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You need the joint distribution of $X_{t_1}$ and $X_{t_2}$ in order to calculate $E[X_{t_1}X_{t_2}]$ and nobody has claimed that the joint distribution of $X_{t_1}$ and $X_{t_2}$ is the same as the joint distribution of $X_{t_1}$ and $X_{t_3}$. Stationarity requires that the joint distribution of $X_{t_1}$ and $X_{t_2}$ be the same as the joint distribution ...


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Summation or integration of the spectral components yields the total power (for a physical process) yes, that's how "power density" is defined ... or variance (in a statistical process) For any bound density, that's true. But would the total power correspond to the uncentralized second moment, so variance + mean²? Yes, but if you have a process ...


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Histograms of images can differ, widely. However, when features are inspected, one often uses derivative filters at different scales, or morphological decompositions, or independent component analysis. A traditional and heuristic model for the resulting coefficients of a component is that of the Generalized Gaussian-Laplacian Distribution, or GGD: $$ C_{...


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