Definition of "Power" in "Power Spectrum" (for translator)

Question

I'm a technical translator who recently undertook translation of documents related to signal processing. Being a novice in the field, I'm searching the web for terminology and concepts.

It appears that local web content includes two instances of translation for "power spectrum":

• (electric power) spectrum
• (power) spectrum

Upon my query, the requestor says it's not appropriate to translate "power spectrum" as "(electric power) spectrum". But there are quite a number of translation as "(electric power) spectrum", so I'd like to know the exact definition of "power" in the "power spectrum" to make sure that the translation as "(electric power) spectrum" is wrong.

The following is a Wikipedia page that my requestor provided as a reference:

https://en.wikipedia.org/wiki/Spectral_density#Power_spectral_density

... For continuous signals over all time, such as stationary processes, one must rather define the power spectral density (PSD); this describes how power of a signal or time series is distributed over frequency, as in the simple example given previously. Here, power can be the actual physical power, or more often, for convenience with abstract signals, is simply identified with the squared value of the signal.

My questions are as follows:

• Is the highlighted part applicable as definition of "power" in "power spectrum" as well?
  • If so, is "(electric power) spectrum" incorrect translation because the "power" spans other types of physical power in addition to "electric power" (and also because "power" can imply the squared value)?
  • Otherwise, could someone provide better explanation?

Thank you.

Answer 1

the requestor says it's not appropriate to translate "power spectrum" as "(electric power) spectrum".

And I'd agree with him.

Let's start with the last of your questions:

Otherwise, could someone provide better explanation?

What's the layman area where one meets the term "spectrum"? Right, it's this rainbow:

^{Zátonyi Sándor, (ifj.) Fizped / CC BY-SA (https://creativecommons.org/licenses/by-sa/3.0)}

What's depicted here is how a prism splits white light, which contains a continuum of frequencies of light, into components that all have a different frequency.

The power spectrum is just the answer to the question "how much power is there in the white light at the frequency of this specific color?".

No electricity involved at all. Just light.

Generally, in DSP, if you try too hard to identify magnitudes with any particular physical entitity, you'll often "phrase yourself into a corner", because DSP is just applied math, and that math doesn't care whether the signal analyzed is the amplitude of an electromagnetic wave like light, the intensity of pixels in an image, the instantaneous position of a vibrating string of a guitar, air pressure variations caused by that string, blood pressure, the magnitude of a gravity disturbance caused by rotating supermassive star pairs, or the voltage at some measurement device.

In fact, the power spectral density is as much a mathematical concept with no relation to any specific physical entity as you'll encounter: It's literally just "if you have a random function of a single real-valued number, and you can calculate the autocorrelation of that over a difference on that number axis, then the Fourier transform of that is called the power spectral density".

Physics is just good to us in that this really describes something that can be measured as power, if the random function can be understood as an amplitude. But again, nothing here says that anything is about electricity.

Is the highlighted part applicable as definition of "power" in "power spectrum" as well?

Yes. It's what I'd recommend to use. Power is just the square of some amplitude signal.

If so, is "(electric power) spectrum" incorrect translation because the "power" spans other types of physical power in addition to "electric power" (and also because "power" can imply the squared value)?

yes. and yes.