Spectrum
A spectrum (plural spectra or spectrums) is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by analogy to many fields. Thus one might talk about the spectrum of political opinion, or the spectrum of activity of a drug, or the autism spectrum. In these uses, values within a spectrum are not necessarily precisely defined numbers as in optics; exact values within the spectrum are not precisely quantifiable.  Such use implies a broad range of conditions or behaviors grouped together and studied under a single title for ease of discussion.
In most modern usages of spectrum there is a unifying theme between extremes at either end.  Some older usages of the word did not have a unifying theme, but they led to modern ones through a sequence of events set out below.  Modern usages in mathematics did evolve from a unifying theme, but this may be difficult to recognize.

# Origins
In Latin spectrum means "image" or "apparition", including the meaning "spectre". 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 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 or power as a function of frequency or wavelength, also known as a spectral density.
The term spectrum was soon applied to other waves, such as sound waves, and now applies to any signal that can be decomposed into frequency components. 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.  Looking at light through a prism separates visible light into its colors according to wavelength. It separates them according to its dispersion relation and a grating separates according to the grating equation and if massive particles are measured often their speed is measured. To get a spectrum, the measured function has to be transformed in their independent variable to frequencies and the dependent variable has to be reduced in regions, where the independent variable is stretched. For this imagine that the spectrum of pulse with a finite number of particles is measured on a film or a CCD. Assuming no particles are lost, any nonlinearity (compared to frequency) on the spectral separation concentrates particles at some points of the film. The same is true for taking a spectrum by scanning a monochromator with a fixed slit width. Violet at one end has the shortest wavelength and red at the other end has the longest wavelength of visible light.  The colors in order are violet, blue, green, yellow, orange, red.  As the wavelengths get bigger below the red visible light they become infrared, microwave, and radio.  As the wavelengths get smaller above violet light, they become ultra-violet, x-ray, and gamma ray.