15 May 2017

Edge Effects

When detecting oscillations with the continuous transform one have to worry about edge effects.
The math behind continuous wavelet transform assumes that one dimension linear intensity curve I’m processing is continuous, meaning it does not have end nor beginning. That causes artificial power to arise at the edges of the results when one examines the data. Just to illustrate what I mean, here is the summation of the results through part of my data set:
Screen Shot 2017-04-26 at 17.26.45

At the bottom of the graph in the first panel, you can see the perfectly formed semicircles that carry the largest power, they are the darkest. It’s like, at the very end and the very beginning of the dataset we have a huge spike in power. The same is visible if we sum all registered power over time, the graph in a bottom panel.
Peaks at the beginning and end are almost 3 times larger than max power in the rest of the dataset. So not only that they are not real, but they also are drowning the rest of the signal.
So it is very important to do something to remove those effects. The wavelet analysis experience and experience with Fourier transform offers a solution, so-called, padding the data. Basically, you add to the data more points, artificially lengthening it.
There are also several options on how to pad the data, by adding zeroes, by adding some constant value, or by mirroring data.
For my dataset, the power curve assumes a theoretically approved shape only if I do mirroring of the data. So I picked that method.

Screen Shot 2017-04-26 at 17.36.09
Power curve similar to a typical curve for the solar atmosphere. X-axis presents a period of oscillations, y-axis amount of registered power.

The other methods leave some residual power peaks that drown the signal.
The way I treated this is a neat illustration of why scientist are skeptical when someone comes with an explanation that does not fit previous knowledge. We are building every step, testing our methods on already confirmed knowledge. Every single step is double checked on previously known facts. Because, if a new explanation cannot explain an old known fact, then it is wrong. Every new explanation has to be able to explain all other well-known facts that came before.
I will take the Einstein's theory of relativity as an example. It explains gravity and includes a Newton Law of Gravity as a special case (If you pick certain variables you get exactly the same thing Newton got when he was developing his theory.)
Everything in science follows this principle. That’s why science has peer reviews, and that’s why scientist demand citations of previous works for every claim someone makes.

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