So, what is your point?
You are the one that had a hissy fit when I pointed out that the Fourier transform is simply correlation.
Now you have changed your mind?
Yeah, sure, you find that equation in that form anywhere....
But it's not.. It LOOKS like a correlation because it's the integral of vector product. There are hundred of definitions in physics that look "similiar".. It the PURPOSE of the functions that matter and the prior constraints on symmetry, range, and basis function that make them all different.
Correlation and Convolution are ALMOST EXACTLY THE SAME.. Looks almost the same, computes almost the same. Tell me grasshopper --- what is the difference there?
It doesn't just "look like" correlation, it is correlation.
How hard is this to grasp for you? Each cosine and sine term, at integer frequencies, is correlated to original signal, yielding a multiplying factor.
It "look like" because it is. This is how math works. If A=B and B=C then A=B.
And the actual point, the one that Abraham has made repeatedly, is that just because we can come up with a series of functions that, when added together, create the same result as the original function, doesn't mean anything.
We can come up with all sorts of sets of equations that, when correlated to the original signal and added together with the appropriate multiplying constant, duplicate the original signal. We can do it with square waves, triangle waves, sine and cosines. We can even do it with a set of sinc functions that are both shifted in time and are multiples of the fundamental frequency. None of it means anything.
All you are saying, with your ""Fourier combinations of periodic functions causing ramps" is that we can come up with all sorts of imaginary sets of functions that duplicate the original signal.
The problem is one of reality getting in the way. In reality, there isn't some other set of functions that correlate and add up to the signal in question, the temperature rise.
