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86-399: Four rubber rectangular pads connected to a main module with one oscillator producing pulse and sawtooth waveforms. It also had a white noise generator, Low Frequency Oscillator (LFO) with triangle and pulse waveforms, a mixer and a low-pass filter with Resonance and Cutoff controls. It also had an envelope generator with attack, decay, sustain, and release. Made from 1975 to 1981. This model

172-574: 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. Pixel In digital imaging ,

258-412: A native resolution , and it should (ideally) be matched to the video card resolution. Each pixel is made up of triads , with the number of these triads determining the native resolution. On older, historically available, CRT monitors the resolution was possibly adjustable (still lower than what modern monitor achieve), while on some such monitors (or TV sets) the beam sweep rate was fixed, resulting in

344-411: A pixel (abbreviated px ), pel , or picture element is the smallest addressable element in a raster image , or the smallest addressable element in a dot matrix display device . In most digital display devices , pixels are the smallest element that can be manipulated through software. Each pixel is a sample of an original image; more samples typically provide more accurate representations of

430-545: A regular two-dimensional grid . By using this arrangement, many common operations can be implemented by uniformly applying the same operation to each pixel independently. Other arrangements of pixels are possible, with some sampling patterns even changing the shape (or kernel ) of each pixel across the image. For this reason, care must be taken when acquiring an image on one device and displaying it on another, or when converting image data from one pixel format to another. For example: Computer monitors (and TV sets) generally have

516-412: A sphere or a torus . An infinite-bandwidth white noise signal is a purely theoretical construction. The bandwidth of white noise 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

602-548: A "pixel" may refer to a fixed length rather than a true pixel on the screen to accommodate different pixel densities . A typical definition, such as in CSS , is that a "physical" pixel is 1 ⁄ 96 inch (0.26 mm). Doing so makes sure a given element will display as the same size no matter what screen resolution views it. There may, however, be some further adjustments between a "physical" pixel and an on-screen logical pixel. As screens are viewed at difference distances (consider

688-649: 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

774-425: 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 the dependencies are very subtle, and their pairwise correlations can be assumed to be zero. Often

860-480: A display device, or pixels in a digital camera (photosensor elements). This list is not exhaustive and, depending on context, synonyms include pel, sample, byte, bit, dot, and spot. Pixels can be used as a unit of measure such as: 2400 pixels per inch, 640 pixels per line, or spaced 10 pixels apart. The measures " dots per inch " (dpi) and " pixels per inch " (ppi) are sometimes used interchangeably, but have distinct meanings, especially for printer devices, where dpi

946-466: A distance. In some displays, such as LCD, LED, and plasma displays, these single-color regions are separately addressable elements, which have come to be known as subpixels , mostly RGB colors. For example, LCDs typically divide each pixel vertically into three subpixels. When the square pixel is divided into three subpixels, each subpixel is necessarily rectangular. In display industry terminology, subpixels are often referred to as pixels , as they are

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1032-450: A fixed native resolution . What it is depends on the monitor, and size. See below for historical exceptions. Computers can use pixels to display an image, often an abstract image that represents a GUI . The resolution of this image is called the display resolution and is determined by the video card of the computer. Flat-panel monitors (and TV sets), e.g. OLED or LCD monitors, or E-ink , also use pixels to display an image, and have

1118-426: A fixed native resolution. Most CRT monitors do not have a fixed beam sweep rate, meaning they do not have a native resolution at all – instead they have a set of resolutions that are equally well supported. To produce the sharpest images possible on an flat-panel, e.g. OLED or LCD, the user must ensure the display resolution of the computer matches the native resolution of the monitor. The pixel scale used in astronomy

1204-557: A low-pass filter with cutoff, resonance and decay controls and was manufactured from 1977 to 1982. Virtually the same machine as its predecessor, but with more flexible modulation controls. Manufactured during the same time as the Synare 3. Very similar to its predecessor, but with an actual drumhead rather than a rubber pad. Had modulation route and depth controls. Made from approximately 1979–1983. Very rare. Can be seen in video of " Love Don't Live Here Anymore " by Rose Royce . Variant of

1290-453: A measured intensity level. In most digital cameras, the sensor array is covered with a patterned color filter mosaic having red, green, and blue regions in the Bayer filter arrangement so that each sensor element can record the intensity of a single primary color of light. The camera interpolates the color information of neighboring sensor elements, through a process called demosaicing , to create

1376-470: 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

1462-471: A phone, a computer display, and a TV), the desired length (a "reference pixel") is scaled relative to a reference viewing distance (28 inches (71 cm) in CSS). In addition, as true screen pixel densities are rarely multiples of 96 dpi, some rounding is often applied so that a logical pixel is an integer amount of actual pixels. Doing so avoids render artifacts. The final "pixel" obtained after these two steps becomes

1548-760: 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}

1634-702: 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}

1720-411: A separate parameter. A major improvement over the Synare 1 was the introduction of a fairly advanced sequencer with multiple patterns, and the ability to change patterns and octaves on the fly. This model also featured twelve pads rather than the four of the Synare 1. The retail price in 1976 was $ 1,395.00, and as a result the Synare 2 remains a very rare item. Noted for its flying saucer appearance, this

1806-410: A similar hissing sound. In the context of phylogenetically based statistical methods , the term white noise can refer to 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

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1892-449: A single realization of white noise is a random shock . In some contexts, it 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

1978-426: A statistical model for signals and signal sources, not to any specific signal. White noise draws its name from white light , although light that appears white generally does not have a flat power spectral density over the visible band . 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 ;

2064-588: A total number of 640 × 480 = 307,200 pixels, or 0.3 megapixels. The pixels, or color samples, that form a digitized image (such as a JPEG file used on a web page) may or may not be in one-to-one correspondence with screen pixels, depending on how a computer displays an image. In computing, an image composed of pixels is known as a bitmapped image or a raster image . The word raster originates from television scanning patterns, and has been widely used to describe similar halftone printing and storage techniques. For convenience, pixels are normally arranged in

2150-413: A white noise signal may be sequential in time, or arranged along one or more spatial dimensions. In digital image processing , 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

2236-447: 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 ,

2322-441: 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 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,

2408-409: Is a measure of the printer's density of dot (e.g. ink droplet) placement. For example, a high-quality photographic image may be printed with 600 ppi on a 1200 dpi inkjet printer. Even higher dpi numbers, such as the 4800 dpi quoted by printer manufacturers since 2002, do not mean much in terms of achievable resolution . The more pixels used to represent an image, the closer the result can resemble

2494-468: 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 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

2580-772: 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

2666-494: 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}}

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2752-429: 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

2838-403: Is available: this means that each 24-bit pixel has an extra 8 bits to describe its opacity (for purposes of combining with another image). Many display and image-acquisition systems are not capable of displaying or sensing the different color channels at the same site. Therefore, the pixel grid is divided into single-color regions that contribute to the displayed or sensed color when viewed at

2924-419: 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 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

3010-515: 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

3096-430: Is often used instead of pixel . For example, IBM used it in their Technical Reference for the original PC . Pixilation , spelled with a second i , is an unrelated filmmaking technique that dates to the beginnings of cinema, in which live actors are posed frame by frame and photographed to create stop-motion animation. An archaic British word meaning "possession by spirits ( pixies )", the term has been used to describe

3182-544: 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

3268-445: 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]}

3354-461: Is sometimes used), while in yet other contexts (like MRI) it may refer to a set of component intensities for a spatial position. Software on early consumer computers was necessarily rendered at a low resolution, with large pixels visible to the naked eye; graphics made under these limitations may be called pixel art , especially in reference to video games. Modern computers and displays, however, can easily render orders of magnitude more pixels than

3440-411: 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 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

3526-407: Is the white noise measure . White noise is commonly used in the production of electronic music , usually either directly or as an input for 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

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3612-630: Is the angular distance between two objects on the sky that fall one pixel apart on the detector (CCD or infrared chip). The scale s measured in radians is the ratio of the pixel spacing p and focal length f of the preceding optics, s = p / f . (The focal length is the product of the focal ratio by the diameter of the associated lens or mirror.) Because s is usually expressed in units of arcseconds per pixel, because 1 radian equals (180/π) × 3600 ≈ 206,265 arcseconds, and because focal lengths are often given in millimeters and pixel sizes in micrometers which yields another factor of 1,000,

3698-775: 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

3784-424: 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

3870-475: 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 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

3956-565: The Sigma 35 mm f/1.4 DG HSM lens mounted on a Nikon D800 has the highest measured P-MPix. However, with a value of 23 MP, it still wipes off more than one-third of the D800's 36.3 MP sensor. In August 2019, Xiaomi released the Redmi Note 8 Pro as the world's first smartphone with 64 MP camera. On December 12, 2019 Samsung released Samsung A71 that also has a 64 MP camera. In late 2019, Xiaomi announced

4042-410: 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 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,

4128-410: The "anchor" to which all other absolute measurements (e.g. the "centimeter") are based on. Worked example, with a 30-inch (76 cm) 2160p TV placed 56 inches (140 cm) away from the viewer: A browser will then choose to use the 1.721× pixel size, or round to a 2× ratio. A megapixel ( MP ) is a million pixels; the term is used not only for the number of pixels in an image but also to express

4214-436: The "total" pixel count. The number of pixels is sometimes quoted as the "resolution" of a photo. This measure of resolution can be calculated by multiplying the width and height of a sensor in pixels. Digital cameras use photosensitive electronics, either charge-coupled device (CCD) or complementary metal–oxide–semiconductor (CMOS) image sensors, consisting of a large number of single sensor elements, each of which records

4300-717: 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 }

4386-556: The Synare 4. A small box that could be mounted to the rim of a drum on a drumset. One VCO that could be pitch modulated by an LFO and an envelope generator. White noise In signal processing , white noise is a random signal having equal intensity at different frequencies , giving it a constant power spectral density . The term is used with this or similar meanings in many scientific and technical disciplines, including physics , acoustical engineering , telecommunications , and statistical forecasting . White noise refers to

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4472-662: The allocation of the primary colors (green has twice as many elements as red or blue in the Bayer arrangement). DxO Labs invented the Perceptual MegaPixel (P-MPix) to measure the sharpness that a camera produces when paired to a particular lens – as opposed to the MP a manufacturer states for a camera product, which is based only on the camera's sensor. The new P-MPix claims to be a more accurate and relevant value for photographers to consider when weighing up camera sharpness. As of mid-2013,

4558-433: The animation process since the early 1950s; various animators, including Norman McLaren and Grant Munro , are credited with popularizing it. A pixel is generally thought of as the smallest single component of a digital image . However, the definition is highly context-sensitive. For example, there can be " printed pixels " in a page, or pixels carried by electronic signals, or represented by digital values, or pixels on

4644-502: 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

4730-557: 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, 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

4816-529: The basic addressable elements in a viewpoint of hardware, and hence pixel circuits rather than subpixel circuits is used. Most digital camera image sensors use single-color sensor regions, for example using the Bayer filter pattern, and in the camera industry these are known as pixels just like in the display industry, not subpixels . For systems with subpixels, two different approaches can be taken: This latter approach, referred to as subpixel rendering , uses knowledge of pixel geometry to manipulate

4902-430: The context. For an audio signal , the relevant range is the band of audible sound frequencies (between 20 and 20,000 Hz ). Such 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

4988-534: 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,

5074-431: 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

5160-521: The depth is normally the sum of the bits allocated to each of the red, green, and blue components. Highcolor , usually meaning 16 bpp, normally has five bits for red and blue each, and six bits for green, as the human eye is more sensitive to errors in green than in the other two primary colors. For applications involving transparency, the 16 bits may be divided into five bits each of red, green, and blue, with one bit left for transparency. A 24-bit depth allows 8 bits per component. On some systems, 32-bit depth

5246-431: 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,

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5332-480: The final image. These sensor elements are often called "pixels", even though they only record one channel (only red or green or blue) of the final color image. Thus, two of the three color channels for each sensor must be interpolated and a so-called N-megapixel camera that produces an N-megapixel image provides only one-third of the information that an image of the same size could get from a scanner. Thus, certain color contrasts may look fuzzier than others, depending on

5418-452: The first camera phone with 108 MP 1/1.33-inch across sensor. The sensor is larger than most of bridge camera with 1/2.3-inch across sensor. One new method to add megapixels has been introduced in a Micro Four Thirds System camera, which only uses a 16 MP sensor but can produce a 64 MP RAW (40 MP JPEG) image by making two exposures, shifting the sensor by a half pixel between them. Using a tripod to take level multi-shots within an instance,

5504-427: The formula is often quoted as s = 206 p / f . The number of distinct colors that can be represented by a pixel depends on the number of bits per pixel (bpp). A 1 bpp image uses 1 bit for each pixel, so each pixel can be either on or off. Each additional bit doubles the number of colors available, so a 2 bpp image can have 4 colors, and a 3 bpp image can have 8 colors: For color depths of 15 or more bits per pixel,

5590-469: 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

5676-432: 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

5762-534: 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

5848-575: 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

5934-519: 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}

6020-401: The number of image sensor elements of digital cameras or the number of display elements of digital displays . For example, a camera that makes a 2048 × 1536 pixel image (3,145,728 finished image pixels) typically uses a few extra rows and columns of sensor elements and is commonly said to have "3.2 megapixels" or "3.4 megapixels", depending on whether the number reported is the "effective" or

6106-462: The original. The intensity of each pixel is variable. In color imaging systems, a color is typically represented by three or four component intensities such as red, green, and blue , or cyan, magenta, yellow, and black . In some contexts (such as descriptions of camera sensors ), pixel refers to a single scalar element of a multi-component representation (called a photosite in the camera sensor context, although sensel ' sensor element '

6192-429: The original. The number of pixels in an image is sometimes called the resolution, though resolution has a more specific definition. Pixel counts can be expressed as a single number, as in a "three-megapixel" digital camera, which has a nominal three million pixels, or as a pair of numbers, as in a "640 by 480 display", which has 640 pixels from side to side and 480 from top to bottom (as in a VGA display) and therefore has

6278-538: The probability distribution with respect to the value, in this context the probability of the signal falling within any particular range of amplitudes, while 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 ,

6364-433: The product of the distributions of the individual components. A necessary (but, in general, not sufficient ) condition for statistical independence of two variables 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

6450-425: 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

6536-473: 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

6622-453: The three colored subpixels separately, producing an increase in the apparent resolution of color displays. While CRT displays use red-green-blue-masked phosphor areas, dictated by a mesh grid called the shadow mask, it would require a difficult calibration step to be aligned with the displayed pixel raster, and so CRTs do not use subpixel rendering. The concept of subpixels is related to samples . In graphic, web design, and user interfaces,

6708-427: The values 1 or -1 will be white if the sequence is statistically uncorrelated. Noise having a continuous distribution, such as 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

6794-456: 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, 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

6880-447: 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

6966-657: The word pictures , in reference to movies. By 1938, "pix" was being used in reference to still pictures by photojournalists. The word "pixel" was first published in 1965 by Frederic C. Billingsley of JPL , to describe the picture elements of scanned images from space probes to the Moon and Mars. Billingsley had learned the word from Keith E. McFarland, at the Link Division of General Precision in Palo Alto , who in turn said he did not know where it originated. McFarland said simply it

7052-706: Was "in use at the time" ( c.  1963 ). The concept of a "picture element" dates to the earliest days of television, for example as " Bildpunkt " (the German word for pixel , literally 'picture point') in the 1888 German patent of Paul Nipkow . According to various etymologies, the earliest publication of the term picture element itself was in Wireless World magazine in 1927, though it had been used earlier in various U.S. patents filed as early as 1911. Some authors explain pixel as picture cell, as early as 1972. In graphics and in image and video processing, pel

7138-458: Was manufactured from 1976 to 1982 and was Star's flagship. It was very much like the Synare 1, with one oscillator providing sawtooth, pulse, or white noise. It added assignable functions, such as the ability to route the LFO in order to simultaneously modulate several parameters. The LFO also provided a sawtooth waveform. The pitch of the oscillator could set to a wide range of octaves, then fine tuned with

7224-484: Was previously possible, necessitating the use of large measurements like the megapixel (one million pixels). The word pixel is a combination of pix (from "pictures", shortened to "pics") and el (for " element "); similar formations with ' el' include the words voxel ' volume pixel ' , and texel ' texture pixel ' . The word pix appeared in Variety magazine headlines in 1932, as an abbreviation for

7310-482: Was the first affordable model for most musicians. As well as the ability to be run on batteries, the model featured 2 oscillators with no variable waveforms, a white-noise generator, as well as a sweep function, which could be used up or down to achieve a descending 'booming' sound which was used extensively in disco records of the era. Oscillator 1 was the noise generator with a 'tune' function. The amplifier section had volume, attack, and decay controls. This model also had

7396-507: 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") 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

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