In probability theory and statistics, the raised cosine distribution is a continuous probability distribution supported on the interval . The probability density function (PDF) is
and zero otherwise. The cumulative distribution function (CDF) is
for and zero for and unity for .
The moments of the raised cosine distribution are somewhat complicated in the general case, but are considerably simplified for the standard raised cosine distribution. The standard raised cosine distribution is just the raised cosine distribution with and . Because the standard raised cosine distribution is an even function, the odd moments are zero. The even moments are given by:
where is a generalized hypergeometric function.
and 26 Related for: Raised cosine distribution information
In probability theory and statistics, the raisedcosinedistribution is a continuous probability distribution supported on the interval [ μ − s , μ + s...
Quantile-parameterized distribution#Transformations) The raisedcosinedistribution on [ μ − s , μ + s {\displaystyle \mu -s,\mu +s} ] The reciprocal distribution The triangular...
In statistics, a symmetric probability distribution is a probability distribution—an assignment of probabilities to possible occurrences—which is unchanged...
named after Richard Hamming. Window function Apodization RaisedcosinedistributionRaised-cosine filter Nuttall 1981, p 84 (3) Nuttall 1981, p 86 (17) Nuttall...
is also known as raisedcosine, because the zero-phase version, w 0 ( n ) , {\displaystyle w_{0}(n),} is one lobe of an elevated cosine function. This function...
distribution Logistic distribution Normal distributionRaisedcosinedistribution Uniform distribution Wigner semicircle distribution Skewness Kurtosis Location...
statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional...
applications, it is named Hann function or raised-cosine filter. Likewise, the havercosine is used in raised-cosinedistributions in probability theory and statistics...
also suggested in 1781 two other distributions for errors - a raisedcosinedistribution and a logarithmic distribution. Laplace gave (1781) a formula for...
elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively...
of the Poisson bracket), as the cosine bracket leads to the classical Hamilton–Jacobi equation. The sine and cosine bracket also stand in relation to...
structures for FBGs; uniform positive-only index change, Gaussian apodized, raised-cosine apodized, chirped, discrete phase shift, and superstructure. The first...
Laplace distributions are extensions of the Laplace distribution and the asymmetric Laplace distribution to multiple variables. The marginal distributions of...
not aligned with the reflection will have a cosine less than one which rapidly approaches zero when raised to a high power. Although the above formulation...
Approximately, the power flowing over an AC line is proportional to the cosine of the phase angle of the voltage and current at the ends. This angle varies...
then finally published as JPEG for distribution. JPEG uses a lossy form of compression based on the discrete cosine transform (DCT). This mathematical...
"almost any smooth distribution that tapers off to subthreshold levels at low and high frequencies would have done as well as the cosine curve actually employed...
whose cosine is a m p {\displaystyle {\tfrac {a}{{m}^{p}}}} ; let C be the entire circumference. Assume, [measured] at the same radius, the cosines of the...
power flowing in the line. The power factor can also be computed as the cosine of the angle θ by which the current waveform lags or leads the voltage waveform...
(These are a consequence of the trigonometric identities for the sine and cosine function.) In other words, the absolute values are multiplied and the arguments...
calculations. He also showed that the correlation varied as the squared cosine of the angle between the polarizer settings and decreased exponentially...
jitter CRC jitter Total jitter Constellation diagram Signal integrity Raised-cosine filter Extinction ratio Christopher M. Miller "High-Speed Digital Transmitter...
r={\sqrt {x^{2}+y^{2}}}.} Using the geometrical interpretation of sine and cosine and their periodicity in 2π, any complex number z may be denoted as z =...
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![{\displaystyle x\in [\mu -s,\mu +s]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/021cb61824dc30c9ce4228710410d45d7b8ea2dd)
![{\displaystyle {\frac {1}{2s}}\left[1+\cos \left({\frac {x-\mu }{s}}\,\pi \right)\right]\,={\frac {1}{s}}\operatorname {hvc} \left({\frac {x-\mu }{s}}\,\pi \right)\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0d8fe6565ff842d25cf9ac9946e3454f278992d8)
![{\displaystyle {\frac {1}{2}}\left[1+{\frac {x-\mu }{s}}+{\frac {1}{\pi }}\sin \left({\frac {x-\mu }{s}}\,\pi \right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8a5fe6b908cecf264d0bc4a34c554b027ad3bb88)
![{\displaystyle [\mu -s,\mu +s]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4092914759a1beeec30258141ccc43c0686f8459)
![{\displaystyle f(x;\mu ,s)={\frac {1}{2s}}\left[1+\cos \left({\frac {x-\mu }{s}}\,\pi \right)\right]\,={\frac {1}{s}}\operatorname {hvc} \left({\frac {x-\mu }{s}}\,\pi \right){\text{ for }}\mu -s\leq x\leq \mu +s}](https://wikimedia.org/api/rest_v1/media/math/render/svg/10e881d815068ad8b253740178c997fe2d569289)
![{\displaystyle F(x;\mu ,s)={\frac {1}{2}}\left[1+{\frac {x-\mu }{s}}+{\frac {1}{\pi }}\sin \left({\frac {x-\mu }{s}}\,\pi \right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d946fb3c3452f89b48341393ced089a0699fdffd)
![{\displaystyle {\begin{aligned}\operatorname {E} (x^{2n})&={\frac {1}{2}}\int _{-1}^{1}[1+\cos(x\pi )]x^{2n}\,dx=\int _{-1}^{1}x^{2n}\operatorname {hvc} (x\pi )\,dx\\[5pt]&={\frac {1}{n+1}}+{\frac {1}{1+2n}}\,_{1}F_{2}\left(n+{\frac {1}{2}};{\frac {1}{2}},n+{\frac {3}{2}};{\frac {-\pi ^{2}}{4}}\right)\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bd88646853daa97101c07fa637ef17568602b698)
