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questions

First off, I hope you don't treat this as a personal attack. I respect your accomplishments and intelligence and I am just trying to understand what you are writing, because to me it is confusing.

You say, "at any point in time, the signal I was playing around decomposes into two (and only two) sine waves"

OK, does this mean that you have generated a signal by superposition of 2 sine waves? If so, I understand what you have.

Otherwise, I have further questions. This statement would seem to be directly in contradiction with your other statement above that at any point, you have a sine wave.

I guess I am mainly confused by the terminology itself. A function cannot be decomposed into frequency components at a single point. Any interval can be decomposed into frequency components, but a short interval will have by its nature a multitude of components extending up to infinity.

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