The distribution of a quantity, such as particle flux, as a function of energy.A spectrum is the distribution of a physical quantity — such as particle flux, light intensity, or sound power — as a function of energy, frequency, or wavelength. In physics, the term is most often associated with electromagnetic radiation: the familiar rainbow of visible light is just the narrow slice of the electromagnetic spectrum our eyes can detect. But the concept extends far beyond light: cosmic-ray spectra show how many particles arrive at each energy, and the spectrum of a star's X-ray emission reveals the temperature and composition of its outer layers.
Isaac Newton first used a prism in 1666 to show that white light is composed of colors, but the modern quantitative concept of a spectrum emerged in the 19th century with Joseph von Fraunhofer's observation of dark lines in the solar spectrum and Gustav Kirchhoff's work on emission and absorption spectra.
To produce a spectrum, you separate a mixed signal into its components by some physical property. A prism or diffraction grating spreads light by wavelength; a particle detector measures the energy of each incoming particle and tallies the counts. The result is a plot or histogram showing how much of the quantity exists at each energy or frequency. The shape of that curve — whether it peaks, falls off steeply, or shows sharp lines — carries information about the processes that generated the signal.
Spectra are used everywhere from astronomy (identifying elements in distant stars) to medicine (MRI and spectroscopy for tissue analysis) and telecommunications (frequency allocation for radio and Wi-Fi).
The word 'spectrum' comes from the Latin for 'apparition' or 'ghost' — Newton used it to describe the colored image that appeared after light passed through a prism.
| c | variable | cross-correlation value — cross correlation |
| v | variable | Doppler shift velocity — velocity metre per second |
| λ | variable | wavelength — wavelength metre |
| S1 | variable | first spectrum — spectrum |
| S2 | variable | second spectrum — spectrum |
| S̄1 | variable | mean of first spectrum over wavelength — mean spectrum |
| S̄2 | variable | mean of second spectrum over wavelength — mean spectrum |
| σ | variable | standard deviation of spectrum — standard deviation |
| ∑ | operator | sum over wavelength bins — summation |
