The noun spectrum (plural: spectra) has a variety of meanings.
Originally a spectrum was what is now called a spectre, i.e., a phantom or apparition. Spectral evidence is testimony about what was done by spectres of persons not present physically, or hearsay evidence about what ghosts or apparitions of Satan said. It was used to convict a number of persons of witchcraft at Salem, Massachusetts in the late 17th century.
Modern (17th through 21st centuries) meaning in the physical sciences
In the 17th century the word spectrum was introduced into optics, referring to the range of colors observed when white light was dispersed through a prism. Soon the term referred to a plot of light intensity as a function of frequency or wavelength. Max Planck later realized that frequency represents electromagnetic energy:
- E = hν
The word spectrum then took on the obvious analogous meaning in reference to other sorts of waves, such as sound wave, or other sorts of decomposition into frequency components. Thus a spectrum is a usually 2-dimensional plot, of a compound signal, depicting the components by another measure. Sometimes, the word spectrum refers to the compound signal itself, such as the "spectrum of visible light", a reference to those electromagnetic waves which are visible to the human eye.
- The electromagnetic spectrum is the power spectrum of an electromagnetic signal. It can be measured by spectroscopy.
- The optical spectrum is the electromagnetic spectrum of visible light
- The power spectrum is the distribution of the energy of a function in the frequency domain, which is actually the same as the magnitude of the frequency spectrum. See spectroscopy, spectrum of gravity waves .
- Spectroscopy is the study of spectra.
- The spectrogram is the result of calculating the frequency spectrum of windowed frames of the signal.
- In telecommunication, a spread spectrum is any of certain kinds of signal transmission.
Physical acoustics of music
- See timbre. Spectrum is one of the determinants of the timbre or quality of a sound. It is the relative strength of pitches called harmonics and partials (collectively overtones) at various frequencies usually above the fundamental frequency, which is the actual note named (eg. an A).
Meanings of spectrum in mathematics
The various meanings of the word spectrum in mathematics are derived (some fairly directly; some less so) from the meanings in the physical sciences.
- The frequency spectrum is the result of a Fourier-related transform of a mathematical function into the frequency domain.
- The spectrum of an operator has to do with the invertibility of an operator in function spaces.
- The spectrum of a matrix is the spectrum of an operator where the matrix is considered as operator. Precisely, it is the set of the matrix's eigenvalues.
- A (strange) construction, similar to the frequency spectrum, is the cepstrum of the quefrency.
- Finding a spectrum is a method of cycles analysis.
- The spectrum of a ring is the set of prime ideals of a ring.
- The spectrum of a Boolean algebra is the Stone space of the Boolean algebra.
The meanings of spectrum in some other disciplines, including pharmacology, politics, and psychology evolved by analogy with the meanings in the physical sciences: just as dispersed colored light ranged from one end of the rainbow to the other, so also other things that range from one extreme to another were called spectra.
- The spectrum of activity of an antibiotic evaluates how wide a range of infections can be treated.
- There is a political spectrum which is said to go from left to right.
- There exists the concept of a bipolar spectrum.