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3

First of all, if you use a logarithmic graph, it is customary to use dB. In order to convert a FFT in decibels, we use 20*log10, not log10. Second of all, the "unwanted" frequencies are 10^-30 times smaller than the wanted frequencies, i.e. they are insignificant. . The unwanted frequencies are most likely due to the limited precision of floating-point ...

2

Your equation is a little muddled. It'll be easier for folks here if you state it this way: $$g(x) = A_0 + \sum_{k=1}^L a_k \cos( 2\pi f x k + \phi_k)$$ I can't explain the downvote. What you are trying to do is find the coefficients and phases for a Fourier Series for your function. Why your optiminzing best fit doesn't work, I don't know and I don't ...

2

Since an FFT is a linear operator, adding up the complex results of a sequence of FFTs of short windows is the same as doing a single short FFT on the the vector addition of all those short windows. Note that for signals that are exactly integer periodic in the FFT width (sequential 0% overlapped windows), the vector addition will constructively interfere. ...

1

Eq. $(2)$ is indeed the periodogram of the truncated signal where said signal is the sample path $x(t)$ of the random process. There is nothing random about this sample path, which is why dropping the Expectation operator makes sense when one goes from $(1)$ to $(2)$. Dropping the limit is asking everyone to take your word for it that the $T$-second ...

1

I cross-posted this to the astronomy stack exchange and I received a satisfactory answer. Those interested can read the below. https://astronomy.stackexchange.com/questions/29956/making-sense-of-the-lomb-scargle-periodogram

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