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If I plot a periodogram of let's say sin(20x) + 2sin(80x) and it looks like this:
What does it say, i.e., how do I interpret this periodogram? How could I compute the values in the graph by hand from sin(20x) + 2sin(80x)? I don't understand how to get from sin(20x) + 2sin(80x) to the periodogram.
This was plotted in R using periodogram() function.
Periodogram is used to estimate power spectral density(PSD) of a signal, which allows you to calculate how much power it contains given a frequency or frequency band. Frequencies with higher peaks imply that the signal has a strong(dominant) sinusoidal component with exactly the same frequency. In your plot, $f \approx 0.28$ seems to be the most important frequency component of your signal.
To compute PSD by hand at plot it , one way is to compute the Fourier transform of the auto-correlation function of your signal.
