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91-397: White noise is primarily a signal or sound with a flat frequency spectrum. White Noise may also refer to: White noise In discrete time , white noise is a discrete signal whose samples are regarded as a sequence of serially uncorrelated random variables with zero mean and finite variance ; a single realization of white noise is a random shock . In some contexts, it

182-614: A digital-to-analog converter . The quality of the white noise will depend on the quality of the algorithm used. The term is sometimes used as a colloquialism to describe a backdrop of ambient sound, creating an indistinct or seamless commotion. Following are some examples: The term can also be used metaphorically, as in the novel White Noise (1985) by Don DeLillo which explores the symptoms of modern culture that came together so as to make it difficult for an individual to actualize their ideas and personality. Audio synthesis A synthesizer (also synthesiser or synth )

273-443: A normal distribution with zero mean and the same variance σ 2 {\displaystyle \sigma ^{2}} , w is said to be a Gaussian white noise vector. In that case, the joint distribution of w is a multivariate normal distribution ; the independence between the variables then implies that the distribution has spherical symmetry in n -dimensional space. Therefore, any orthogonal transformation of

364-456: A normal distribution , can of course be white. It is often incorrectly assumed that Gaussian noise (i.e., noise with a Gaussian amplitude distribution – see normal distribution ) necessarily refers to white noise, yet neither property implies the other. Gaussianity refers to the probability distribution with respect to the value, in this context the probability of the signal falling within any particular range of amplitudes, while

455-649: A Gaussian white noise w {\displaystyle w} is defined as a stochastic tempered distribution, i.e. a random variable with values in the space S ′ ( R ) {\displaystyle {\mathcal {S}}'(\mathbb {R} )} of tempered distributions . Analogous to the case for finite-dimensional random vectors, a probability law on the infinite-dimensional space S ′ ( R ) {\displaystyle {\mathcal {S}}'(\mathbb {R} )} can be defined via its characteristic function (existence and uniqueness are guaranteed by an extension of

546-582: A Moog to compose a soundtrack for the televised footage of the Apollo 11 moonwalk , creating a link between electronic music and space in the American popular imagination. ARP synthesizers were used to create sound effects for the 1977 science fiction films Close Encounters of the Third Kind and Star Wars , including the "voice" of the robot R2-D2 . In the 70s and 80s, synthesizers were used in

637-461: A bestselling album of Bach compositions arranged for Moog synthesizer by Wendy Carlos , demonstrated that synthesizers could be more than "random noise machines", taking them to the mainstream. However, debates were held about the appropriateness of synthesizers in baroque music , and according to the Guardian they were quickly abandoned in "serious classical circles". Today, the synthesizer

728-449: A filter to create other types of noise signal. It is used extensively in audio synthesis , typically to recreate percussive instruments such as cymbals or snare drums which have high noise content in their frequency domain. A simple example of white noise is a nonexistent radio station (static). White noise is also used to obtain the impulse response of an electrical circuit, in particular of amplifiers and other audio equipment. It

819-413: A lack of phylogenetic pattern in comparative data. In nontechnical contexts, it is sometimes used to mean "random talk without meaningful contents". Any distribution of values is possible (although it must have zero DC component ). Even a binary signal which can only take on the values 1 or -1 will be white if the sequence is statistically uncorrelated. Noise having a continuous distribution, such as

910-470: A non-white random vector (that is, a list of random variables) whose elements have a prescribed covariance matrix . Conversely, a random vector with known covariance matrix can be transformed into a white random vector by a suitable whitening transformation . White noise may be generated digitally with a digital signal processor , microprocessor , or microcontroller . Generating white noise typically entails feeding an appropriate stream of random numbers to

1001-562: A pop staple, used on songs by A-ha , Kenny Loggins , Kool & the Gang . Its "E PIANO 1" preset became particularly famous, especially for power ballads , and was used by artists including Whitney Houston , Chicago , Prince , Phil Collins , Luther Vandross , Billy Ocean , and Celine Dion . Korg M1 presets were widely used in 1990s house music, beginning with Madonna 's 1990 single " Vogue ". Synthesizers are common in film and television soundtracks. In 1969, Mort Garson used

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1092-456: A random variable with values in R ) is said to be a white noise vector or white random vector if its components each have a probability distribution with zero mean and finite variance , and are statistically independent : that is, their joint probability distribution must be the product of the distributions of the individual components. A necessary (but, in general, not sufficient ) condition for statistical independence of two variables

1183-515: A random vector w can be defined as the expected value of the squared modulus of each coefficient of its Fourier transform W , that is, P i = E(| W i | ). Under that definition, a Gaussian white noise vector will have a perfectly flat power spectrum, with P i  =  σ for all  i . If w is a white random vector, but not a Gaussian one, its Fourier coefficients W i will not be completely independent of each other; although for large n and common probability distributions

1274-760: A random vector that is Gaussian white noise in the weak but not in the strong sense is x = [ x 1 , x 2 ] {\displaystyle x=[x_{1},x_{2}]} where x 1 {\displaystyle x_{1}} is a normal random variable with zero mean, and x 2 {\displaystyle x_{2}} is equal to + x 1 {\displaystyle +x_{1}} or to − x 1 {\displaystyle -x_{1}} , with equal probability. These two variables are uncorrelated and individually normally distributed, but they are not jointly normally distributed and are not independent. If x {\displaystyle x}

1365-702: A real-valued random variable . Also the covariance E ( w ( t 1 ) ⋅ w ( t 2 ) ) {\displaystyle \mathrm {E} (w(t_{1})\cdot w(t_{2}))} becomes infinite when t 1 = t 2 {\displaystyle t_{1}=t_{2}} ; and the autocorrelation function R ( t 1 , t 2 ) {\displaystyle \mathrm {R} (t_{1},t_{2})} must be defined as N δ ( t 1 − t 2 ) {\displaystyle N\delta (t_{1}-t_{2})} , where N {\displaystyle N}

1456-463: A second ADSR envelope. An "envelope modulation" ("env mod") parameter on many synthesizers with filter envelopes determines how much the envelope affects the filter. If turned all the way down, the filter produces a flat sound with no envelope. When turned up the envelope becomes more noticeable, expanding the minimum and maximum range of the filter. The envelope applied on the filter helps the sound designer generating long notes or short notes by moving

1547-426: A signal is heard by the human ear as a hissing sound, resembling the /h/ sound in a sustained aspiration. On the other hand, the sh sound /ʃ/ in ash is a colored noise because it has a formant structure. In music and acoustics , the term white noise may be used for any signal that has a similar hissing sound. In the context of phylogenetically based statistical methods , the term white noise can refer to

1638-442: A small study found that white noise background stimulation improves cognitive functioning among secondary students with attention deficit hyperactivity disorder (ADHD), while decreasing performance of non-ADHD students. Other work indicates it is effective in improving the mood and performance of workers by masking background office noise, but decreases cognitive performance in complex card sorting tasks. Similarly, an experiment

1729-405: A sound depending on how each module is connected to other modules by patch cables . Moog developed a means of controlling pitch through voltage , the voltage-controlled oscillator . This, along with Moog components such as envelopes , noise generators , filters , and sequencers , became standard components in synthesizers. Around the same period, the American engineer Don Buchla created

1820-589: A starting price of $ 13,000, its use was limited to universities, studios and wealthy artists. The Roland D-50 (1987) blended Roland's linear arithmetic algorithm with samples, and was the first mass-produced synthesizer with built-in digital effects such as delay , reverb and chorus . In 1988, the Japanese manufacturer Korg released the M1 , a digital synthesizer workstation featuring sampled transients and loops . With more than 250,000 units sold, it remains

1911-588: A synthesized melody. Soft Cell used a synthesized melody on their 1981 hit " Tainted Love ". Nick Rhodes , keyboardist of Duran Duran , used synthesizers including the Roland Jupiter-4 and Jupiter-8 . Chart hits include Depeche Mode 's " Just Can't Get Enough " (1981), the Human League 's " Don't You Want Me " and works by Ultravox . In the 1980s, digital synthesizers were widely used in pop music. The Yamaha DX7, released in 1983, became

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2002-510: A wave of new software instruments. Propellerhead's Reason , released in 2000, introduced an array of recognizable virtual studio equipment. The market for patchable and modular synthesizers rebounded in the late 1990s. In the 2000s, older analog synthesizers regained popularity, sometimes selling for much more than their original prices. In the 2010s, new, affordable analog synthesizers were introduced by companies including Moog, Korg, Arturia and Dave Smith Instruments . The renewed interest

2093-447: Is r σ 2 {\displaystyle r\sigma ^{2}} , where r {\displaystyle r} is the width of the intersection I ∩ J {\displaystyle I\cap J} of the two intervals I , J {\displaystyle I,J} . This model is called a Gaussian white noise signal (or process). In the mathematical field known as white noise analysis ,

2184-458: Is a preamp that boosts (amplifies) the electronic signal before passing it on to an external or built-in power amplifier, as well as a means to control its amplitude (volume) using an attenuator . The gain of the VCA is affected by a control voltage (CV), coming from an envelope generator, an LFO, the keyboard or some other source. Voltage-controlled filters (VCFs) "shape" the sound generated by

2275-428: Is a common synthetic noise source used for sound masking by a tinnitus masker . White noise machines and other white noise sources are sold as privacy enhancers and sleep aids (see music and sleep ) and to mask tinnitus . The Marpac Sleep-Mate was the first domestic use white noise machine built in 1962 by traveling salesman Jim Buckwalter. Alternatively, the use of an AM radio tuned to unused frequencies ("static")

2366-772: Is a random variable that is statistically independent of its entire history before t {\displaystyle t} . A weaker definition requires independence only between the values w ( t 1 ) {\displaystyle w(t_{1})} and w ( t 2 ) {\displaystyle w(t_{2})} at every pair of distinct times t 1 {\displaystyle t_{1}} and t 2 {\displaystyle t_{2}} . An even weaker definition requires only that such pairs w ( t 1 ) {\displaystyle w(t_{1})} and w ( t 2 ) {\displaystyle w(t_{2})} be uncorrelated. As in

2457-494: Is a real random variable with normal distribution, zero mean, and variance ( b − a ) σ 2 {\displaystyle (b-a)\sigma ^{2}} ; and also that the covariance E ( W I ⋅ W J ) {\displaystyle \mathrm {E} (W_{I}\cdot W_{J})} of the integrals W I {\displaystyle W_{I}} , W J {\displaystyle W_{J}}

2548-538: Is a simpler and more cost-effective source of white noise. However, white noise generated from a common commercial radio receiver tuned to an unused frequency is extremely vulnerable to being contaminated with spurious signals, such as adjacent radio stations, harmonics from non-adjacent radio stations, electrical equipment in the vicinity of the receiving antenna causing interference, or even atmospheric events such as solar flares and especially lightning. The effects of white noise upon cognitive function are mixed. Recently,

2639-502: Is also required that the samples be independent and have identical probability distribution (in other words independent and identically distributed random variables are the simplest representation of white noise). In particular, if each sample has a normal distribution with zero mean, the signal is said to be additive white Gaussian noise . The samples of a white noise signal may be sequential in time, or arranged along one or more spatial dimensions. In digital image processing ,

2730-429: Is also true if the noise is heteroskedastic  – that is, if it has different variances for different data points. Alternatively, in the subset of regression analysis known as time series analysis there are often no explanatory variables other than the past values of the variable being modeled (the dependent variable ). In this case the noise process is often modeled as a moving average process, in which

2821-746: Is an electronic musical instrument that generates audio signals . Synthesizers typically create sounds by generating waveforms through methods including subtractive synthesis , additive synthesis and frequency modulation synthesis . These sounds may be altered by components such as filters , which cut or boost frequencies ; envelopes , which control articulation , or how notes begin and end; and low-frequency oscillators , which modulate parameters such as pitch, volume, or filter characteristics affecting timbre . Synthesizers are typically played with keyboards or controlled by sequencers , software or other instruments, and may be synchronized to other equipment via MIDI . Synthesizer-like instruments emerged in

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2912-641: Is as important, and as ubiquitous, in modern music today as the human voice." As electricity became more widely available, the early 20th century saw the invention of electronic musical instruments including the Telharmonium , Trautonium , Ondes Martenot , and theremin . In the late 1930s, the Hammond Organ Company built the Novachord , a large instrument powered by 72 voltage-controlled amplifiers and 146 vacuum tubes . In 1948,

3003-411: Is credited to the appeal of imperfect "organic" sounds and simpler interfaces, and modern surface-mount technology making analog synthesizers cheaper and faster to manufacture. Early synthesizers were viewed as avant-garde , valued by the 1960s psychedelic and counter-cultural scenes for their ability to make new sounds, but with little perceived commercial potential. Switched-On Bach (1968) ,

3094-402: Is limited in practice by the mechanism of noise generation, by the transmission medium and by finite observation capabilities. Thus, random signals are considered white noise if they are observed to have a flat spectrum over the range of frequencies that are relevant to the context. For an audio signal , the relevant range is the band of audible sound frequencies (between 20 and 20,000 Hz ). Such

3185-515: Is non-zero. Hypothesis testing typically assumes that the noise values are mutually uncorrelated with zero mean and have the same Gaussian probability distribution – in other words, that the noise is Gaussian white (not just white). If there is non-zero correlation between the noise values underlying different observations then the estimated model parameters are still unbiased , but estimates of their uncertainties (such as confidence intervals ) will be biased (not accurate on average). This

3276-505: Is not used for testing loudspeakers as its spectrum contains too great an amount of high-frequency content. Pink noise , which differs from white noise in that it has equal energy in each octave, is used for testing transducers such as loudspeakers and microphones. White noise is used as the basis of some random number generators . For example, Random.org uses a system of atmospheric antennas to generate random digit patterns from sources that can be well-modeled by white noise. White noise

3367-449: Is one of the most important instruments in the music industry, used in nearly every genre. It is considered by the authors of Analog Days as "the only innovation that can stand alongside the electric guitar as a great new instrument of the age of electricity ... Both led to new forms of music, and both had massive popular appeal." According to Fact in 2016, "The synthesizer is as important, and as ubiquitous, in modern music today as

3458-544: Is rotated by 45 degrees, its two components will still be uncorrelated, but their distribution will no longer be normal. In some situations, one may relax the definition by allowing each component of a white random vector w {\displaystyle w} to have non-zero expected value μ {\displaystyle \mu } . In image processing especially, where samples are typically restricted to positive values, one often takes μ {\displaystyle \mu } to be one half of

3549-449: Is some real constant and δ {\displaystyle \delta } is the Dirac delta function . In this approach, one usually specifies that the integral W I {\displaystyle W_{I}} of w ( t ) {\displaystyle w(t)} over an interval I = [ a , b ] {\displaystyle I=[a,b]}

3640-446: Is that they be statistically uncorrelated ; that is, their covariance is zero. Therefore, the covariance matrix R of the components of a white noise vector w with n elements must be an n by n diagonal matrix , where each diagonal element R ii is the variance of component w i ; and the correlation matrix must be the n by n identity matrix. If, in addition to being independent, every variable in w also has

3731-576: Is the ADSR (attack, decay, sustain, release) envelope: Low-frequency oscillators (LFOs) produce waveforms used to modulate parameters, such as the pitch of oscillators (producing vibrato ). Arpeggiators, included in many synthesizer models, take input chords and convert them into arpeggios . They usually include controls for speed, range and mode (the movement of the arpeggio). Synthesizers are often controlled with electronic or digital keyboards or MIDI controller keyboards, which may be built into

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3822-780: Is the natural pairing of the tempered distribution w ( ω ) {\displaystyle w(\omega )} with the Schwartz function φ {\displaystyle \varphi } , taken scenariowise for ω ∈ Ω {\displaystyle \omega \in \Omega } , and ‖ φ ‖ 2 2 = ∫ R | φ ( x ) | 2 d x {\displaystyle \|\varphi \|_{2}^{2}=\int _{\mathbb {R} }\vert \varphi (x)\vert ^{2}\,\mathrm {d} x} . In statistics and econometrics one often assumes that an observed series of data values

3913-424: Is the sum of the values generated by a deterministic linear process , depending on certain independent (explanatory) variables , and on a series of random noise values. Then regression analysis is used to infer the parameters of the model process from the observed data, e.g. by ordinary least squares , and to test the null hypothesis that each of the parameters is zero against the alternative hypothesis that it

4004-574: The American Federation of Musicians (AFM). Robert Moog felt that the AFM had not realized that his instrument had to be studied like any other, and instead imagined that "all the sounds that musicians could make somehow existed in the Moog — all you had to do was push a button that said ' Jascha Heifetz ' and out would come the most fantastic violin player". The musician Walter Sear persuaded

4095-528: The Buchla Modular Electronic Music System . Instead of a conventional keyboard , Buchla's system used touchplates which transmitted control voltages depending on finger position and force. However, the Moog's keyboard made it more accessible and marketable to musicians, and keyboards became the standard means of controlling synthesizers. Moog and Buchla initially avoided the word synthesizer for their instruments, as it

4186-702: The OB-X (1979). In 1978, the American company Sequential Circuits released the Prophet-5 , the first fully programmable polyphonic synthesizer. Whereas previous synthesizers required users to adjust cables and knobs to change sounds, with no guarantee of exactly recreating a sound, the Prophet-5 used microprocessors to store sounds in patch memory. This facilitated a move from synthesizers creating unpredictable sounds to producing "a standard package of familiar sounds". The synthesizer market grew dramatically in

4277-631: The Roland TR-808 and TR-909 drum machines, became a foundation of electronic dance music genres such as house and techno when producers acquired cheap second-hand units later in the decade. The authors of Analog Days connect the synthesizer's origins in 1960s psychedelia to the raves and British " second summer of love " of the 1980s and the club scenes of the 1990s and 2000s. Gary Numan's 1979 hits " Are 'Friends' Electric? " and " Cars " made heavy use of synthesizers. OMD 's " Enola Gay " (1980) used distinctive electronic percussion and

4368-423: The pixels of a white noise image are typically arranged in a rectangular grid, and are assumed to be independent random variables with uniform probability distribution over some interval. The concept can be defined also for signals spread over more complicated domains, such as a sphere or a torus . An infinite-bandwidth white noise signal is a purely theoretical construction. The bandwidth of white noise

4459-525: The 1980s. 1982 saw the introduction of MIDI , a standardized means of synchronizing electronic instruments; it remains an industry standard. An influential sampling synthesizer , the Fairlight CMI , was released in 1979, with the ability to record and play back samples at different pitches. Though its high price made it inaccessible to amateurs, it was adopted by high-profile pop musicians including Kate Bush and Peter Gabriel . The success of

4550-409: The 21st century, analog synthesizers returned to popularity with the advent of cheaper manufacturing. Synthesizers were initially viewed as avant-garde , valued by the 1960s psychedelic and countercultural scenes but with little perceived commercial potential. Switched-On Bach (1968) , a bestselling album of Bach compositions arranged for synthesizer by Wendy Carlos , took synthesizers to

4641-482: The AFM that the synthesizer demanded skill, and the category of "synthesizer player" was accepted into the union/ However, players were subject to "suspicion and hostility" for years. In 1982, following a tour by Barry Manilow using synthesizers instead of an orchestra, the British Musicians' Union attempted to ban synthesizers, attracting controversy. That decade, a few musicians skilled at programming

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4732-717: The Bochner–Minlos theorem, which goes under the name Bochner–Minlos–Sazanov theorem); analogously to the case of the multivariate normal distribution X ∼ N n ( μ , Σ ) {\displaystyle X\sim {\mathcal {N}}_{n}(\mu ,\Sigma )} , which has characteristic function the white noise w : Ω → S ′ ( R ) {\displaystyle w:\Omega \to {\mathcal {S}}'(\mathbb {R} )} must satisfy where ⟨ w , φ ⟩ {\displaystyle \langle w,\varphi \rangle }

4823-707: The Canadian engineer Hugh Le Caine completed the electronic sackbut , a precursor to voltage-controlled synthesizers , with keyboard sensitivity allowing for vibrato , glissando , and attack control. In 1957, Harry Olson and Herbert Belar completed the RCA Mark II Sound Synthesizer at the RCA laboratories in Princeton, New Jersey. The instrument read punched paper tape that controlled an analog synthesizer containing 750 vacuum tubes. It

4914-763: The Fairlight drove competition, improving sampling technology and lowering prices. Early competing samplers included the E-mu Emulator in 1981 and the Akai S-series in 1985. In 1983, Yamaha released the first commercially successful digital synthesizer , the Yamaha DX7 . Based on frequency modulation (FM) synthesis developed by the Stanford University engineer John Chowning , the DX7

5005-824: The Minimoog, Pro-One , and TB-303 , and drum machines such as the TR-808 . Other synthesizer clones include the MiniMOD (a series of Eurorack modules based on the Minimoog), the Intellijel Atlantis (based on the SH-101 ), and the x0x Heart (based on the TB-303). Creating clones of older hardware is legal where the patents have expired. In 1997, Mackie lost their lawsuit against Behringer as copyright law in

5096-622: The United States in the mid-20th century with instruments such as the RCA Mark II , which was controlled with punch cards and used hundreds of vacuum tubes . The Moog synthesizer , developed by Robert Moog and first sold in 1964, is credited for pioneering concepts such as voltage-controlled oscillators , envelopes, noise generators , filters, and sequencers. In 1970, the smaller, cheaper Minimoog standardized synthesizers as self-contained instruments with built-in keyboards, unlike

5187-489: The Yamaha DX7 found employment creating sounds for other acts. Synthesizers generate audio through various forms of analog and digital synthesis. Oscillators produce waveforms (such as sawtooth , sine , or pulse waves ) with different timbres . Voltage-controlled amplifiers (VCAs) control the volume or gain of the audio signal. VCAs can be modulated by other components, such as LFOs and envelopes. A VCA

5278-478: The amateur electronics market, such as a design published in Practical Electronics in 1973. By the mid-1970s, ARP was the world's largest synthesizer manufacturer, though it closed in 1981. Early synthesizers were monophonic , meaning they could only play one note at a time. Some of the earliest commercial polyphonic synthesizers were created by the American engineer Tom Oberheim , such as

5369-502: The autocorrelation function R W ( n ) = E ⁡ [ W ( k + n ) W ( k ) ] {\displaystyle R_{W}(n)=\operatorname {E} [W(k+n)W(k)]} has a nonzero value only for n = 0 {\displaystyle n=0} , i.e. R W ( n ) = σ 2 δ ( n ) {\displaystyle R_{W}(n)=\sigma ^{2}\delta (n)} . In order to define

5460-472: The bestselling synthesizer in history. The advent of digital synthesizers led to a downturn in interest in analog synthesizers in the following decade. 1997 saw the release of ReBirth by Propellerhead Software and Reality by Seer Systems , the first software synthesizers that could be played in real time via MIDI. In 1999, an update to the music software Cubase allowed users to run software instruments (including synthesizers) as plug-ins , triggering

5551-534: The covariance E ( w ( t 1 ) ⋅ w ( t 2 ) ) {\displaystyle \mathrm {E} (w(t_{1})\cdot w(t_{2}))} between the values at two times t 1 {\displaystyle t_{1}} and t 2 {\displaystyle t_{2}} is well-defined: it is zero if the times are distinct, and σ 2 {\displaystyle \sigma ^{2}} if they are equal. However, by this definition,

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5642-431: The current value of the dependent variable depends on current and past values of a sequential white noise process. These two ideas are crucial in applications such as channel estimation and channel equalization in communications and audio . These concepts are also used in data compression . In particular, by a suitable linear transformation (a coloring transformation ), a white random vector can be used to produce

5733-548: The dependencies are very subtle, and their pairwise correlations can be assumed to be zero. Often the weaker condition statistically uncorrelated is used in the definition of white noise, instead of statistically independent. However, some of the commonly expected properties of white noise (such as flat power spectrum) may not hold for this weaker version. Under this assumption, the stricter version can be referred to explicitly as independent white noise vector. Other authors use strongly white and weakly white instead. An example of

5824-431: The discrete case, some authors adopt the weaker definition for white noise, and use the qualifier independent to refer to either of the stronger definitions. Others use weakly white and strongly white to distinguish between them. However, a precise definition of these concepts is not trivial, because some quantities that are finite sums in the finite discrete case must be replaced by integrals that may not converge. Indeed,

5915-450: The emergence of synth-pop from the late 1970s to the early 1980s. The work of German krautrock bands such as Kraftwerk and Tangerine Dream , British acts such as John Foxx , Gary Numan and David Bowie , African-American acts such as George Clinton and Zapp , and Japanese electronic acts such as Yellow Magic Orchestra and Kitaro were influential in the development of the genre. The Roland TB-303 (1981), in conjunction with

6006-744: The first string synthesizer , designed to emulate string sections . After retail stores started selling synthesizers in 1971, other synthesizer companies were established, including ARP in the US and EMS in the UK. ARP's products included the ARP 2600 , which folded into a carrying case and had built-in speakers, and the Odyssey , a rival to the Minimoog. The less expensive EMS synthesizers were used by European art rock and progressive rock acts including Brian Eno and Pink Floyd . Designs for synthesizers appeared in

6097-577: The heads of a drum kit ; touchplates, which send signals depending on finger position and force; controllers designed for microtonal tunings ; touchscreen devices such as tablets and smartphones ; and fingerpads. Synthesizer clones are unlicensed recreations of previous synthesizers, often marketed as affordable versions of famous musical equipment. Clones are available as physical instruments and software. Companies that have sold software clones include Arturia and Native Instruments . Behringer manufactures equipment modelled on instruments including

6188-664: The human voice." The Moog was adopted by 1960s rock acts including the Doors , the Grateful Dead , the Rolling Stones , the Beatles , and Keith Emerson . Emerson was the first major rock musician to perform with the Moog and it became a trademark of his performances, helping take his band Emerson, Lake & Palmer to global stardom. According to Analog Days , the likes of Emerson, with his Moog performances, "did for

6279-469: The integral over any interval with positive width r {\displaystyle r} would be simply the width times the expectation: r μ {\displaystyle r\mu } . This property renders the concept inadequate as a model of white noise signals either in a physical or mathematical sense. Therefore, most authors define the signal w {\displaystyle w} indirectly by specifying random values for

6370-432: The integrals of w ( t ) {\displaystyle w(t)} and | w ( t ) | 2 {\displaystyle |w(t)|^{2}} over each interval [ a , a + r ] {\displaystyle [a,a+r]} . In this approach, however, the value of w ( t ) {\displaystyle w(t)} at an isolated time cannot be defined as

6461-466: The keyboard what Jimi Hendrix did for the guitar". String synthesizers were used by 1970s progressive rock bands including Camel , Caravan , Electric Light Orchestra , Gentle Giant and Renaissance . The portable Minimoog (1970), much smaller than the modular synthesizers before it, made synthesizers more common in live performance. Early synthesizers could only play one note at a time , making them suitable for basslines, leads and solos. With

6552-489: The larger modular synthesizers before it. In 1978, Sequential Circuits released the Prophet-5 , which used microprocessors to allow users to store sounds for the first time. MIDI, a standardized means of synchronizing electronic instruments, was introduced in 1982 and remains an industry standard. The Yamaha DX7 , launched in 1983, was a major success and popularized digital synthesis . Software synthesizers now can be run as plug-ins or embedded on microchips . In

6643-508: The mainstream. They were adopted by electronic acts and pop and rock groups in the 1960s and 1970s and were widely used in 1980s music. Sampling , introduced with the Fairlight synthesizer in 1979, has influenced genres such as electronic and hip hop music. Today, the synthesizer is used in nearly every genre of music and is considered one of the most important instruments in the music industry. According to Fact in 2016, "The synthesizer

6734-539: The maximum sample value. In that case, the Fourier coefficient W 0 {\displaystyle W_{0}} corresponding to the zero-frequency component (essentially, the average of the w i {\displaystyle w_{i}} ) will also have a non-zero expected value μ n {\displaystyle \mu {\sqrt {n}}} ; and the power spectrum P {\displaystyle P} will be flat only over

6825-575: The non-zero frequencies. A discrete-time stochastic process W ( n ) {\displaystyle W(n)} is a generalization of a random vector with a finite number of components to infinitely many components. A discrete-time stochastic process W ( n ) {\displaystyle W(n)} is called white noise if its mean is equal to zero for all n {\displaystyle n} , i.e. E ⁡ [ W ( n ) ] = 0 {\displaystyle \operatorname {E} [W(n)]=0} and if

6916-519: The notion of white noise in the theory of continuous-time signals, one must replace the concept of a random vector by a continuous-time random signal; that is, a random process that generates a function w {\displaystyle w} of a real-valued parameter t {\displaystyle t} . Such a process is said to be white noise in the strongest sense if the value w ( t ) {\displaystyle w(t)} for any time t {\displaystyle t}

7007-521: The oscillators in the frequency domain, often under the control of an envelope or LFO. These are essential to subtractive synthesis. Filters are particularly important in subtractive synthesis , being designed to pass some frequency regions (or "bands") through unattenuated while significantly attenuating ("subtracting") others. The low-pass filter is most frequently used, but band-pass filters , band-reject filters and high-pass filters are also sometimes available. The filter may be controlled with

7098-423: The parameters up and down such as decay, sustain and finally release. For instance by using a short decay with no sustain, the sound generated is commonly known as a stab . Sound designers may prefer shaping the sound with a filter instead of volume. Envelopes control how sounds change over time. They may control parameters such as amplitude (volume), filters (frequencies), or pitch. The most common envelope

7189-450: The rise of polyphonic synthesizers in the 70s and 80s, "the keyboard in rock once more started to revert to the background, to be used for fills and atmosphere rather than for soloing". Some acts felt that using synthesizers was "cheating"; Queen wrote in their album liner notes that they did not use them. The Minimoog took a place in mainstream African-American music , most notably in the work of Stevie Wonder , and in jazz , such as

7280-550: The scores for thrillers and horror films including A Clockwork Orange (1971), Apocalypse Now (1979), The Fog (1980) and Manhunter (1986). Brad Fiedel used a Prophet synthesizer to record the soundtrack for The Terminator (1984), and the filmmaker John Carpenter used them extensively for his soundtracks. Synthesizers were used to create themes for television shows including Knight Rider (1982) , Twin Peaks (1990) and Stranger Things (2016). The rise of

7371-425: The set of all possible instances of a signal w {\displaystyle w} is no longer a finite-dimensional space R n {\displaystyle \mathbb {R} ^{n}} , but an infinite-dimensional function space . Moreover, by any definition a white noise signal w {\displaystyle w} would have to be essentially discontinuous at every point; therefore even

7462-473: The simplest operations on w {\displaystyle w} , like integration over a finite interval, require advanced mathematical machinery. Some authors require each value w ( t ) {\displaystyle w(t)} to be a real-valued random variable with expectation μ {\displaystyle \mu } and some finite variance σ 2 {\displaystyle \sigma ^{2}} . Then

7553-399: The synthesizer led to major changes in music industry jobs, comparable to the earlier arrival of sound in film , which put live musicians accompanying silent films out of work. With its ability to imitate instruments such as strings and horns, the synthesizer threatened the jobs of session musicians . For a period, the Moog was banned from use in commercial work, a restriction negotiated by

7644-509: The synthesizer unit or attached via connections such as CV/gate , USB , or MIDI . Keyboards may offer expression such as velocity sensitivity and aftertouch, allowing for more control over the sound. Other controllers include ribbon controllers , which track the movement of the finger across a touch-sensitive surface; wind controllers , played similarly to woodwind instruments ; motion-sensitive controllers similar to video game motion controllers ; electronic drum pads , played similarly to

7735-528: The term 'white' refers to the way the signal power is distributed (i.e., independently) over time or among frequencies. One form of white noise is the generalized mean-square derivative of the Wiener process or Brownian motion . A generalization to random elements on infinite dimensional spaces, such as random fields , is the white noise measure . White noise is commonly used in the production of electronic music , usually either directly or as an input for

7826-449: The vector will result in a Gaussian white random vector. In particular, under most types of discrete Fourier transform , such as FFT and Hartley , the transform W of w will be a Gaussian white noise vector, too; that is, the n Fourier coefficients of w will be independent Gaussian variables with zero mean and the same variance σ 2 {\displaystyle \sigma ^{2}} . The power spectrum P of

7917-519: The work of Sun Ra . In the late 1970s and the early 1980s, the Minimoog was widely used in the emerging disco genre by artists including Abba and Giorgio Moroder . Sampling, introduced with the Fairlight synthesizer in 1979, has influenced all genres of music and had a major influence on the development of electronic and hip hop music. In the 1970s, electronic music composers such as Jean Michel Jarre and Isao Tomita released successful synthesizer-led instrumental albums. This influenced

8008-667: Was acquired by the Columbia-Princeton Electronic Music Center and used almost exclusively by Milton Babbitt , a composer at Princeton University . The authors of Analog Days define "the early years of the synthesizer" as between 1964 and the mid-1970s, beginning with the debut of the Moog synthesizer . Designed by the American engineer Robert Moog , the instrument was a modular synthesizer system composed of numerous separate electronic modules, each capable of generating, shaping, or controlling

8099-596: Was associated with the RCA synthesizer; however, by the 1970s, it had become the standard term. In 1970, Moog launched a cheaper, smaller synthesizer, the Minimoog . It was the first synthesizer sold in music stores, and was more practical for live performance. It standardized the concept of synthesizers as self-contained instruments with built-in keyboards. In the early 1970s, the British composer Ken Freeman introduced

8190-496: Was carried out on sixty-six healthy participants to observe the benefits of using white noise in a learning environment. The experiment involved the participants identifying different images whilst having different sounds in the background. Overall the experiment showed that white noise does in fact have benefits in relation to learning. The experiments showed that white noise improved the participants' learning abilities and their recognition memory slightly. A random vector (that is,

8281-559: Was characterized by its "harsh", "glassy" and "chilly" sounds, compared to the "warm" and "fuzzy" sounds of analog synthesis. The DX7 was the first synthesizer to sell more than 100,000 units and remains one of the bestselling in history. It was widely used in 1980s pop music. Digital synthesizers typically contained preset sounds emulating acoustic instruments, with algorithms controlled with menus and buttons. The Synclavier , made with FM technology licensed from Yamaha, offered features such as 16-bit sampling and digital recording. With

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