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Old January 2nd, 2018, 09:29 AM
Doug Kerr Doug Kerr is offline
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Join Date: May 2006
Location: Alamogordo, New Mexico, USA
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It is important to note that we most often, when working with visible electromagnetic radiation, mention the wavelengths involved rather than the frequencies (even though the two have a simple direct relationship, one being the reciprocal of the other).

And consistent with that, when we speak of the power spectral density (PSD) of an instance of radiation, it is customary, to be more thorough with its name, to plot the power spectral wavelength density function as the "spectrum" of the radiation.

Thus the horizontal axis of our plot is wavelength, and the vertical axis is power per unit wavelength.

But when we deal with radiation of lower frequencies (as in work on "radio"), we more often (today) mention the frequency of the radiation (although wavelength is indeed often of great interest). And consistent with that, in that regime, when we speak of the power spectral density (PSD) of an instance of radiation, it is customary, to be more thorough with its name, to plot the power spectral frequency density function as the "spectrum" of the radiation.

Thus the horizontal axis of our plot is frequency, and the vertical axis is power per unit frequency.

Now we might thank that, if we were asked to take the plot of the SPD of an instance of light and change it into the power spectral frequency density function form. We might think that what w need to do is to relabel the axes and perhaps do some sort of scaling of them, to suit the new units.

But there is much more to it than that. For one thing, since frequency is the reciprocal of wavelength, for openers the horizontal axis is reversed between the wavelength spectrum and the frequency spectrum (I will use those short terms for conciseness).

But also, as we move to the right on our frequency spectrum, a unit change in wavelength leads to greater and greater change in frequency. Thus, in a sense, the frequency spectrum plot is increasingly stretched to the right as we go further to the right.

Now our vertical axis was originally in terms of power per unit wavelength, but is now in terms of power per unit frequency. But, again due to the "reciprocal" nature of wavelength and frequency, at the bottom end of our frequency "range" one unit of frequency may correspond to a certain number of units of wavelength, while at the top end of the frequency range, one unit of frequency will correspond to a lesser number of units of wavelength.

The result of this is that as we go to the right on our frequency spectrum, the vertical height of the curve will decline compared to where it was at the corresponding spot on the wavelength spectrum.

Now all this has little to do with our normal adventures in considering the matter of the "spectrum" of light. But those who also deal with the spectrum of radio signals (Will Thompson, for example) could be misdirected by the matter I discuss in this note.

************

My apologies for not having illuminated this discussion with some illustrations. They are under preparation.

Later.

Best regards,

Doug
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