Timeline for Energy and Power: Power Spectral Density is units of Energy
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| May 3 at 1:33 | comment | added | Dan Boschen | yes I understand that quite well; same thing happens when you apply windowing with discrete time signals - that is part of the “when we convert to a PSD”: we make accurate PSD measurements routinely from a spectrum analyzer measurement so didn’t mean for that to distract from my point with that sentence | |
| May 2 at 20:47 | comment | added | ahavens | @DanBoschen ", I believe when I make a measurement with a spectrum analyzer (understanding their design and function) I am measuring power over a range of frequencies (given by the resolution bandwidth)." This is correct, but what you might be missing is that if the RBW is > bin spacing, you essentially have double counting, you are not showing power spectral density but power. So one bin shows all the power, and the bins next to it show some of the power. If you want to integrate over a frequency range, you have to also divide by the RBW to get a useful result. | |
| May 2 at 20:32 | comment | added | ahavens | The issue is fundamental to the choice of sin and cos as the basis functions for the Fourier transform. If you chose basis functions with time locality like wavelets, I expect you could get get a meaningful energy interpretation from the transform domain en.wikipedia.org/wiki/Wavelet_transform | |
| May 2 at 20:22 | comment | added | ahavens | I would not try and use energy in the frequency domain, it does not really make sense, since you don't have the time dimension any more so you concepts are going to be inherently degenerate. In the frequency domain the signals are considered to continue for infinite time so all your energies are infinity, which is not really the answer you are looking for. In discrete terms the energy is a function of the window length and shape, rather than just the signal itself. | |
| May 2 at 11:47 | comment | added | Dan Boschen | All that aside, I believe when I make a measurement with a spectrum analyzer (understanding their design and function) I am measuring power over a range of frequencies (given by the resolution bandwidth). If I convert that to a power spectral density (to get Watts/Hz and thus each value given is the energy in Joules). As I introduced in my question, following all that logic the total energy is the sum of this or equivalently with discrete DFT values $N\sum |X[k]|^2$. But the total "Signal Energy" for signal processing is $\sum |X[k]|^2$. So "Signal Energy" is NOT physical energy. | |
| May 2 at 11:40 | comment | added | Dan Boschen | So if we are to justify what the term means using this analogy and hold that as it's definition, we will be disappointed and confused when we see it "misused". Given the opportunity for this confusion, I am sure we could find ample evidence that supports either explanation but what Matt detailed, and I hopefully summarized correctly, as an additional answer makes the most sense to me and is consistent with "trusted" sources of DSP literature and text books where a lot of the terminology (which is all this is) originates. As I stated in my answer, I personally don't it, but that's what it is. | |
| May 2 at 11:33 | comment | added | Dan Boschen | Thanks ahavens! Yes I'm an RF engineer and hear you on the relationship to working with Spectrum Analyzers. I think the point here that in signal processing x[n] isn't always a samples of a voltage, nor even a function of time $n$, or even always real. So what you describe is the case from which the terms "Energy Signal" and "Power Signal" originated, but as a signal processing definition doesn't actually have to do with power or energy at all, it is just the manner in which we square and sum and the name we give to that, which then applies to any "signal" in signal processing apps. | |
| May 2 at 1:04 | history | answered | ahavens | CC BY-SA 4.0 |