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I have data for a function $G(x,y,t)$ where $x,y$ show space position (2D) and $t$ is time. I know from Fourier transformation definition that:

$G(x,y,t)=\int q \:dq \: d\omega \: d\theta\: \hat{G}(q,\theta,\omega) e^{\omega t+i q(x\: cos\theta+y \:sin\theta)}$

I want to use the data to find $\omega$ as a function of $q$ for different values of $\theta$ for example $\theta=\pi/3$ and $q=0.1$. Could somebody please help me in this regard?

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