Spherical harmonicsIn mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields. Since the spherical harmonics form a complete set of orthogonal functions and thus an orthonormal basis, each function defined on the surface of a sphere can be written as a sum of these spherical harmonics. This is similar to periodic functions defined on a circle that can be expressed as a sum of circular functions (sines and cosines) via Fourier series.
Radiation resistanceRadiation resistance is that part of an antenna's feedpoint electrical resistance caused by the emission of radio waves from the antenna. In radio transmission, a radio transmitter is connected to an antenna. The transmitter generates a radio frequency alternating current which is applied to the antenna, and the antenna radiates the energy in the alternating current as radio waves. Because the antenna is absorbing the energy it is radiating from the transmitter, the antenna's input terminals present a resistance to the current from the transmitter.
Spin-weighted spherical harmonicsIn special functions, a topic in mathematics, spin-weighted spherical harmonics are generalizations of the standard spherical harmonics and—like the usual spherical harmonics—are functions on the sphere. Unlike ordinary spherical harmonics, the spin-weighted harmonics are U(1) gauge fields rather than scalar fields: mathematically, they take values in a complex line bundle. The spin-weighted harmonics are organized by degree l, just like ordinary spherical harmonics, but have an additional spin weight s that reflects the additional U(1) symmetry.
Radiation patternIn the field of antenna design the term radiation pattern (or antenna pattern or far-field pattern) refers to the directional (angular) dependence of the strength of the radio waves from the antenna or other source. Particularly in the fields of fiber optics, lasers, and integrated optics, the term radiation pattern may also be used as a synonym for the near-field pattern or Fresnel pattern. This refers to the positional dependence of the electromagnetic field in the near field, or Fresnel region of the source.
Spherical basisIn pure and applied mathematics, particularly quantum mechanics and computer graphics and their applications, a spherical basis is the basis used to express spherical tensors. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. While spherical polar coordinates are one orthogonal coordinate system for expressing vectors and tensors using polar and azimuthal angles and radial distance, the spherical basis are constructed from the standard basis and use complex numbers.
Harmonic analysisHarmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on the real line, or by Fourier series for periodic functions. Generalizing these transforms to other domains is generally called Fourier analysis, although the term is sometimes used interchangeably with harmonic analysis.
Electromagnetic radiationIn physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. Types of EMR include radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays, all of which are part of the electromagnetic spectrum. Classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of electric and magnetic fields.
Neutrino oscillationNeutrino oscillation is a quantum mechanical phenomenon in which a neutrino created with a specific lepton family number ("lepton flavor": electron, muon, or tau) can later be measured to have a different lepton family number. The probability of measuring a particular flavor for a neutrino varies between three known states, as it propagates through space. First predicted by Bruno Pontecorvo in 1957, neutrino oscillation has since been observed by a multitude of experiments in several different contexts.
Near and far fieldThe near field and far field are regions of the electromagnetic (EM) field around an object, such as a transmitting antenna, or the result of radiation scattering off an object. Non-radiative near-field behaviors dominate close to the antenna or scattering object, while electromagnetic radiation far-field behaviors dominate at greater distances. Far-field E (electric) and B (magnetic) field strength decreases as the distance from the source increases, resulting in an inverse-square law for the radiated power intensity of electromagnetic radiation.
Neutral particle oscillationIn particle physics, neutral particle oscillation is the transmutation of a particle with zero electric charge into another neutral particle due to a change of a non-zero internal quantum number, via an interaction that does not conserve that quantum number. Neutral particle oscillations were first investigated in 1954 by Murray Gell-mann and Abraham Pais. For example, a neutron cannot transmute into an antineutron as that would violate the conservation of baryon number.
Cherenkov radiationCherenkov radiation (tʃəˈrɛŋkɒf; Эффект Вавилова–Черенкова) is electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium at a speed greater than the phase velocity (speed of propagation of a wavefront in a medium) of light in that medium. A classic example of Cherenkov radiation is the characteristic blue glow of an underwater nuclear reactor. Its cause is similar to the cause of a sonic boom, the sharp sound heard when faster-than-sound movement occurs.
Fresnel diffractionIn optics, the Fresnel diffraction equation for near-field diffraction is an approximation of the Kirchhoff–Fresnel diffraction that can be applied to the propagation of waves in the near field. It is used to calculate the diffraction pattern created by waves passing through an aperture or around an object, when viewed from relatively close to the object. In contrast the diffraction pattern in the far field region is given by the Fraunhofer diffraction equation. The near field can be specified by the Fresnel number, F, of the optical arrangement.
Audio engineerAn audio engineer (also known as a sound engineer or recording engineer) helps to produce a recording or a live performance, balancing and adjusting sound sources using equalization, dynamics processing and audio effects, mixing, reproduction, and reinforcement of sound. Audio engineers work on the "technical aspect of recording—the placing of microphones, pre-amp knobs, the setting of levels. The physical recording of any project is done by an engineer... the nuts and bolts.
Fade (audio engineering)In audio engineering, a fade is a gradual increase or decrease in the level of an audio signal. The term can also be used for film cinematography or theatre lighting in much the same way (see fade (filmmaking) and fade (lighting)). A recorded song may be gradually reduced to silence at its end (fade-out), or may gradually increase from silence at the beginning (fade-in). Fading-out can serve as a recording solution for pieces of music that contain no obvious ending.
Professional audioProfessional audio, abbreviated as pro audio, refers to both an activity and a category of high-quality, studio-grade audio equipment. Typically it encompasses sound recording, sound reinforcement system setup and audio mixing, and studio music production by trained sound engineers, audio engineers, record producers, and audio technicians who work in live event support and recording using mixing consoles, recording equipment and sound reinforcement systems.
Digital audioDigital audio is a representation of sound recorded in, or converted into, digital form. In digital audio, the sound wave of the audio signal is typically encoded as numerical samples in a continuous sequence. For example, in CD audio, samples are taken 44,100 times per second, each with 16-bit sample depth. Digital audio is also the name for the entire technology of sound recording and reproduction using audio signals that have been encoded in digital form.
Broadcast engineeringBroadcast engineering is the field of electrical engineering, and now to some extent computer engineering and information technology, which deals with radio and television broadcasting. Audio engineering and RF engineering are also essential parts of broadcast engineering, being their own subsets of electrical engineering. Broadcast engineering involves both the studio and transmitter aspects (the entire airchain), as well as remote broadcasts. Every station has a broadcast engineer, though one may now serve an entire station group in a city.
Latency (audio)Latency refers to a short period of delay (usually measured in milliseconds) between when an audio signal enters a system and when it emerges. Potential contributors to latency in an audio system include analog-to-digital conversion, buffering, digital signal processing, transmission time, digital-to-analog conversion and the speed of sound in the transmission medium. Latency can be a critical performance metric in professional audio including sound reinforcement systems, foldback systems (especially those using in-ear monitors) live radio and television.
N-sphereIn mathematics, an n-sphere or a hypersphere is a topological space that is homeomorphic to a standard n-sphere, which is the set of points in (n + 1)-dimensional Euclidean space that are situated at a constant distance r from a fixed point, called the center. It is the generalization of an ordinary sphere in the ordinary three-dimensional space. The "radius" of a sphere is the constant distance of its points to the center. When the sphere has unit radius, it is usual to call it the unit n-sphere or simply the n-sphere for brevity.
3-sphereIn mathematics, a 3-sphere, glome or hypersphere is a higher-dimensional analogue of a sphere. It may be embedded in 4-dimensional Euclidean space as the set of points equidistant from a fixed central point. Analogous to how the boundary of a ball in three dimensions is an ordinary sphere (or 2-sphere, a two-dimensional surface), the boundary of a ball in four dimensions is a 3-sphere (an object with three dimensions). A 3-sphere is an example of a 3-manifold and an n-sphere.
