# Can the FFT be employed to make a dataset as Multivariate Normal distributed?

I have dataset composed of a large number of images with a large size (i.e., 32x32px), and I'm trying to adapt a feature extraction framework which assumes that the input dataset is Multivariate Normal distributed.

My question is: is applying a 2D-FFT to the whole dataset a good way to transform the data-distribution to a Multivariate Normal (by Central Limit Theorem arguments)?

In other words, if $$X$$ is an image of the data-set, I want that its transformation $$\tilde{X}$$ is such that $$\tilde{X} \sim \mathcal{N}(\mu,\Sigma)$$, where $$\mu \in \mathbb{R}^{1024}$$ and $$\Sigma \in \mathbb{R}^{1024\times1024}$$.

If not, is there another possible way to do that?

• What does it mean multivariate in this context? Do you mean each image is sampled from a Gaussian Distribution of dimensions 1024?
– Royi
Commented Jul 21, 2023 at 9:29
• Yes, I added some details to the question to make it more clear. Commented Jul 21, 2023 at 9:41