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I am trying to understand the spectral analysis example posted by you. I see that you have chose fixed weights i.e. 1234321. I am trying to understand the use of weights and why these were particularly chosen and not any other numbers.What do 1234321 signify?
The estimate of the spectral density corresponds to the smoothing of the periodogram, and it is often a better estimator of the real spectral density of the observed phenomenon.
Weights choosen in this particular example (1234321) correspond to a simple triangular weighting smoothing.
The spectral density estimates are then computed with these weigths to smooth the periodogram.
It works as a weighted moving average i.e it assigns the greatest weight to the observation in the center of the window, and symmetrically decreases weights to the observation further away from the center.
It helps so to reduce the problem of spectral leakage.
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