Why does the Power Spectral Density depend on the signal length?

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Paul F Lang 2018-3-20

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https://ww2.mathworks.cn/matlabcentral/answers/389553-why-does-the-power-spectral-density-depend-on-the-signal-length

回答： Wilson A N 2018-4-12

When I run the first two sections of the code found in https://uk.mathworks.com/help/signal/ug/power-spectral-density-estimates-using-fft.html and increase the signal duration to t = 0:1/Fs:100-1/Fs; this heavily alters the PSD. Shouldn't power be a quantity that is time independent? I think I am missing sth. fundamental, as it also appears to me that the energy spectral density (as defined under https://en.wikipedia.org/wiki/Spectral_density#Energy_spectral_density) is proportional to the square of the signal duration (and I expect energy to be proportional to the first power of time).

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Answer 1

Wilson A N 2018-4-12

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Usually, Power Spectral Densities are calculated for power signals where the energy of the signal is infinite. Similarly, Energy Spectral Densities are for energy signals where the power is zero.

To clarify, in a periodic signal, the signal has infinite energy. To identify a measure for the energy of the periodic signal we resort in using power of a signal which is defined within a specified time. Hence there is an implicit dependence on time of the signal. The following link may prove to be useful:

https://dsp.stackexchange.com/questions/10148/power-spectral-density-vs-energy-spectral-density