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My assumption that $g(x,y)$ should be "wrap-padded" was wrong. Cross correlation is zero padded, so the image should be zero padded before taking the DFT. In other words, $\bar g(x,y) = \begin{cases} & g(x,y) \text{ if } x \in [0,m) \text{ and } y \in [0,n) \\ & 0 \text{ if } x \notin [0,m) \text{ and } y \notin [0,n) \\ \end{cases}$ In ...


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This looks like something which can be done with wavelets analysis. You can try a naive version, take some function whose integral is zero (seems like you can take a triangle) and calculate the convolution of your signals with scaled versions of the function, If there's an underlying oscillatory signal you'll see it when the proper scale is used. I did ...


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"Fitting an ellipse" is not the way to detect correlation. First, find the (coefficient of) correlation $r.$ As noted in the Comment, you will find that it is very nearly $0$ for the data in your plot. A brief and elementary discussion of $r$ follows. For normal data, there is a statistical test using $r$ to see whether the underlying bivariate population ...


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It is difficult to gauge the confidence level of fitting an ellipse corresponding to error as what you will conclude will be if the shape and orientation of the ellipse shows a certain correlation then the data may have that correlation? a bit vague right! The errors will be the parameters of the ellipse equation, so the axes of the ellipse should not ...


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Since so many of your values are $(0,0)$, there probably isn't much harm (and maybe some benefit, since some people repeat terms more than others) in just asking for each tweet, "Did they mention NFL?" and "Did they mention NBA?". There are 4 possible combinations of yes/no for these questions. You want to know if the answers to the questions are independent ...


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There's no such thing as validity or relevance without some further context. If you have a sample consisting of pairs $(x_1,y_1),\ldots,(x_n,y_n)$ you can find a correlation between $\pm 1$ (inclusive). "Bivariate" in this context simply means the data consists of a bunch of ordered pairs. In regard to probability distributions, a bivariate distribution ...



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