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From what you've said, you have two sample sets:
$$x_n, n = 0 \ldots N-1$$ and $$y_m, m = 0 \ldots M-1$$
where $M \ne N$ and you want to compare the distributions of the underlying processes.
Do you know anything about the expected distribution of the measurements?
If they're Gaussian, then you can just calculate the sample mean and sample standard deviation ...
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Image Processing Context
In classic Image Processing the filters used are known.
Hence being separable is a property of a given filter which is suitable to the task.
In this context, separability only means we can have a more efficient way to apply the filter computationally while the end result is the same.
So, in Image Processing, if you have a filter ...
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You have many great code examples at our community:
2D Frequency Domain Convolution Using FFT (Convolution Theorem).
Kernel Convolution in Frequency Domain - Cyclic Padding.
2D Image Convolution: Spatial Domain vs. Frequency Domain Convolution in the Computational Complexity Sense.
Applying Image Filtering (Circular Convolution) in Frequency Domain.
...
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Each column represents a wedge, like this:
Your program needs to fill the wedge rather than just drawing a line.
For each point on a column, you have to draw an arc rather than a single point.
The width of the arc (in degrees) is given by the number of columns and the viewing angle of the device.
You have to draw arcs along your line of the appropriate ...
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We need to separate the concept of edge detection from the tools we use to apply the procedure.
Edges are local property of the image. Being so local means we don't analyze the image in frequency domain but in spatial domain.
Yet, a common step for edge detection is applying High Pass / Gradient Filter. Since those are Linear Shift Invariant operators we may ...
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For any given problem definition, there's a filter that -- if you ignore execution time and hardware expense -- is "best"*. In general, that "best" filter isn't separable. Depending on the problem at hand, the degree to which the optimum degrades if you find the best separable filter will vary.
So -- sometimes a non-separable filter ...
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You can create noise with the same frequency-domain characteristic as your example noise image simply by multiplying a white noise frequency spectrum by the magnitude of the frequency spectrum you are trying to emulate. White noise is expected to have equal power at all frequencies (though this will not be exactly the case), so the multiplication will "...
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In short, there is on the one hand a pair-wise definition: two pixels are "simply" connected when they fulfill certain conditions on pixel spatial adjacency and/or brightness. Typically, for pixels of intensity $I_{m,n}$,
they can be said connected locally if $|m-m'|\le 1$ and $|n-n'|\le 1$ (for the 8-topology, or $|I_{m,n}-I_{m',n'}|\le 1$ if ...
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