I searched with google and know that angle() is to calculate phase. And I found that this function involves in something about 'unwrapping', introduced in some posts. I don't understand that, but this is not my problem. I am wondering that how I can understand variables (x,y) of eq.(1). Because (xi, yi, theta_i) are given values, i.e. each point in the coordinate system and its direction.

[Honglei Chen]

I don't really understand what you are asking for, could you provide an example? In general, the coordinate itself doesn't really matter, as long as the system is shift invariant.