Timeline for Separating two complex-valued datasets that have been multiplied together
Current License: CC BY-SA 3.0
8 events
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| Oct 11, 2012 at 17:14 | comment | added | Nicholas Kinar | OK, I have updated my question above. Does this give more information on how to set the problem up? | |
| Oct 11, 2012 at 16:47 | comment | added | whuber♦ | The measure of roughness depends on the meaning of $A$ and $B$ and on what you are trying to achieve. If, say, $A$ is a "signal" and $B$ is "noise", then you need to characterize the noise as well as the signal. It's starting to sound like you may have a well-known problem in smoothing signals that has become (unnecessarily) more complicated through some preliminary analysis. Perhaps it would be best to state the problem you are actually trying to solve rather than this abstract formulation based on mathematical transformations of your data. | |
| Oct 11, 2012 at 16:33 | comment | added | Nicholas Kinar | Thanks, whuber; what additional information do I need or is required to allow for the proposal of these changes? What is a good measure of the roughness of $A$ or $B$? I will update my question above. Is there an example (i.e. tutorial, paper or book) that demonstrates how these constraints can be applied? Please ask if anyone requires additional information. | |
| Oct 11, 2012 at 16:06 | comment | added | whuber♦ | Nicholas, you have a lot of freedom to impose severe constraints on $A$ and $B$. For instance, in some cases one solution is that $A$ is constant! That guarantees lack of correlation, smoothness, and low variability. This suggests you focus on your fifth criterion (skewnesses). Perhaps you might try to achieve low skewness while minimizing some measure of the roughness of $A$. But we cannot propose these changes: they have to reflect the phenomena measured by $A$ and $B$, about which you have left us ignorant. | |
| Oct 11, 2012 at 15:33 | comment | added | Nicholas Kinar | Thanks again, Bitwise. How might I set up the numerical algorithm to enforce a certain distribution? I am not seeking perfection here (that is the domain of exact mathematics); I am only looking for a method to "approximately" separate A and B using some sort of statistical information or method. | |
| Oct 11, 2012 at 15:21 | comment | added | Bitwise | @NicholasKinar the example I gave is just one simple deconstruction, but there are many possible deconstructions. Enforcing a certain distribution on A and B might be a strict enough constraint. | |
| Oct 11, 2012 at 15:14 | comment | added | Nicholas Kinar | Thanks for your response, Bitwise. Given additional constraints (i.e. distribution of the datasets), I would wonder if A and B might be approximated in some way. What if B does not equal C, and A does not equal 1 at all coordinates? Both A and B can be said to have a statistical distribution (but at this time, I do not know the distributions). | |
| Oct 11, 2012 at 15:08 | history | answered | Bitwise | CC BY-SA 3.0 |