Frequency spectrum in the context of Summation

A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word laser originated as an acronym for light amplification by stimulated emission of radiation. The first laser was built in 1960 by Theodore Maiman at Hughes Research Laboratories, based on theoretical work by Charles H. Townes and Arthur Leonard Schawlow and the optical amplifier patented by Gordon Gould.

A laser differs from other sources of light in that it emits light that is coherent. Spatial coherence allows a laser to be focused to a tight spot, enabling uses such as optical communication, laser cutting, and lithography. It also allows a laser beam to stay narrow over great distances (collimation), used in laser pointers, lidar, and free-space optical communication. Lasers can also have high temporal coherence, which permits them to emit light with a very narrow frequency spectrum. Temporal coherence can also be used to produce ultrashort pulses of light with a broad spectrum but durations measured in attoseconds.

Acoustic phonetics is a subfield of phonetics, which deals with acoustic aspects of speech sounds. Acoustic phonetics investigates features of waveforms as they pertain to the time domain (e.g. duration, amplitude, fundamental frequency), frequency domain (e.g. frequency spectrum), or combined spectrotemporal domains. Acoustic phonetics is also concerned with how these properties relate to other branches of phonetics (e.g. articulatory or auditory phonetics), as well as abstract linguistic concepts such as phonemes, phrases, or utterances.

The study of acoustic phonetics was greatly enhanced in the late 19th century by the invention of the Edison phonograph. The phonograph allowed the speech signal to be recorded and then later processed and analyzed. By replaying the same speech signal from the phonograph several times, filtering it each time with a different band-pass filter, a spectrogram of the speech utterance could be built up. A series of papers by Ludimar Hermann published in Pflügers Archiv in the last two decades of the 19th century investigated the spectral properties of vowels and consonants using the Edison phonograph, and it was in these papers that the term formant was first introduced. Hermann also played back vowel recordings made with the Edison phonograph at different speeds to distinguish between Willis' and Wheatstone's theories of vowel production.

A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. The radiation emitted by a black body in thermal equilibrium with its environment is called black-body radiation. The name "black body" is given because it absorbs all colors of light. In contrast, a white body is one with a "rough surface that reflects all incident rays completely and uniformly in all directions."

A black body in thermal equilibrium (that is, at a constant temperature) emits electromagnetic black-body radiation. The radiation is emitted according to Planck's law, meaning that it has a spectrum that is determined by the temperature alone (see figure at right), not by the body's shape or composition.

Flanging /ˈflændʒɪŋ/ is an audio effect produced by mixing two identical signals together, one signal delayed by a small and (usually) gradually changing period, usually smaller than 20 milliseconds. This produces a swept comb filter effect: peaks and notches are produced in the resulting frequency spectrum, related to each other in a linear harmonic series. Varying the time delay causes these to sweep up and down the frequency spectrum. A flanger is an effects unit that creates this effect.

Part of the output signal is usually fed back to the input (a re-circulating delay line), producing a resonance effect that further enhances the intensity of the peaks and troughs. The phase of the fed-back signal is sometimes inverted, producing another variation on the flanger sound.

In telecommunications, a carrier wave, carrier signal, or just carrier, is a periodic waveform (usually sinusoidal) that conveys information through a process called modulation. One or more of the wave's properties, such as amplitude or frequency, are modified by an information bearing signal, called the message signal or modulation signal. The carrier frequency is usually much higher than the message signal frequency because it is usually impractical to transmit signals with low frequencies due to larger wavelength than antenna size.

The purpose of the carrier is usually either to transmit the information through space as an electromagnetic wave (as in radio communication), or to allow several carriers at different frequencies to share a common physical transmission medium by frequency division multiplexing (as in a cable television system).

Johnson–Nyquist noise (thermal noise, Johnson noise, or Nyquist noise) is the voltage or current noise generated by the thermal agitation of the charge carriers (usually the electrons) inside an electrical conductor at equilibrium, which happens regardless of any applied voltage. Thermal noise is present in all electrical circuits, and in sensitive electronic equipment (such as radio receivers) can drown out weak signals, and can be the limiting factor on sensitivity of electrical measuring instruments. Thermal noise is proportional to absolute temperature, so some sensitive electronic equipment such as radio telescope receivers are cooled to cryogenic temperatures to improve their signal-to-noise ratio. The generic, statistical physical derivation of this noise is called the fluctuation-dissipation theorem, where generalized impedance or generalized susceptibility is used to characterize the medium.

Thermal noise in an ideal resistor is approximately white, meaning that its power spectral density is nearly constant throughout the frequency spectrum (Figure 2). When limited to a finite bandwidth and viewed in the time domain (as sketched in Figure 1), thermal noise has a nearly Gaussian amplitude distribution.

Fourier-transform spectroscopy (FTS) is a measurement technique whereby spectra are collected based on measurements of the coherence of a radiative source, using time-domain or space-domain measurements of the radiation, electromagnetic or not. It can be applied to a variety of types of spectroscopy including optical spectroscopy, infrared spectroscopy (FTIR, FT-NIRS), nuclear magnetic resonance (NMR) and magnetic resonance spectroscopic imaging (MRSI), mass spectrometry and electron spin resonance spectroscopy.

There are several methods for measuring the temporal coherence of the light (see: field-autocorrelation), including the continuous-wave and the pulsed Fourier-transform spectrometer or Fourier-transform spectrograph.The term "Fourier-transform spectroscopy" reflects the fact that in all these techniques, a Fourier transform is required to turn the raw data into the actual spectrum, and in many of the cases in optics involving interferometers, is based on the Wiener–Khinchin theorem.

In astronomy, reflection nebulae are clouds of interstellar dust which might reflect the light of a nearby star or stars. The energy from the nearby stars is insufficient to ionize the gas of the nebula to create an emission nebula, but is enough to give sufficient scattering to make the dust visible. Thus, the frequency spectrum shown by reflection nebulae is similar to that of the illuminating stars. Among the microscopic particles responsible for the scattering are carbon compounds (e. g. diamond dust) and compounds of other elements such as iron and nickel. The latter two are often aligned with the galactic magnetic field and cause the scattered light to be slightly polarized.

A distributed-element filter is an electronic filter in which capacitance, inductance, and resistance (the elements of the circuit) are not localised in discrete capacitors, inductors, and resistors as they are in conventional filters. Its purpose is to allow a range of signal frequencies to pass, but to block others. Conventional filters are constructed from inductors and capacitors, and the circuits so built are described by the lumped element model, which considers each element to be "lumped together" at one place. That model is conceptually simple, but it becomes increasingly unreliable as the frequency of the signal increases, or equivalently as the wavelength decreases. The distributed-element model applies at all frequencies, and is used in transmission-line theory; many distributed-element components are made of short lengths of transmission line. In the distributed view of circuits, the elements are distributed along the length of conductors and are inextricably mixed together. The filter design is usually concerned only with inductance and capacitance, but because of this mixing of elements they cannot be treated as separate "lumped" capacitors and inductors. There is no precise frequency above which distributed element filters must be used but they are especially associated with the microwave band (wavelength less than one metre).

Distributed-element filters are used in many of the same applications as lumped element filters, such as selectivity of radio channel, bandlimiting of noise and multiplexing of many signals into one channel. Distributed-element filters may be constructed to have any of the bandforms possible with lumped elements (low-pass, band-pass, etc.) with the exception of high-pass, which is usually only approximated. All filter classes used in lumped element designs (Butterworth, Chebyshev, etc.) can be implemented using a distributed-element approach.

Pink noise, 1⁄f noise, fractional noise or fractal noise is a signal or process with a frequency spectrum such that the power spectral density (power per frequency interval) is inversely proportional to the frequency of the signal. In pink noise, each octave interval (halving or doubling in frequency) carries an equal amount of noise energy.

Pink noise sounds like a waterfall. It is often used to tune loudspeaker systems in professional audio. Pink noise is one of the most commonly observed signals in biological systems.

Frequency deviation (${\displaystyle f_{\Delta }}$) is used in FM radio to describe the difference between the minimum or maximum extent of a frequency modulated signal, and the nominal center or carrier frequency. The term is sometimes mistakenly used as synonymous with frequency drift, which is an unintended offset of an oscillator from its nominal frequency.

The frequency deviation of a radio is of particular importance in relation to bandwidth, because less deviation means that more channels can fit into the same amount of frequency spectrum. The FM broadcasting range between 87.5 and 108 MHz uses a typical channel spacing of 100 or 200 kHz, with a maximum frequency deviation of +/-75 kHz, in some cases leaving a buffer above the highest and below the lowest frequency to reduce interaction with other channels.