Copyright © Philip M. Parker, INSEAD. Terms of Use.
Definition: Equalizer |
EqualizerNoun1. Electronic equipment that reduces frequency distortion. 2. An equivalent counterbalancing weight. 3. A score that makes the match even. Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved. |
Date "equalizer" was first used in popular English literature: sometime before 1790. (references) |
| Domain | Definition |
Computing | The element connected in the forward path or in an auxiliary feedback path of a feedback control system and whose transfer function is such that the overall performances of the feedback control system are improved. Source: European Union. (references) |
Electrical Engineering | A network which corrects a circuit's transmission-frequency characteristics to allow it to transmit selected frequencies in a uniform manner. Source: European Union. (references) |
| The connection made between points on a winding to minimise any undesirable potential difference between these points. Source: European Union. (references) | |
| The apparatus designed to compensate over a certain frequency range the amplitude/frequency distortion or the phase/frequency distortion introduced by lines or equipment. Source: European Union. (references) | |
| A device to reduce distortion in a system by introducing networks that compensate for the particular type of distortion over the required frequency band. Source: European Union. (references) | |
Food & Agriculture | A device that provides for equal distribution of coating, cream etc. Source: European Union. (references) |
Mechanical Engineering | A connection between two points of a refrigeration system to equalize pressures or levels, for example between the crankcases of compressors in parallel. Source: European Union. (references) |
Occupations | Operates equalizer saw to saw barrel-stave bolts into specified lengths with square ends: Adjusts distance between saws. Lays bolt on carriage of equalizer and starts saws. Pushes carriage between saws to trim and square ends of bolts. Withdraws carriage and removes bolts. (references) |
Source: compiled by the editor from various references; see credits. | |
(From Wikipedia, the free Encyclopedia)
This article is about equalisers in mathematics. For equalizers in audio signal processing, see Equalization.In mathematics, an equaliser, or equalizer, is a set of arguments where two or more functions have equal values. An equaliser is the solution set of an equation. In certain contexts, a difference kernel is the equaliser of exactly two functions.
Definitions
Let X and Y be sets. Let f and g be functions, both from X to Y. Then the equaliser of f and g is the set of elements x of X such that f(x) equals g(x) in Y. Symbolically:
The equaliser may be denoted Eq(f,g) or a variation on that theme (such as with lowercase letters "eq"). In informal contexts, the notation {f = g} is common.
The definition above used two functions f and g, but there is no need to restrict to only two functions, or even to only finitely many functions. In general, if F is a set of functions from X to Y, then the equaliser of the members of F is the set of elements x of X such that, given any two members f and g of F, f(x) equals g(x) in Y. Symbolically:
This equaliser may be denoted Eq(F), or Eq(f,g,h,...) if F is the set {f,g,h,...}. In the latter case, one may also find {f = g = h = ···} in informal contexts.
As a degenerate case of the general definition, let F be a singleton {f}. Since f(x) always equals itself, the equaliser must be the entire domain X. As an even more degenerate case, let F be the empty set {}. Then the equaliser is again the entire domain X, since the universal quantification in the definition is vacuously true.
Difference kernels
A binary equaliser (that is, an equaliser of just two functions) is also called a difference kernel. This may also be denoted DiffKer(f,g), Ker(f,g), or Ker(f - g). The last notation shows where this terminology comes from, and why it is most common in the context of abstract algebra: The difference kernel of f and g is simply the kernel of the difference f - g. Conversely, the kernel of a single function f can be reconstructed as the difference kernel Eq(f,0), where 0 is the constant function with value zero.
Of course, all of this presumes an algebraic context where the kernel of a function is its preimage under zero; that is not true in all situations. However, the terminology "difference kernel" has no other meaning.
In category theory
Equalisers can be defined by a universal property, which allows the notion to be generalised from the category of sets to arbitrary categories.
In the general context, X and Y are objects, while f and g are morphisms from X to Y. These objects and morphisms form a diagram in the category in question, and the equaliser is simply the limit of that diagram.
In more explicit terms, the equaliser consists of an object E and a morphism eq from E to X satisfying f·eq = g·eq (where "·" denotes composition of morphisms); and such that, given any other object O and morphism m from O to X, if f·m = g·m, then there exists a unique morphism u from O to E such that eq·u = m.
There should be a picture here.
In any universal algebraic category, including the categories where difference kernels are used, as well as the category of sets itself, the object E can always be taken to be the ordinary notion of equaliser, and the morphism eq can in that case be taken to be the inclusion function of E as a subset of X.
The generalisation of this to more than two morphisms is straightforward; simply use a larger diagram with more morphisms in it. The degenerate case of only one morphism is also straightforward; then eq can be any isomorphism from an object E to X.
The degenerate case of no morphisms at all might be confusing at first; it may seem that the diagram in question consists of only the objects X and Y, with no morphsims. The limit of that diagram is the product of X and Y, which doesn't agree with the set-theoretic definition above. However, the correct interpretation is that the diagram is based on X and includes Y only because Y is the codomain of a morphism in the diagram. Then if there are no morphisms involved, then the diagram consists of X alone, so the limit is again any isomorphism between E and X.
It can be proved that any equaliser in any category is a monomorphism. If the converse holds in a given category, then that category is said to be regular (in the sense of monomorphisms). More generally, a regular monomorphism in any category is any morphism m that is an equaliser of some set of morphisms. Some authorities require (more strictly) that m be a binary equaliser, that is an equaliser of exactly two morphisms. However, if the category in question is complete, then both definitions agree.
The notion of difference kernel also makes sense in a category-theoretic context. The terminology "difference kernel" is common throughout category theory for any binary equaliser. In the case of a preadditive category (a category enriched over the category of Abelian groups), the term "difference kernel" may be interpreted literally, since subtraction of morphisms makes sense. That is, Eq(f,g) = Ker(f - g), where Ker denotes the category-theoretic kernel.
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Equaliser."
(From Wikipedia, the free Encyclopedia)
Methods and media for sound recording are varied and have undergone significant changes between the first time sound was actually recorded for later playback until now.
Technology
Mechanical Recording
The first devices for recording sound were mechanical in nature.
In 1796 a Swiss watchmaker named Antoine Favre described his idea for what we now call the cylinder musical box. This can be considered an early method of recording a melody, although it does not record an arbitrary sound and does not record automatically. "Playback" however is automatic.
The Player piano was a device that could playback a piano performance which had earlier been mechanically recorded onto a piano roll.
The first recording of sound waves
Leon Scott invented the 'phonoautograph', the first device to record arbitrary sound in 1857. It used a membrane (which vibrated in response to sound) attched to a pen, which traced a line roughly corresponding to the sound wave form on to a moving roll of paper. Although able to record sound, the phonoautograph was unable to play back the recording; it was of little use other than as a laboratory curiousity.
The Phonograph and the Gramophone
The phonograph built expanding on the principles of the phonoautograph. Invented by Thomas Edison in 1877, the phonograph was a device with a cylinder covered with a soft material such as tinfoil, lead, or wax on which a stylus drew grooves. The depth of the grooves made by the stylus corresponded to change in air pressure created by the original sound. The recording could be played back by tracing a needle through the groove and amplifying, through mechanical means, the resulting vibrations. A disadvantage of the early phonographs was the difficulty of reproducing the phonograph cylinders in mass production.This changed with the advent of the gramophone (phonograph in American English), which was patented by Emile Berliner in 1887. The gramophone imprinted grooves on a disk record. Instead of recording the varying the depth of the groove (vertically), as with the phonograph, the vibration of the recording stylus was across the width of the track ( horizontally). The depth of the groove remained constant.
In audio fidelity terms the disc record was inherently neither better than or worse than than the phonograph cylinder, but the disc records were easier and cheaper to mass produce. Reproduction of these disks was relatively simple by pressing a master image on a plate of shellac. The speed at with the disks were spun around was eventually standardized at 78 rotations per minute (rpm). Later innovations allowed lower rotations: 45 and 33 rpm, and the material was changed to vinyl. (see analogue disc record for a more detailed discussion)
Both phonograph cylinders and gramophone discs were played on mechanical devices most commonly hand wound with a clockwork motor. The sound was amplified by a cone that was attached to the diaphragm. The disc record largely surplanted the competing cylinder record by the late 1910s.
The advent of electrical recording in 1924, and electrical playback in 1925 drastically improved the quality of the recording process of disc records.
Magnetic Recording
Around 1900 V. Poulsen introduced a method of recording sound to magnetic wire. Tape replaced wire as the recording medium in 1924 thanks to German engineer C. Stille. An electrical signal, which is analogous to the sound that is to be recorded, is fed to the record head of a tape recorder. The tape is magnetized as it moves with a constant speed past a recording head. A playback head can then pick up the changes in magnetic field from the tape and convert it into an electrical signal.
On Christmas day 1932 the British Broadcasting Corporation first used a tape recorder for their broadcasts.
A tape allows multiple tracks in parallel to each other. This allowed for stereo sound (2 tracks), and quadrophonic sound (4 tracks). In a professional setting today, such as a studio, audio engineers may use 24 tracks or more for their recordings, one (or more) tracks for every instrument played.
Until 1963, when Philips introduced the Compact audio cassette, tape recording had been largely on open reel tape recorders. The Compact audio cassette added much needed convenience to the tape recording format. Although it was much lower in quality than open reel formats.
In 1965 Dolby Laboatories invented a noise reduction system for analogue tape. This improved the perceived level of tape hiss, which is inherant to the medium. Originally this system, known as Dolby A, was only used in professional recording. Dolby, however went on to develop more advanced noise reduction techniques for both professional and consumer formats, including the Compact audio cassette.
Other magnetic recording formats:
- 8-Track cartridge
Recording on Film
To avoid synchronization problems, on sound films the sound track is recorded optically on to the side of the strip of motion picture film.
The first attempts to record sound to an optical medium occurred around 1900. In 1906 Lauste applied for a patent to record sound on film, but was ahead of his time. In 1923 de Forest applied for a patent to record to film. In 1927 the sound film The Jazz Singer was released; while not the first, it made a tremendous hit and made the public and the film industry realize that sound film was more than a mere novelty.
There are two methods for recording on film. Variable density recording uses changes in the darkness of the soundtrack side of the film to represent the soundwave. Variable width recording uses changes in the width of a dark strip to represent the soundwave.
In both cases light that is sent through the part of the film that corresponds to the soundtrack changes in intensity, proportional to the original sound, and that light is not projected on the screen but converted into an electrical signal by a light sensitive device.
Digital Recording
Early digital audio recorders use a device to make it possible to record digital audio on a U-matic video machine. This was followed by digital open reel multitrack recorders. With the improvement in digital storage technology, a variety of recording media is used to record digital audio today.
Digital Audio Tape (DAT) recorded the raw audio sampled at 48 kHz with a resolution of 16 bits. DAT is still used in studios. A failed digital tape recording system is the Digital Compact Cassette (DCC).
In the consumer market, tapes and gramophones were largely displaced by the compact disc (CD) and a lesser extent the minidisc. These recording media are fully digital and require complex electronics to play back.
Sound files can be stored on any computer storage medium.
Mention hard disk recorder
Technique
The earliest methods of recording sound involved the live recording of the performance directly to the recording medium. This was an entirely mechanical process, often called "Acoustical recording". The sound of the performers was captured by a diaphragm with the cutting needle connect to it. The needle made the grooves in the recording medium.
To make this process as efficient as possible the diaphragm was located at the apex of a cone and the performer(s) would crowd around the other end. If a performer was too loud then they would need to move back from the mouth of the cone to avoid drowning out the other performers. As a result of this, in early Jazz recordings a block of wood was used in place of the bass drum.
The advent of electrical recording made it possible to use microphones to capture the sound of the performance. The leading record labels switched to the electric microphone process in 1925, and most other record companies followed their lead by the end of the decade. Electrical recording increased the flexibity and sound quality. However once the performance was still cut to the recording medium, so if a mistake was made the recording was useless.
Electrical recording made it possible to record one part to disc and then play that back while playing another part, recording both parts to a second disc. This is called over-dubbing. The first commercially issued records using over-dubbing were released by the Victor Talking Machine Company in the late 1920s. However overdubbing was of limited use until the advent of analogue audio tape. Use of tape overdubbing was pioneered by Les Paul and is called 'sound on sound' recording. In this way performances could be built up over time.
The analogue tape recorder made it possible to erase or record over a previous recording so that mistakes could be fixed. Another advantage of recording on tape is the ability to cut the tape and join it back together. This allows the recording to be edited. Pieces of the recording can be removed, or rearranged. See Audio editing, Audio mixing
Mention Multitrack Recording here.
The advent of electronic instruments (especially keyboardss and synthesisers), effects and other instruments has lead to the importance of MIDI in recording. For example, using MIDI timecode, it is possible to have different equipment 'trigger' without direct human intervention at the time of recording.
In more recent times, computers (digital audio workstation) have found an increasing role in the recording studio, as their use eases the tasks of cutting and looping, as well as allowing for instantaneous changes, such as duplication of parts, the addition of affects and the rearranging of parts of the recording.
See also: binaural recording, microphone technique
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Sound recording."
| The following table is compiled from various sources, across various languages. When English abbreviations or acronyms come from a non-English source, this is noted. | |||
| Entry | Source | Expression | Field |
| EQ | English | Equalizer | N/A |
Source: compiled by the editor, based on several corpora (additional references). | |||
Synonyms: EqualizerSynonyms: balance (n), counterbalance (n), counterpoise (n), counterweight (n), equaliser (n). (additional references) |
| Synonyms by domain: equaliser (electrical engineering). |
Crosswords: Equalizer |
| Specialty definitions using "equalizer": airflow-equalizing device ♦ BOTTOM-PRECIPITATOR OPERATOR, Briggs equalizer ♦ equalizer operator ♦ STAVE-BOLT EQUALIZER. (references) |
| Domain | Usage | |
Movie/TV Titles | Equalizer 2000 (1986) The Equalizer (1985) | |
Source: compiled by the editor from various references; see credits. | ||
| Domain | Title | ||
Books | |||
Periodicals |
| ||
High Tech |
| ||
Source: compiled by the editor from various references; see credits. | |||
| Thumbnail | Description & Credit |  | Equalizer. Credit: Library of Congress. |
Source: pictures compiled by the editor from various references; see picture credits. | |||
 |  |
| "Equalizer" by Carlos P. Commentary: "..." | "Eq_01" by A. Carlos Herrera Commentary: "Equalizer." |
Source: photographs selected by the editor, with permission from the photographers. | |
| Author | Quotation |
Ann Landers | Trouble is the common denominator of living. It is the great equalizer. |
Source: compiled by the editor from various references. | |
| "Equalizer" is generally used as a noun (singular) -- approximately 100.00% of the time. "Equalizer" is used about 27 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted) |
| Parts of Speech | Percent | Usage per 100 Million Words | Rank in English |
| Noun (singular) | 100% | 27 | 66,962 |
Source: compiled by the editor from several corpora; see credits.
Expressions using "equalizer": Bode equalizer ♦ sound equalizer. Additional references. | |
| Source: compiled by the editor from various references; see credits. |
| The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com. |
| Language | Translations for "equalizer"; alternative meanings/domain in parentheses. | |
Albanian | barazues tensionash, barazues. (various references) | |
Arabic | المسوي (planer), المساوي. (various references) | |
Bulgarian | уравнител (leveller), балансир (balance), пистолет (air brush, gun, pistol, shooting iron), изравнителен гол, изравнител. (various references) | |
Chinese | 调平器 (equaliser). (various references) | |
Danish | egalisator, equalizer (equaliser), modforvrænger (equaliser), balance (balance, balance sheet, balance-wheel, blend, equalizing bar, equilibrium), genskabelsesenhed (equaliser), genskabelsesudstyr (equaliser), kompensationsbalance (balance beam, compensating beam), kompenseringsdel (compensating element, equaliser), afbalanceringsanordning til tov (compensation), kompenseringsenhed (compensating element, equaliser), udligningsudstyr (equaliser), modforvraenger (equaliser), regenerator (equaliser, repeater, telephone amplifier, telephone repeater), svingstang (equalizing bar, swing bar), tobaksmaengde-regulator, udligningsenhed (equaliser), udligningsforbindelse (equaliser), udligningsledning, kompenseringselement (compensating element, equaliser). (various references) | |
Dutch | evenwichtsverbinding (equaliser), equipotentiaalverbinding (equaliser), equalizer (equaliser), egaliseer-apparaat, egalisator (equaliser), egalisatienetwerk (equaliser), effeningselement (equaliser), vereffeningscircuit (equaliser), vereffenaar (equaliser), kabelbalanceerinrichting (compensation), drukvereffeningsleiding, compenserend element (compensating element, equaliser), compensatiehefboom (balance beam, compensating beam), balanshefboom (equalizing bar), balans (balance, balance sheet, equilibrium, fly, scales). (various references) | |
Finnish | tasoitusyhdistys (equaliser), tasausjohto, tasain (balancing network, equaliser, impedance simulating network, piloted counterbore), taajuuskorjain (equaliser), korjauspiiri (equaliser), korjain (equaliser), kompensointielin (compensating element, equaliser). (various references) | |
French | connexion équipotentielle (equaliser), égalisateur de pression, égaliseur (equaliser), équilibreur (equaliser), balancier (equalizing bar), balancier compensateur, but égalisateur, égalisateur (equaliser), compensateur de phase (equaliser), revolver, correcteur (equaliser), correcteur d'affaiblissement (equaliser), correcteur de distorsions, dispositif d'égalisation des câbles, flingue, point égalisateur, redresseur, compensateur. (various references) | |
German | Entzerrer (regenerative repeater), Ausgleicher (adjuster, compensator). (various references) | |
Greek | συσκευή ισοστάθμισης (compensation), συσκευή ισομερούς κατανομής, εξισωτήσ, εξισωτής (equaliser), εξισορροπητική ράβδος (equalizing bar), εξισορροπητής (equaliser), εξομοιωτής πίεσης, αντισταθμιστική ράβδος (balance beam, compensating beam). (various references) | |
Hebrew | משוה (equator), מקזז (compensatory, counterbalancing, offsetting), שוין. (various references) | |
Hungarian | egyenlítő gól. (various references) | |
Italian | equilibratore (balancer, equaliser, moderator), equalizzatore (equaliser). (various references) | |
Japanese Kanji | イギリス帝国 (British Empire, equal, equal opportunity, equal partner, equipment, icon, iconography, igloo, ignition key, iguana, Islam, Israel, Istanbul, salmon roe). (various references) | |
Japanese Katakana | イコライザー , イコライザ . (various references) | |
Pig Latin | equalizeray.(various references) | |
Portuguese | igualador (sway-beam), compensador (compensatory, sway-beam). (various references) | |
Russian | балансир (beam, reciprocating-lever, rock bottom, sway-beam). (various references) | |
Serbo-Croatian | ekvilajzer. (various references) | |
Spanish | igualador (equaliser). (various references) | |
Swedish | utjämnare (leveller). (various references) | |
Turkish | tabanca (colt, gat, gun, heater, peashooter, persuader, pistol, pop, revolver, rod), dengeleyici (stabilizer), beraberlik golü. (various references) | |
Ukrainian | компенсатор (compensator), зрівнювач, балансир (balance, balance beam, beam, sway-beam). (various references) | |
Vietnamese | người làm cho bằng nhau, bộ cân bằng. (various references) | |
| Source: compiled by the editor from various translation references. | ||
Derivations | |
Words beginning with "equalizer": equalizers. (additional references) | |
| |
"Equalizer" is suggested in spellcheckers for the following: Aquilifer, equaline, equalister, Equiluz, nebulizer. (additional references) | |
| Source: compiled by the editor, based on several corpora (additional references). | |
| # of Phoneme Matches | Pronunciation | Word(s) rhyming with "equalizer" (pronounced ē"kwulī'zer) |
| 7 | -k w u l ī' z er | tranquilizer. |
| 5 | -u l ī' z er | analyzer, fertilizer, stabilizer, sterilizer. |
| 3 | -ī' z er | energizer, advertiser, appetizer, atomizer, colonizer, compromiser, exerciser, franchiser, ionizer, itemizer, merchandiser, moisturizer, organizer, oxidizer, plasticizer, polarizer, popularizer, supervisor, sympathizer, synthesizer, womanizer. |
Source: compiled by the editor (additional references); see credits. | ||
Scrabble® Enable2K-Verified Anagrams | |
| Words within the letters "a-e-e-i-l-q-r-u-z" | |
-1 letter: equalize, queazier. | |
-2 letters: realize, relique. | |
-3 letters: lazier, quaere, quezal. | |
-4 letters: aerie, ariel, aurei, azure, equal, laree, quail, quale, quare, queer, quire, razee, uraei, ureal, urial, zaire. | |
-5 letters: alee, aril, earl, ilea, izar, lair, lari, laze, lear, leer, liar, lier, lieu, lira, lire, lure, quai, quiz, rail, rale, raze, real, reel, rial, riel, rile, rule, urea. | |
| Words containing the letters "a-e-e-i-l-q-r-u-z" | |
+1 letter: equalizers. | |
| Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro. | |
| 1. Definition 2. Synonyms 3. Crosswords 4. Usage: Modern | 5. Usage: Commercial 6. Images: Slideshow 7. Images: Photo Album 8. Images: Digital Art | 9. Quotations: Familiar 10. Usage Frequency 11. Expressions 12. Expressions: Internet | 13. Translations: Modern 14. Abbreviations 15. Acronyms 16. Derivations | 17. Rhymes 18. Anagrams 19. Bibliography |
Copyright © Philip M. Parker, INSEAD. Terms of Use.
