White noise

Note that this power spectral density corresponds to a delta function for the covariance function of w(t). Conversely, other sects consider Venus to be some form of paradise or an advanced secret base for angels/aliens to operate from. so that w(t) is a white noise random process with zero mean and constant, unit power spectral density. Its extremely high surface temperature and impenetrable cloud cover cause people to believe that the fires of Hell burn on the surface, obscured from our earthly view. The final form of the whitening procedure is as follows:. There are some religious sects who believe that Hell may be located on Venus. Additionally, we must be sure that H(ω) is strictly positive for all so that H_inv(ω) does not have any singularities. Until it was penetrated by probes, Venus's opaque cloud layer gave science fiction writers free rein in imagining the planet's surface, and they frequently imagined it to be Earthlike.

We choose the minimum phase filter so that the resulting inverse filter is stable. The association with sex and femininity is supposed to relate to the period of 266 days between the conjunction and maximum elongation of Venus, which corresponds more or less to the length of human pregnancy. Choosing the minimum phase H(ω) so that its poles and zeros lie inside the left half s-plane, we can then whiten x(t) with the following inverse filter. Alchemists constructed the symbol from a circle (representing spirit) above a cross (representing matter). We factor the power spectral density S_x(ω) as described above. The Venus symbol also represents femininity, and in ancient alchemy stood for copper. We can whiten this signal using frequency domain techniques. Its symbol is the sign also used in biology for the female sex, a stylized representation of the goddess Venus's hand mirror: a circle with a small cross underneath (Unicode: ♀).

Suppose we have a wide-sense stationary, continuous-time random process defined with the same mean μ, covariance function K_x(τ), and power spectral density S_x(ω) as above. To the Jews it is known as Noga ("shining"), Ayeleth-ha-Shakhar ("deer of the dawn") and Kochav-ha-'Erev ("star of the evening"). Thus, the resultant signal has the same 2nd moment properties as the desired signal x(t). The Maasai people in Africa named the planet Kileken, and have a myth about it called "The Orphan Boy." The Morning Star was called the Bearer of Light ("phōsphoros" or "eōsphoros" in Greek and "Lucifer" in Latin, a term later used of the fallen angel cast out of heaven, see Isaiah 14:12). where w(t) is a continuous-time, white-noise signal with the following 1st and 2nd moment properties:. Venus was known to ancient Babylonians around 1600 BC, and to the Mayan civilization (the Mayans developed a religious calendar based on Venus's motion) and must have been known long before in prehistoric times, given that it is the third brightest object in the sky after the Sun and Moon. We can simulate x(t) by constructing the following linear, time-invariant filter. When viewed from Earth, the successive conjunctions of Venus plot the points of a pentagram around the Sun in an eight-year cycle (see Orbit).

Choosing a minimum phase H(ω) so that its poles and zeros lie inside the left half s-plane, we can then simulate x(t) with H(ω) as the transfer function of the filter. It is most likely to have originated from the observations of prehistoric astronomers. If S_x(ω) is a rational function, we can then factor it into pole-zero form as. The pentagram has long been associated with the planet Venus and the worship of the goddess Venus, or her equivalent. if and only if S_x(ω) satisfies the Paley-Wiener criterion. Some speculate that the mysterious dark streaks seen in the atmosphere through ultraviolet filters could be colonies of microbes absorbing sunlight for their metabolism. Because K_x(τ) is Hermitian symmetric and positive semi-definite, it follows that S_x(ω) is real and can be factored as. Recent spectrographic observations have found carbonyl sulfide in the atmosphere of Venus, a chemical that is very difficult to make via natural processes and usually associated with life.

We can simulate this signal using frequency domain techniques. Some speculate that spores from Earth could hitch a ride on small passing asteroids and survive a trip to Venus's atmosphere. and power spectral density. However, the cloud cover supports fairly life-friendly conditions at higher altitudes. We can simulate any wide-sense stationary, continuous-time random process with constant mean μ and covariance function. Space probes in the 1960's made it pretty clear that the surface of Venus is far too hot to support life as we know it. For whitening, we feed any arbitrary random signal into a specially chosen filter so that the output of the filter is a white noise signal. For elongations and other aspects, see Aspects of Venus.

We choose the filter so that the output signal simulates the 1st and 2nd moments of any arbitrary random process. Venus sky movement patterns have been observed several times within the past 4000 years by a number of people, including the Greeks. For simulating, we create a filter into which we feed a white noise signal. Venus is now known to be moonless. We can extend the same two concepts of simulating and whitening to the case of continuous time random signals or processes. These sightings have since been discredited, and are thought to have been either spurious internal reflections, mostly faint stars that happened to be in the right place at the right time, or maybe even asteroids passing by the planet. Thus, with the above transformation, we can whiten the random vector to have zero mean and the identity covariance matrix. German astronomers called the moon Kleinchen (literally "tiny"), and sporadic sightings by astronomers continued until 1892.

By diagonalizing K_xx, we get the following:. Venus was once thought to possess a moon, named Neith after the chief goddess of Sais, Egypt (whose veil no mortal raised), first observed by Giovanni Domenico Cassini in 1672. and covariance matrix. There are about 30 arachnoids on Venus. Thus, the output of this transformation has expectation. They are quite different from the volcanoes on earth, and are formed differently too. The method for whitening a vector with mean and covariance matrix K_xx is to perform the following calculation:. There are also other bodies that spout lava, known as arachnoids, for their spiderweb-like look.

and covariance matrix. Venus has many active volcanoes similar to those on Earth, so there is a lot of lava present on the surface. Thus, the output of this transformation has expectation. Because of dryness, Venus's rocks are much harder than Earth's, which leads to steeper mountains, cliffs and other features. where. Molecular oxygen is thought to have combined with atoms in the crust (large amounts of oxygen, however, remain in the atmosphere in the form of carbon dioxide). We can simulate the 1st and 2nd moment properties of this random vector with mean and covariance matrix K_xx via the following transformation of a white vector :. Therefore, the hydrogen escaped into space because of its low molecular mass; the ratio of hydrogen to deuterium (a heavier isotope of hydrogen which doesn't escape as quickly) in Venus's atmosphere seems to support this theory.

where E is the orthogonal matrix of eigenvectors and Λ is the diagonal matrix of eigenvalues. It is thought that Venus originally had as much water as Earth, but that water vapor in the upper atmosphere was split into hydrogen and oxygen due to solar wind. Since this matrix is Hermitian symmetric and positive semidefinite, by the spectral theorem from linear algebra, we can diagonalize or factor the matrix in the following way. As a result, solar wind strikes Venus's upper atmosphere without mediation. Suppose that a random vector has covariance matrix K_xx. This may be due to its slow rotation being insufficient to drive an internal dynamo of liquid iron. These concepts are also used in data compression. Venus's intrinsic magnetic field has been found very weak compared to other planets in the solar system.

These two ideas are crucial in applications such as channel estimation and channel equalization in communications and audio. Other recent findings suggest that Venus is still volcanically active in isolated geological hotspots. To whiten an arbitrary random vector, we transform it by a different carefully chosen matrix so that the output random vector is a white random vector. It is theorized that Venus does not have mobile plate tectonics as Earth does, but instead undergoes massive volcanic upwellings at regular intervals that inundate its surface with fresh lava. We choose the transformation matrix so that the mean and covariance matrix of the transformed white random vector matches the mean and covariance matrix of the arbitrary random vector that we are simulating. Recent results from the Magellan gravity data indicate that Venus's crust is stronger and thicker than had previously been assumed. To simulate an arbitrary random vector, we transform a white random vector with a carefully chosen matrix. The interior of Venus is probably similar to that of Earth: an iron core about 3000 km in radius, with a molten rocky mantle making up the majority of the planet.

Two theoretical applications using a white random vector are the simulation and whitening of another arbitrary random vector. This suggests that Venus underwent a major resurfacing event in the not too distant geological past. Since this power spectral density is the same at all frequencies, we call it white as an analogy to the frequency spectrum of white light. The oldest features present on Venus seem to be only around 800 million years old, with most of the terrain being considerably younger (though still not less than several hundred million years for the most part). since the Fourier transform of the delta function is equal to 1. Nearly 90% of Venus's surface appears to consist of recently (in the geological sense) solidified basaltic lava, with very few meteorite craters. The above autocorrelation function implies the following power spectral density. Because of this, no impact crater smaller than about 3 km (2 mi) in diameter can form.

I.e., it is a zero mean process for all time and has infinite power at zero time shift since its autocorrelation function is the Dirac delta function. Venus' thick atmosphere causes meteors to decelerate as they fall toward the surface, and even large meteors will strike the surface at too low a speed to form an impact crater if they have less than a certain threshold kinetic energy. A continuous time random process w(t) where is a white noise process if and only if its mean function and autocorrelation function satisfy the following:. With only the exception of Maxwell Montes, all surface features on Venus are named after real or mythological females. When the autocorrelation matrix is a multiple of the identity, we say that it has spherical correlation. Between these highlands are a number of broad depressions, including Atalanta Planitia, Guinevere Planitia, and Lavinia Planitia. I.e., it is a zero mean random vector, and its autocorrelation matrix is a multiple of the identity matrix. In the southern hemisphere is the larger Aphrodite Terra, about the size of South America.

A random vector is a white random vector if and only if its mean vector and autocorrelation matrix are the following:. Ishtar Terra is about the size of Australia. White noise machines are sold as privacy enhancers and sleep aids. The northern highland is named Ishtar Terra and has Venus's highest mountains, named the Maxwell Montes (roughly 2 km taller than Mount Everest) after James Clerk Maxwell, which surround the plateau Lakshmi Planum. White noise can be used to disorient individuals prior to interrogation and may be used as part of sensory deprivation techniques. Venus has two major continent-like highlands on its surface, rising over vast plains. White noise is used as the basis of some random number generators. 16.

He or she can then adjust the overall EQ to ensure a balanced mix. 28, 2002, p. To set up the EQ for a concert or other performance in a venue, a short burst of pink noise is sent through the PA system and monitored from various points in the venue so that the engineer can tell if the acoustics of the building naturally boost or cut any frequencies. New Scientist, Sept. It is also used to generate impulse responses. Some have suggested that microbes exist in the clouds (which also contain droplets of water), and produce these components from water, carbon monoxide and sulfur dioxide. It is used extensively in audio synthesis, typically to recreate percussive instruments such as cymbals which have high noise content in their frequency domain. It is unclear how the carbonyl sulfide could be formed--it is often a sign of biological activity.

White noise has also been used in electronic music, where it is used either directly or as an input for a filter to create other types of noise signal. Hydrogen sulfide reacts with sulfur dioxide, which implies that some process must be creating these components. urban traffic noise). The atmosphere also contains hydrogen sulfide (H₂S) and carbonyl sulfide (COS). White noise is used by some sirens for emergency vehicles, due to its ability to cut through background noise (e.g. (This makes the surface temperature hot enough to melt lead.). Here in order to submerge distracting, undesirable noises (for example conversations, etc.,) in interior spaces, a constant low level of noise is generated and provided as a background sound. The minimal value of the temperature, listed in the table, refers to cloud tops —the surface temperature is never below 400 °C (750 °F).

One use for white noise is in the field of architectural acoustics. The mean surface temperature of Venus, as given by NASA, is 464 °C (864 °F). There are also other "colors" of noise, the most commonly used being pink and brown. The temperature at the tops of these clouds is approximately −45 °C (−50 °F). White noise is the generalized mean-square derivative of the Wiener process or Brownian motion. The clouds are mainly composed of sulfur dioxide and sulfuric acid droplets and cover the planet completely, obscuring any surface details from the human eye. Gaussian white noise has the useful statistical property that its values are independent (see Statistical independence). However, owing to the high density of the atmosphere at Venus's surface, even such slow winds exert a significant amount of force against obstructions.

These models are used so frequently that the term additive white Gaussian noise has a standard abbreviation: AWGN. There are strong 300 km/h (200 mph) winds at the cloud tops, but winds at the surface are very slow, no more than a few miles per hour. Gaussian white noise is a good approximation of many real-world situations and generates mathematically tractable models. The immense quantity of CO₂ in the atmosphere is what traps the heat by the greenhouse mechanism. Thus, the two words "Gaussian" and "white" are often both specified in mathematical models of systems. The cloud cover keeps the planet much cooler than it would be otherwise. However, neither property implies the other. A common conceptual misunderstanding regarding Venus is the mistaken belief that its thick cloud cover traps heat, as the opposite is actually true.

It is often incorrectly assumed that Gaussian noise (see normal distribution) is necessarily white noise. In the absence of any greenhouse effect, the temperature at the surface of Venus would be quite similar to Earth. Noise having a continuous distribution, such as a normal distribution, can of course be white. Thus, despite being closer to the Sun than Earth, the surface of Venus is not as well heated and even less well lit by the Sun. For example, a binary signal which can only take on the values 1 or 0 will be white if the sequence of zeros and ones is statistically uncorrelated. Venus's bolometric albedo is approximately 60%, and its visual light albedo is even greater. Any distribution of values is possible (although it must have zero DC component). This prevents most of the sunlight from ever heating the surface.

Being uncorrelated in time does not however restrict the values a signal can take. The solar irradiance is so much lower at the surface of Venus because the planet's thick cloud cover reflects the majority of the sunlight back into space. The image to the right displays a finite length, discrete time realization of a white noise process generated from a computer. Upper atmosphere winds circling the planet approximately every 4 days help distribute the heat to other areas on the surface. the distribution of a signal across all angles in the night sky). Owing to the thermal inertia and convection of its dense atmosphere, the temperature does not vary significantly between the night and day sides of Venus despite its extremely slow rotation of less than one rotation per Venusian year, meaning that, at the equator, Venus' surface rotates at a mere 6.5 km/h (4 mph). The signal is then "white" in the spatial frequency domain (this is equally true for signals in the angular frequency domain, e.g. This makes Venus's surface hotter than Mercury's, even though Venus is nearly twice as distant from the Sun and only receives 25% of the solar irradiance (2613.9 W/m² in the upper atmosphere, and just 1071.1 W/m² at the surface).

The term white noise is also commonly applied to a noise signal in the spatial domain which has zero autocorrelation with itself over the relevant space dimensions. This enormously CO₂-rich atmosphere results in a strong greenhouse effect that raises the surface temperature more than 400 °C (750 °F) above what it would be otherwise, causing temperatures at the surface to reach extremes as great as 500 °C (930 °F) in low elevation regions near the planet's equator. . Venus has an atmosphere consisting mainly of carbon dioxide and a small amount of nitrogen, with a pressure at the surface about 90 times that of Earth (a pressure equivalent to a depth of 1 kilometer under Earth's oceans); its atmosphere is also roughly 90 times more massive than ours. In practice, a signal can be "white" with a flat spectrum over a defined frequency band. This may simply be a coincidence, but there is some speculation that this may be the result of tidal locking, with tidal forces affecting Venus' rotation whenever the planets get close enough together —although the tides raised by Venus on Earth are vanishingly small. By having power at all frequencies, the total power of such a signal is infinite. In addition to this unusual retrograde rotation, the periods of Venus' rotation and of its orbit are synchronized in such a way that it always presents the same face toward Earth when the two planets are at their closest approach (5.001 Venusian solar days between each inferior conjunction).

An infinite-bandwidth white noise signal is purely a theoretical construct. [1] If the Sun could be seen from Venus' surface, it would appear to rise in the west and set in the east for a 116.75 day-night cycle (Venus' mean solar day), and a Venusian year would thus last 1.92 Venusian "days". In other words, the signal's power spectral density has equal power in any band, at any centre frequency, having a given bandwidth. (Pluto and Uranus also have retrograde rotation, though Uranus's axis, tilted at 97.86 degrees, almost lies in its orbital plane.) A slow retrograde rotation is thought to have developed as a consequence of tidal forces, friction, and solar heating of Venus' thick atmosphere. White noise (Sample (help·info)) is a random signal (or process) with a flat power spectral density. Venus has a slow retrograde rotation, meaning it rotates from east to west, instead of west to east as most of the other major planets do. This will be the closest approach of Venus to earth until December 16th, 2101 when Venus will reach a distance of 0.26431736 AU = 39,541,578 kilometres to earth.

On December 16th, 1850, Venus reached the lowest distance to earth since 1800, with a value of 0.26413854 AU = 39,514,827 kilometres. At inferior conjunction, Venus can get closer to earth than any other planet--little more than 100 times the Moon's average distance. Another association is with the Moon, because 2920 days equal almost exactly 99 lunations (29.5 * 99 = 2920.5). This was known as the Sothis cycle in ancient Egypt, and was familiar to the Maya as well.

Since 5 * 584 = 2920, which is equivalent to 8 * 365 Venus returns to the same point in the sky every 8 years (minus two leap days). After these 584 days Venus is visible in a position 72 degrees away from the previous one. The cycle between one maximum elongation and the next lasts 584 days. It is sometimes referred to as the "Morning Star" or the "Evening Star", and when it is visible in dark skies it is by far the brightest star-like object in the sky.

However, when at its brightest, Venus may be seen during the daytime, making it the only heavenly body that can be seen both day and night besides the Moon. As Venus is closer to the Sun than the Earth, it always appears in roughly the same direction from Earth as the Sun (the greatest elongation is 47.8°), so on Earth it can usually only be seen a few hours before sunrise or a few hours after sunset. Although all planets' orbits are elliptical, Venus's orbit is the closest to circular, with an eccentricity of less than 1%. The Chinese, Korean, Japanese and Vietnamese cultures refer to the planet as the metal star, 金星, based on the Five Elements.

Other less common adjectives include Venerean, Venerian, and Veneran. Some astronomers use Cytherean, which comes from Cytherea, another name for Aphrodite in ancient Greek Mythology. The adjective Venusian is commonly used for Venus, but the Latin adjective is Venereal, which is avoided because of its modern association with sexually transmitted diseases. Venus is named after the Roman goddess of love, Venus.

. The planet Venus is also termed Lucifer when appearing as the morning star. A terrestrial planet, it is sometimes called Earth's "sister planet", as the two are very similar in size and bulk composition. Venus is the second planet from the Sun.

The terraforming of Venus provides the setting of Pamela Sargent's Venus series, Venus of Dreams, Venus of Shadows, and Children of Venus.. A more scientifically accurate depiction of the planet is offered in Ben Bova's novel Venus (2000, ISBN 031287216X)-. Also, on her forehead is the planet's symbol. Her image colours are gold and orange--similar to the colour of the planet.

Venus Love Me Chain and Venus Love and Beauty Shock) represent the idea of love and femininity. In mythology, Venus is the Roman goddess of love (Aphrodite in Greek), therefore, Sailor Venus's attacks and weapons (e.g. In the Japanese anime series, Bishoujo Senshi Sailor Moon (1992), Sailor Venus is a soldier representing the planet of the same name. In the cartoon Exosquad, terraformed Venus was portrayed as one of the three habitable planets in the solar system (the others being Earth and Mars).

Much of the population lived in floating cities in the sky. In the show, Venus was revealed to be an arid but habitable world. A presumably terraformed Venus was the setting of one episode of the anime Cowboy Bebop (1998). Clarke's 3001: The Final Odyssey (1997).

Venus is briefly mentioned in Arthur C. In Jacqueline Susann's Yargo (1979), Venus is inhabited by bees that are as big as horses. Venus is the location of several Starfleet Academy training facilities and terraforming stations in the fictional Star Trek universe (1966–). The novel The Land of Crimson Clouds (Strana Bagrovykh Tuch in the original) describes the first successful manned mission to Venus, although a full-scaled colonization of the planet was not initiated until much later (in 2119; see Noon: 22nd Century).

In the Noon Universe created by the Soviet science fiction writers Boris and Arkady Strugatsky, Venus is depicted as an extremely harsh planet covered by strange flora and fauna but also very rich in minerals and heavy metals. Many science-fiction movies and serials of the '50s and '60s, such as Abbott and Costello Go to Mars, Space Ship Sappy and Space Patrol, have used Venus' namesake goddess and her domain to contrive planetary populations of nubile women welcoming (or attacking) all-male astronaut crews. Venus was the home planet of the Mekon, arch-enemy of the 1950s comic book hero Dan Dare. Moore, underwater city-states hire mercenary companies and their battleships to fight their wars on the surface.

L. In the military science fiction classic Clash by Night (1943) by Henry Kuttner (writing as Lawrence O'Donnell) and C. Lewis, Perelandra (1943) takes place on Venus (called by the natives Perelandra), the site of a second garden of Eden. The second book of the Space Trilogy (1938–1945) by C.S.

Lovecraft and Kenneth Sterling short story 'In the Walls of Eryx' (1939), takes place on Venus, but is not considered part of the Cthulhu Mythos. P. The H. [2].

Edgar Rice Burroughs wrote a series of five books on Venus (the Venus series), featuring hero Carson Napier, who discovers that Venus (or Amtor, as it is known by the Venusians) is a world of sky-high trees, warring kingdoms and princesses in need of rescue. Lovecraft's Cthulhu Mythos (1928–), there are mentions of the 'Lords of Venus', and conflicting indications that the Serpent People originated there. P. In H.

In fact, Tolkien chose the name directly from the ancient Old English word for the planet Venus. The star was created when Eärendil the Mariner was set in the sky on his ship, with a Silmaril bound to his brow. Tolkien, Venus is the Star of Eärendil. R.

R. In the mythology of Middle-earth (1937), by J. In Olaf Stapledon's epic Last and First Men (1930), Venus is an oceanic idyll where humans evolve the power of flight. http://news.bbc.co.uk/2/hi/science/nature/3746583.stm - BBC science news.

http://www.newscientist.com/article.ns?id=dn2843 - New Scientist article.