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94-414: Near Instantaneous Companded Audio Multiplex ( NICAM ) is an early form of lossy compression for digital audio . It was originally developed in the early 1970s for point-to-point links within broadcasting networks. In the 1980s, broadcasters began to use NICAM compression for transmissions of stereo TV sound to the public. The idea was first described in 1964. In this, the 'ranging' was to be applied to

188-468: A better representation of data. Another use is for backward compatibility and graceful degradation : in color television, encoding color via a luminance - chrominance transform domain (such as YUV ) means that black-and-white sets display the luminance, while ignoring the color information. Another example is chroma subsampling : the use of color spaces such as YIQ , used in NTSC , allow one to reduce

282-412: 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

376-605: A "sound-select" control on the receiver. The spectrum of NICAM on the PAL system differs from that on the SECAM L system where the NICAM sound carrier is at 5.85 MHz, before the AM sound carrier, and the video bandwidth is reduced from 6.5 MHz to 5.5 MHz. NICAM currently offers the following possibilities. The mode is automatically selected by the inclusion of a 3-bit type field in

470-649: 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

564-425: 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

658-403: A certain amount of information, and there is a lower bound to the size of a file that can still carry all the information. Basic information theory says that there is an absolute limit in reducing the size of this data. When data is compressed, its entropy increases, and it cannot increase indefinitely. For example, a compressed ZIP file is smaller than its original, but repeatedly compressing

752-507: A lossy format and a lossless correction which when combined reproduce the original signal; the correction can be stripped, leaving a smaller, lossily compressed, file. Such formats include MPEG-4 SLS (Scalable to Lossless), WavPack , OptimFROG DualStream , and DTS-HD Master Audio in lossless (XLL) mode ). Researchers have performed lossy compression on text by either using a thesaurus to substitute short words for long ones, or generative text techniques, although these sometimes fall into

846-545: A lot of fine detail during a very loud passage. Developing lossy compression techniques as closely matched to human perception as possible is a complex task. Sometimes the ideal is a file that provides exactly the same perception as the original, with as much digital information as possible removed; other times, perceptible loss of quality is considered a valid tradeoff. The terms "irreversible" and "reversible" are preferred over "lossy" and "lossless" respectively for some applications, such as medical image compression, to circumvent

940-470: 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

1034-760: 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}

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1128-702: 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}

1222-458: A selective loss of the least significant data, rather than losing data across the board. Further, a transform coding may provide a better domain for manipulating or otherwise editing the data – for example, equalization of audio is most naturally expressed in the frequency domain (boost the bass, for instance) rather than in the raw time domain. From this point of view, perceptual encoding is not essentially about discarding data, but rather about

1316-410: 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

1410-449: 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

1504-426: 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 ;

1598-402: A stereo TV programme as well as the mono "compatibility" sound at the same time, or can transmit two or three entirely different sound streams. This latter mode could be used to transmit audio in different languages, in a similar manner to that used for in-flight movies on international flights. In this mode, the user can select which soundtrack to listen to when watching the content by operating

1692-537: A total bandwidth of 2048 kbit/s. This figure was chosen to match the E1 primary multiplex rate, and systems using this rate could make use of the planned PDH national and international telecommunications networks. Several similar systems had been developed in various countries, and in about 1977/78 the BBC Research Department conducted listening tests to evaluate them. The candidates were: It

1786-582: A user acquires a lossily compressed file, (for example, to reduce download time) the retrieved file can be quite different from the original at the bit level while being indistinguishable to the human ear or eye for most practical purposes. Many compression methods focus on the idiosyncrasies of human physiology , taking into account, for instance, that the human eye can see only certain wavelengths of light. The psychoacoustic model describes how sound can be highly compressed without degrading perceived quality. Flaws caused by lossy compression that are noticeable to

1880-531: A way that reduces the size of a computer file needed to store it, or the bandwidth needed to transmit it, with no loss of the full information contained in the original file. A picture, for example, is converted to a digital file by considering it to be an array of dots and specifying the color and brightness of each dot. If the picture contains an area of the same color, it can be compressed without loss by saying "200 red dots" instead of "red dot, red dot, ...(197 more times)..., red dot." The original data contains

1974-413: 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

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2068-447: 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 ,

2162-441: 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,

2256-617: Is a main goal of transform coding, it also allows other goals: one may represent data more accurately for the original amount of space – for example, in principle, if one starts with an analog or high-resolution digital master , an MP3 file of a given size should provide a better representation than a raw uncompressed audio in WAV or AIFF file of the same size. This is because uncompressed audio can only reduce file size by lowering bit rate or depth, whereas compressing audio can reduce size while maintaining bit rate and depth. This compression becomes

2350-468: 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

2444-772: 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

2538-494: 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}}

2632-433: Is a type of data compression used for digital images , digital audio signals , and digital video . The transformation is typically used to enable better (more targeted) quantization . Knowledge of the application is used to choose information to discard, thereby lowering its bandwidth . The remaining information can then be compressed via a variety of methods. When the output is decoded, the result may not be identical to

2726-429: 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

2820-571: Is because these types of data are intended for human interpretation where the mind can easily "fill in the blanks" or see past very minor errors or inconsistencies – ideally lossy compression is transparent (imperceptible), which can be verified via an ABX test . Data files using lossy compression are smaller in size and thus cost less to store and to transmit over the Internet, a crucial consideration for streaming video services such as Netflix and streaming audio services such as Spotify . When

2914-419: 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

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3008-531: Is greater than R, the formula becomes L(NICAM) = L(Measured) + K NICAM sampling is not standard PCM sampling, as commonly employed with the Compact Disc or at the codec level in MP3 , AAC or Ogg audio devices. NICAM sampling more closely resembles Adaptive Differential Pulse Code Modulation , or A-law companding with an extended, rapidly modifiable dynamic range. The two's complement method of signing

3102-515: 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

3196-569: Is noticed by the end-user. Even when noticeable by the user, further data reduction may be desirable (e.g., for real-time communication or to reduce transmission times or storage needs). The most widely used lossy compression algorithm is the discrete cosine transform (DCT), first published by Nasir Ahmed , T. Natarajan and K. R. Rao in 1974. Lossy compression is most commonly used to compress multimedia data ( audio , video , and images ), especially in applications such as streaming media and internet telephony . By contrast, lossless compression

3290-478: Is often the case in practice, to produce a representation with lower resolution or lower fidelity than a given one, one needs to start with the original source signal and encode, or start with a compressed representation and then decompress and re-encode it ( transcoding ), though the latter tends to cause digital generation loss . Another approach is to encode the original signal at several different bitrates, and then either choose which to use (as when streaming over

3384-459: Is presently known. Below is a non-exhaustive list of broadcast grade equipment capable of NICAM coding and or modulation: In order to provide mono "compatibility", the NICAM signal is transmitted on a subcarrier alongside the sound carrier. This means that the FM or AM regular mono sound carrier is left alone for reception by monaural receivers. A NICAM-based stereo-TV infrastructure can transmit

3478-544: 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

3572-449: 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]}

3666-411: 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

3760-407: 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

3854-780: 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

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3948-424: 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

4042-424: Is typically required for text and data files, such as bank records and text articles. It can be advantageous to make a master lossless file which can then be used to produce additional copies from. This allows one to avoid basing new compressed copies off of a lossy source file, which would yield additional artifacts and further unnecessary information loss . It is possible to compress many types of digital data in

4136-475: 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

4230-649: The chrominance channel). While unwanted information is destroyed, the quality of the remaining portion is unchanged. Some other transforms are possible to some extent, such as joining images with the same encoding (composing side by side, as on a grid) or pasting images such as logos onto existing images (both via Jpegjoin ), or scaling. Some changes can be made to the compression without re-encoding: The freeware Windows-only IrfanView has some lossless JPEG operations in its JPG_TRANSFORM plugin . Metadata, such as ID3 tags , Vorbis comments , or Exif information, can usually be modified or removed without modifying

4324-410: 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,

4418-713: The 80s by the BBC . This variant was known as NICAM-728, after the 728 kbit/s bitstream it is sent over. It uses the same audio coding parameters as NICAM-3. The first NICAM digital stereo programme was the First Night of the 92nd edition of the Proms which was broadcast on BBC2 from the Crystal Palace transmitting station in London on 18 July 1986, though programmes were not advertised as being broadcast in stereo on

4512-574: The BBC until Saturday 31 August 1991, by which time the majority of the country's transmitters had been upgraded to broadcast NICAM, and a large number of BBC programmes were being made in stereo. coming as many as 18 months after ITV and Channel 4 had begun advertising this capability to co-inside with the Independent Broadcasting Authority rolling out NICAM on a transmitter-by-transmitter basis which had begun in 1989 with

4606-717: 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 }

4700-524: The Crystal Palace and Emley Moor transmitters. It has been standardized as ETS EN 300 163. Several European countries had implemented NICAM with the PAL and SECAM TV systems Some Asia-Pacific nations and regions have implemented NICAM Some other countries use Zweikanalton analogue stereo instead. Analogue stereo conversion thus begins. No consumer grade equipment capable of NICAM modulation

4794-499: The Nicam broadcast audio signal). They remained compatible with non-HiFi VCR players since the standard audio track was also recorded, and were at times used as an alternative to audio cassette tapes due to their superior frequency range and flat frequency response . While recording in video mode (compatible with DVD-Video ), most DVD recorders can only record one of the three channels (Digital I, Digital II, Analogue mono) allowed by

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4888-501: The analogue signal before the analogue-to-digital converter (ADC) and after the digital-to-analogue converter (DAC) . The application of this to broadcasting, in which the companding was to be done entirely digitally after the ADC and before the DAC, was described in a 1972 BBC Research Report. NICAM was originally intended to provide broadcasters with six high-quality audio channels within

4982-436: The audio tracks by means of a fixed linear recording head, which was inadequate for recording NICAM audio; this significantly limited their sound quality. Many VCRs later included high quality stereo audio recording as an additional feature, in which the incoming high quality stereo audio source (typically FM radio or NICAM TV) was frequency modulated and then recorded, in addition to the usual audio and video VCR tracks, using

5076-502: 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

5170-557: 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

5264-440: The case of audio data, a popular form of transform coding is perceptual coding , which transforms the raw data to a domain that more accurately reflects the information content. For example, rather than expressing a sound file as the amplitude levels over time, one may express it as the frequency spectrum over time, which corresponds more accurately to human audio perception. While data reduction (compression, be it lossy or lossless)

5358-430: 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

5452-534: 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,

5546-431: 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

5640-458: The data stream. The four other options could be implemented at a later date. Only the first two of the ones listed are known to be in general use however. The NICAM packet (except for the header) is scrambled with a nine-bit pseudo-random bit-generator before transmission. Making the NICAM bitstream look more like white noise is important because this reduces signal patterning on adjacent TV channels. There are some latent issues involved with

5734-431: 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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5828-444: The file size as if it had been compressed to a greater degree, but without more loss than this, is sometimes also possible. The primary programs for lossless editing of JPEGs are jpegtran , and the derived exiftran (which also preserves Exif information), and Jpegcrop (which provides a Windows interface). These allow the image to be cropped , rotated, flipped , and flopped , or even converted to grayscale (by dropping

5922-563: The file will cause it to progressively lose quality. This is in contrast with lossless data compression , where data will not be lost via the use of such a procedure. Information-theoretical foundations for lossy data compression are provided by rate-distortion theory . Much like the use of probability in optimal coding theory , rate-distortion theory heavily draws on Bayesian estimation and decision theory in order to model perceptual distortion and even aesthetic judgment. There are two basic lossy compression schemes: In some systems

6016-420: The human eye or ear are known as compression artifacts . The compression ratio (that is, the size of the compressed file compared to that of the uncompressed file) of lossy video codecs is nearly always far superior to that of the audio and still-image equivalents. An important caveat about lossy compression (formally transcoding), is that editing lossily compressed files causes digital generation loss from

6110-554: The image. Thus a partial transmission is enough to preview the final image, in a lower resolution version, without creating a scaled and a full version too. 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

6204-469: 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

6298-432: 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

6392-470: The internet – as in RealNetworks ' " SureStream " – or offering varying downloads, as at Apple's iTunes Store ), or broadcast several, where the best that is successfully received is used, as in various implementations of hierarchical modulation . Similar techniques are used in mipmaps , pyramid representations , and more sophisticated scale space methods. Some audio formats feature a combination of

6486-539: 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

6580-515: The negative implications of "loss". The type and amount of loss can affect the utility of the images. Artifacts or undesirable effects of compression may be clearly discernible yet the result still useful for the intended purpose. Or lossy compressed images may be ' visually lossless ', or in the case of medical images, so-called diagnostically acceptable irreversible compression (DAIC) may have been applied. Some forms of lossy compression can be thought of as an application of transform coding , which

6674-575: 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

6768-519: 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}

6862-523: The original input, but is expected to be close enough for the purpose of the application. The most common form of lossy compression is a transform coding method, the discrete cosine transform (DCT), which was first published by Nasir Ahmed , T. Natarajan and K. R. Rao in 1974. DCT is the most widely used form of lossy compression, for popular image compression formats (such as JPEG ), video coding standards (such as MPEG and H.264/AVC ) and audio compression formats (such as MP3 and AAC ). In

6956-403: The original, format conversion may be needed in the future to achieve compatibility with software or devices ( format shifting ), or to avoid paying patent royalties for decoding or distribution of compressed files. By modifying the compressed data directly without decoding and re-encoding, some editing of lossily compressed files without degradation of quality is possible. Editing which reduces

7050-542: 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 ,

7144-404: The processing of NICAM audio in the transmission chain. ITU (and CCITT) standards specify that the power level of the NICAM signal should be at -20 dB with respect to the power of the vision carrier. When measured with spectrum analyser the actual level of the carrier (L) can be calculated using the following formula: L(NICAM) = L(Measured) + 10 log (R/BWAnalyser) + K note: if BWAnalyser

7238-433: 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

7332-467: The re-encoding. This can be avoided by only producing lossy files from (lossless) originals and only editing (copies of) original files, such as images in raw image format instead of JPEG . If data which has been compressed lossily is decoded and compressed losslessly, the size of the result can be comparable with the size of the data before lossy compression, but the data already lost cannot be recovered. When deciding to use lossy conversion without keeping

7426-407: The related category of lossy data conversion . A general kind of lossy compression is to lower the resolution of an image, as in image scaling , particularly decimation . One may also remove less "lower information" parts of an image, such as by seam carving . Many media transforms, such as Gaussian blur , are, like lossy compression, irreversible: the original signal cannot be reconstructed from

7520-514: The resolution on the components to accord with human perception – humans have highest resolution for black-and-white (luma), lower resolution for mid-spectrum colors like yellow and green, and lowest for red and blues – thus NTSC displays approximately 350 pixels of luma per scanline , 150 pixels of yellow vs. green, and 50 pixels of blue vs. red, which are proportional to human sensitivity to each component. Lossy compression formats suffer from generation loss : repeatedly compressing and decompressing

7614-696: The same high-bandwidth helical scanning technique used for the video signal. Full-size VCRs already made full use of the tape, so the high quality audio signal was recorded diagonally under the video signal, using additional helical scan heads and depth multiplexing . The mono audio track (and on some machines, a non-NICAM, non-Hi-Fi stereo track) was also recorded on the linear track, as before, to ensure backwards-compatibility of recordings made on Hi-Fi machines when played on non-Hi-Fi VCRs. Such devices were often described as "HiFi audio", "Audio FM" / "AFM" (FM standing for "Frequency Modulation") and sometimes informally as "Nicam" VCRs (due to their use in recording

7708-422: The same file will not reduce the size to nothing. Most compression algorithms can recognize when further compression would be pointless and would in fact increase the size of the data. In many cases, files or data streams contain more information than is needed. For example, a picture may have more detail than the eye can distinguish when reproduced at the largest size intended; likewise, an audio file does not need

7802-439: The samples is used, so that: In order to strengthen parity protection for the sound samples, the parity bit is calculated on only the top six bits of each NICAM sample. Early BBC NICAM research showed that uncorrected errors in the least significant four bits were preferable to the reduced overall protection offered by parity-protecting all ten bits. VHS and Betamax home videocassette recorders (VCRs) initially only recorded

7896-425: 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

7990-473: 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

8084-457: The standard. Newer standard such as DVD-VR allows recording all the digital channels (in both stereo and bilingual mode), whereas the mono channel will be lost. Codecs for digital media on computers will often convert NICAM to another digital audio format to save drive space. Related websites or technical explanations Lossy compression Well-designed lossy compression technology often reduces file sizes significantly before degradation

8178-474: The transformed signal. However, in general these will have the same size as the original, and are not a form of compression. Lowering resolution has practical uses, as the NASA New Horizons craft transmitted thumbnails of its encounter with Pluto-Charon before it sent the higher resolution images. Another solution for slow connections is the usage of Image interlacing which progressively defines

8272-430: The two techniques are combined, with transform codecs being used to compress the error signals generated by the predictive stage. The advantage of lossy methods over lossless methods is that in some cases a lossy method can produce a much smaller compressed file than any lossless method, while still meeting the requirements of the application. Lossy methods are most often used for compressing sound, images or videos. This

8366-821: The underlying data. One may wish to downsample or otherwise decrease the resolution of the represented source signal and the quantity of data used for its compressed representation without re-encoding, as in bitrate peeling , but this functionality is not supported in all designs, as not all codecs encode data in a form that allows less important detail to simply be dropped. Some well-known designs that have this capability include JPEG 2000 for still images and H.264/MPEG-4 AVC based Scalable Video Coding for video. Such schemes have also been standardized for older designs as well, such as JPEG images with progressive encoding, and MPEG-2 and MPEG-4 Part 2 video, although those prior schemes had limited success in terms of adoption into real-world common usage. Without this capacity, which

8460-427: 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

8554-456: 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

8648-447: 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

8742-405: Was found that NICAM-2 provided the best sound quality, but reduced programme-modulated noise to an unnecessarily low level at the expense of bit rate. NICAM-3, which had been proposed during the test to address this, was selected as the winner. Audio is encoded using 14 bit pulse-code modulation at a sampling rate of 32 kHz . NICAM's second role – transmission to the public – was developed in

8836-507: 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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