Case 1: I have a 2D Gaussian: ## Ae^{-[\frac { (x-x_o)^2 }{2 \sigma_x ^2} + \frac { (y-y_o)^2 }{2 \sigma_y ^2}]} ## where ## \sigma_x \neq \sigma_y ## (at least not necessarily). Using this as my 2D Gaussian, would the normalization constant be ## A = \frac {1}{2\pi (\sigma_x ^2 + \sigma_y ^2)} ##? In this context, what does ## \sigma = \sqrt{ \sigma_x ^2 + \sigma_y ^2} ## even mean?(adsbygoogle = window.adsbygoogle || []).push({});

Case 2: if ## \sigma_x = \sigma_y = \sigma ## in all cases, then I have: ## Ae^{-[\frac { (x-x_o)^2 + (y-y_o)^2 }{2 \sigma^2}]} ##. Would the normalization constant be ## A = \frac {1}{2\pi \sigma^2} ## in that case?

Also, in terms of physical significance, what is the difference between sigma in the first case and the second case (if any)?

Any help would be great!

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# Meaning of sigma in a 2D sigma

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