In physics, and in particular in optics, the study of waves and digital signal processing, the term group delay has the following meanings: Since antiquity, people have tried to understand the behavior of matter: why unsupported objects drop to the ground, why different materials have different properties, and so forth. ... Optics (appearance or look in ancient Greek) is a branch of physics that describes the behavior and properties of light and the interaction of light with matter. ... A wave is a disturbance that propagates in a periodically repeating fashion, often transferring energy. ... Digital signal processing (DSP) is the study of signals in a digital representation and the processing methods of these signals. ...

1. The rate of change of the total phase shift with respect to angular frequency, d θ/d ω, through a device or transmission medium, where θ is the total phase shift, and ω is the angular frequency in radians per second, equal to 2πf, where f is the frequency in hertz. Waves with the same phase Waves with different phases The phase of a wave relates the position of a feature, typically a peak or a trough of the waveform, to that same feature in another part of the waveform (or, which amounts to the same, on a second waveform). ... Sine waves of various frequencies; the lower waves have higher frequencies than those above. ... A transmission medium is any material substance, such as fiber-optic cable, twisted-wire pair, coaxial cable, dielectric-slab waveguide, water, or air, that can be used for the propagation of signals, usually in the form of modulated radio, light, or acoustic waves, from one point to another. ... Angular frequency is a measure of how fast an object is rotating In physics (specifically mechanics and electrical engineering), angular frequency ω (also called angular speed) is a scalar measure of rotation rate. ... See Radian (band) for the Austrian trio. ... The second (symbol: s) is the SI base unit of time. ... Sine waves of various frequencies; the lower waves have higher frequencies than those above. ... The hertz (symbol Hz) is the SI unit of frequency. ...

2. In an optical fiber, the transit time required for optical power, traveling at a given mode's group velocity, to travel a given distance. Optical fibers Optic Fibres are a crazy new invention by the famous physics geniusDr Hartnett, born in a barn, Dr Hartnett is a dirty Liverpool fan, but one who is much loved by his pupils especially his best friend Carl Roberts!!He loves optic fibres and has them all... 8:17 am, August 6, 1945, Japanese time. ... // Mechanical power In physics, power (symbol: P) is the amount of work W done per unit of time t. ... Mode has several meanings: In statistics, the mode is the value that has the largest number of observations, namely the most frequent value or values. ... The group velocity of a wave is the velocity with which the overall shape of the waves amplitude (known as the envelope of the wave) propagates through space. ...

Note: For optical fiber dispersion measurement purposes, the quantity of interest is group delay per unit length, which is the reciprocal of the group velocity of a particular mode. The measured group delay of a signal through an optical fiber exhibits a wavelength dependence due to the various dispersion mechanisms present in the fiber. In optics, dispersion is a phenomenon that causes the separation of a wave into spectral components with different frequencies, due to a dependence of the waves speed on its frequency. ... Delay is: In sound effects, any of a class of effect that adds one or more delayed versions of the original signal, to create effects such as echo or flanger. ... Signaling, or signal, may mean: Look up signal on Wiktionary, the free dictionary. ... The wavelength is the distance between repeating units of a wave pattern. ... In optics, dispersion is a phenomenon that causes the separation of a wave into spectral components with different frequencies, due to a dependence of the waves speed on its frequency. ...

Source: from Federal Standard 1037C Federal Standard 1037C entitled Telecommunications: Glossary of Telecommunication Terms is a U.S. Federal Standard, issued by the General Services Administration pursuant to the Federal Property and Administrative Services Act of 1949, as amended. ...

It is often desirable that group delay be constant across all frequencies; otherwise there is temporal smearing of the signal. Because group delay is -d θ/d ω, as defined in (1), it therefore follows that a constant group delay can be achieved if the transfer function of the device or medium has a linear phase response (i.e., θ = θ₀ + Kω where K is a constant). The deviation of the group delay from a constant indicates the degree of nonlinearity of the phase. A transfer function is a mathematical representation of the relation between the input and output of a linear time-invariant system. ... The word linear comes from the Latin word linearis, which means created by lines. ...

Group delay in the audio field

Group delay has some importance also in the audio field and especially in the sound reproduction field. Many components of an audio reproduction chain, notably loudspeakers and multiway loudspeakers crossover networks, introduce group delay in the audio signal. It is therefore important to know the treshold of audibility of group delay with respect to frequency, especially if the audio chain is supposed to provide a high fidelity reproduction. At the time of writing no extensive data is available and the best thresholds of audibility table has been provided by Blauert and Laws: A loudspeaker is a device which converts an electrical signal into sound. ... Audio crossovers are a class of electronic filters designed specifically for use in audio applications, especially hi-fi. ... High Fidelity is also the title of a book by Nick Hornby and a film directed by Stephen Frears, based upon Hornbys book. ...

The table above has been published into the following article: The hertz (symbol Hz) is the SI unit of frequency. ... A millisecond is an SI-derived unit of time, equal to one thousandth of a second. ... A kilohertz (kHz) is a unit of frequency equal to 1,000 hertz (1,000 cycles per second). ...

Blauert, J. and Laws, P "Group Delay Distortions in Electroacoustical Systems", Journal of the Acoustical Society of America, Volume 63, Number 5, pp. 1478–1483 (May 1978)

See also

• Audio system measurements

The designer of a system for sound reproduction needs to be able to measure the systems performance in a number of areas. ...

External links

• Discussion of Group Delay in Loudspeakers