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For the first question, I understand that the filters are normalized in energy. Suppose that we first consider uniform or box filters of size $(2L+1)\times(2L+1)$ and unit amplitude. Their Frobenius norm are $2L+1$. If you divide the amplitude by $(2L+1)^2$, then the Frobenius not of all filters will be exactly one. For other filters, such a scale ...

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