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Power spectral density and variance

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iVenki

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How do you say power and variance are one and the same?

For example: Consider this signal. Variance.pngVariance.png


Here I believe that the variance of the signal is zero because there seems to be no variation of the amplitude. Then it also means that the power is also zero which is impossible. I mean you can't have a wave with no power. So help me.
 
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