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I'm not certain how I should compute the angular velocities from the Euler angles because the data contains discontinuities at the boundaries ±180 degrees. Welcome to the wonderful world of trying to comb the hairy ball flat. Do a web search on "Hairy ball theorem", then again on "hairy ball theorem" and "Euler angles". You'll wish you'd never heard of 3D ...


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To be time invariant you would have to show that: $$y(n-k) = (n-1)x(n-k-1) + (n+1)x(n-k+1)$$ (You shift the $x$ and you get a shift in $y$). But you can't get rid of the $(n-k-1)$ and $(n-k+1)$. In general any time you have the time term $n$ by itself it will be time variant unless it cancels out somehow.


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Differential non-linearity specifically is the deviation from ideal between successive bits. For an ADC, the ideal would be the converted signal will not transition to another bit value until the input deviates by 1 bit. If the DNL is greater than 1 bit, non-monotonic behavior could result (an linearly increasing input could result in some transitions ...


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Morphological Erosion is not associative as dilation. Much like addition is associative but not subtraction. Consider the following basic definitions first:$$(A \ominus B)^C = A^C \oplus \widetilde{B} \tag{1}$$ $$(A \oplus B)^C = A^C \ominus \widetilde{B} \tag{2}$$ where $\widetilde{B}$ is the reflection of kernel $B$ and $A^C$ is the compliment of image $A$...


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