White noise

Plot of a Gaussian white noise signal.

In signal processing, white noise is a random signal with a flat (constant) power spectral density. In other words, a signal that contains equal power within any frequency band with a fixed width. The term is used, with this or similar meanings, in many scientific and technical disciplines, including physics, acoustic engineering, telecommunications, statistical forecasting, and many more. (Rigorously speaking, "white noise" refers to a statistical model for signals and signal sources, rather than to any specific signal.)

The term is also used for a discrete signal whose samples are regarded as a sequence of serially uncorrelated random variables with zero mean and finite variance. Depending on the context, one may also require that the samples be independent and have the same probability distribution. In particular, if each sample has a normal distribution with zero mean, the signal is said to be Gaussian white noise. In digital image processing, the pixels of a white noise image are often assumed to be independent random variables with uniform distribution over some interval.

Some "white noise" sound.

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, a random signal is considered "white noise" if it is observed to have a flat spectrum over the range of frequencies that is relevant to the context. For an audio signal, for example, the relevant range is the band of audible sound frequencies, between 20 to 20,000 Hz. Such a signal is heard as a hissing sound, resembling the /sh/ sound in "ash". In music and acoustics, the term white noise may be used for any signal that has a similar hissing sound.

White noise draws its name from white light, which is commonly (if incorrectly) assumed to have a flat power spectral density over the visible band.

The term is sometimes used in non technical contexts, in the metaphoric sense of "random talk without meaningful contents".

Philadelphia

Philadelphia ( /ˌfɪləˈdɛlfiə/) is the largest city in the Commonwealth of Pennsylvania and the fifth-most-populous city in the United States. It is located in the Northeastern United States along the Delaware and Schuylkill rivers, and it is the only consolidated city-county in Pennsylvania. As of the 2010 Census, the city had a population of 1,526,006. Philadelphia is the economic and cultural center of the Delaware Valley, home to 6 million people and the country's fifth-largest metropolitan area. Popular nicknames for Philadelphia are Philly and The City of Brotherly Love, the latter of which comes from the literal meaning of the city's name in Greek (Greek: Φιλαδέλφεια , Modern Greek:) "brotherly love", compounded from philos (φίλος) "loving", and adelphos (ἀδελφός) "brother").

In 1682, William Penn founded the city to serve as capital of Pennsylvania Colony. By the 1750s it was the largest city and busiest port in British America. During the American Revolution, Philadelphia played an instrumental role as a meeting place for the Founding Fathers of the United States, who signed the Declaration of Independence in 1776 and the Constitution in 1787. Philadelphia was one of the nation's capitals during the Revolutionary War, and the city served as the temporary U.S. capital while Washington, D.C. was under construction. During the 19th century, Philadelphia became a major industrial center and railroad hub that grew from an influx of European immigrants. It became a prime destination for African Americans during the Great Migration and surpassed two million occupants by 1950.

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By the 20th century, Philadelphia had become known as "corrupt and contented", with a complacent population and an entrenched Republican political machine. The first major reform came in 1917 when outrage over the election-year murder of a police officer led to the shrinking of the Philadelphia City Council from two houses to just one. In July 1919, Philadelphia was one of more than 36 industrial cities nationally to suffer a race riot of ethnic whites against blacks during Red Summer, in post-World War I unrest, as recent immigrants competed with blacks for jobs. In the 1920s, the public flouting of Prohibition laws, mob violence, and police involvement in illegal activities led to the appointment of Brigadier General Smedley Butler of the U.S. Marine Corps as director of public safety, but political pressure prevented any long-term success in fighting crime and corruption.

In 1940, non-Hispanic whites constituted 86.8% of the city's population. The population peaked at more than two million residents in 1950, then began to decline with the restructuring of industry, which led to the loss of many middle-class union jobs. In addition, suburbanization had been drawing off many of the wealthier residents to outlying railroad commuting towns and newer housing. Revitalization and gentrification of neighborhoods began in the late 1970s and continues into the 21st century, with much of the development in the Center City and University City areas of the city. After many of the old manufacturers and businesses left Philadelphia or shut down, the city started attracting service businesses and began to more aggressively market itself as a tourist destination. Glass-and-granite skyscrapers were built in Center City. Historic areas such as Independence National Historical Park located in Old City and Society Hill were renovated during the reformist mayoral era of the 1950s through the 1980s. They are now among the most desirable living areas of Center City. This has slowed the city's 40-year population decline after it lost nearly one-quarter of its population. The city has attracted more recent immigrants: Hispanics from Central and South America, Asian refugees from Laos, Vietnam and Cambodia. Educated Asians from India have tended to settle in suburbs with other middle and upper class people.

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In pursuit of this aim, a number of important philosophical societies were formed: the Philadelphia Society for Promoting Agriculture (1785), the Pennsylvania Society for the Encouragement of Manufactures and the Useful Arts (1787), The Academy of Natural Sciences (1812), and the Franklin Institute (1824). These set out to establish and finance new industries and attract skilled and knowledgeable emigrants from Europe.
Philadelphia's importance and central location in the colonies made it a natural center for America's revolutionaries. The city hosted the First Continental Congress before the war; the Second Continental Congress, which signed the United States Declaration of Independence, during the war; and the Constitutional Convention after the war. Several battles were fought in and near Philadelphia as well.

Philadelphia served as the temporary capital of the United States, 1790–1800, while the Federal City was under construction in the District of Columbia. In 1793, one of the largest yellow fever epidemics in U.S. history killed as many as 5,000 people in Philadelphia, roughly 10% of the population.

The state government left Philadelphia in 1799, and the federal government left soon after in 1800, but the city remained the young nation's largest; it was a financial and cultural center. New York City soon surpassed Philadelphia in population, but construction of roads, canals, and railroads helped turn Philadelphia into the United States' first major industrial city. Before 1800, its free black community founded the African Methodist Episcopal Church (AME), the first independent black denomination in the country. Throughout the 19th century, Philadelphia had a variety of industries and businesses, the largest being textiles. Major corporations in the 19th and early 20th centuries included the Baldwin Locomotive Works, William Cramp and Sons Ship and Engine Building Company, and the Pennsylvania Railroad. Industry, along with the U.S. Centennial, was celebrated in 1876 with the Centennial Exposition, the first official World's Fair in the United States.

Immigrants, mostly Irish and German, settled in Philadelphia and the surrounding districts. The rise in population of the surrounding districts helped lead to the Act of Consolidation of 1854 which extended the city of Philadelphia to include all of Philadelphia County. In the later half of the century, immigrants from Russia, Eastern Europe and Italy; and African Americans from the southern U.S. settled in the city. Between 1880 and 1930, the African-American population of Philadelphia increased from 31,699 to 219,559. Twentieth-century blacks were part of the Great Migration out of the rural South to northern and midwestern industrial cities.

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In 1681, in partial repayment of a debt, Charles II of England granted William Penn a charter for what would become the Pennsylvania colony. Despite the royal charter, Penn bought the land from the local Lenape to be on good terms with the Native Americans and ensure peace for his colony. According to legend Penn made a treaty of friendship with Lenape chief Tammany under an elm tree at Shackamaxon, in what is now the city's Fishtown section. Penn named the city Philadelphia, which is Greek for brotherly love (from philos, "love" or "friendship", and adelphos, "brother").

As a Quaker, Penn had experienced religious persecution and wanted his colony to be a place where anyone could worship freely. This tolerance, far more than afforded by most other colonies, led to healthier relationships with the local Native tribes and fostered Philadelphia's rapid growth into America's most important city. Penn planned a city on the Delaware River to serve as a port and place for government. Hoping that Philadelphia would become more like an English rural town instead of a city, Penn laid out roads on a grid plan to keep houses and businesses spread far apart, allowing them to be surrounded by gardens and orchards. The city's inhabitants did not follow Penn's plans and crowded by the Delaware River and subdivided and resold their lots. Before Penn left Philadelphia for the last time, he issued the Charter of 1701 establishing Philadelphia as a city. The city soon established itself as an important trading center, poor at first, but with tolerable living conditions by the 1750s. Benjamin Franklin, a leading citizen of the time, helped improve city services and founded new ones, such as one of the American Colonies' first hospitals.

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Before Europeans arrived, the Philadelphia area was home to the Lenape (Delaware) Indians in the village of Shackamaxon. Europeans came to the Delaware Valley in the early 17th century, with the first settlements founded by the Dutch, who in 1623 built Fort Nassau on the Delaware River opposite the Schuylkill River in what is now Brooklawn, New Jersey. The Dutch considered the entire Delaware River valley to be part of their New Netherland colony. In 1638, Swedish settlers led by renegade Dutch established the colony of New Sweden at Fort Christina (present day Wilmington, Delaware) and quickly spread out in the valley. In 1644, New Sweden supported the Susquehannocks in their military defeat of the English colony of Maryland. In 1648, the Dutch built Fort Beversreede on the west bank of the Delaware, south of the Schuylkill near the present-day Eastwick section of Philadelphia, to reassert their dominion over the area.

The Swedes responded by building Fort Nya Korsholm, named New Korsholm after a town that is now in Finland. In 1655, a Dutch military campaign led by New Netherland Director-General Peter Stuyvesant took control of the Swedish colony, ending its claim to independence, although the Swedish and Finnish settlers continued to have their own militia, religion, and court, and to enjoy substantial autonomy under the Dutch. The English conquered the New Netherland colony in 1664, but the situation did not really change until 1682, when the area was included in William Penn's charter for Pennsylvania.

Philadelphia

Philadelphia ( /ˌfɪləˈdɛlfiə/) is the largest city in the Commonwealth of Pennsylvania and the county seat of Philadelphia County, with which it is coterminous. The city is located in the Northeastern United States along the Delaware and Schuylkill rivers and it lies about 80 miles (130 km) southwest of New York City. It is the fifth-most-populous city in the United States,with a 2010 U.S. Census estimated population of 1,526,006. Philadelphia is also the commercial, cultural, and educational center of the Delaware Valley, home to 6 million people and the country's fifth-largest metropolitan area. Popular nicknames for Philadelphia are Philly and The City of Brotherly Love, the latter of which comes from the literal meaning of the city's name in Greek (Greek: Φιλαδέλφεια ([pʰilaˈdelpʰeːa], Modern Greek: [filaˈðelfia]) "brotherly love", compounded from philos (φίλος) "loving", and adelphos (ἀδελφός) "brother").

Philadelphia was founded on October 27, 1682 by William Penn, who planned a city along the Delaware River to serve as a port and place for government. The city grew rapidly, and by the 1750s Philadelphia was the largest city and busiest port in the original 13 American colonies. During the American Revolution, Philadelphia played an instrumental role as a meeting place for the Founding Fathers of the United States, who signed the nation's Declaration of Independence on July 4, 1776 and the Constitution on September 17, 1787. Philadelphia served as one of the nation's many capitals during the Revolutionary War, and the city served as the temporary national capital from 1790 to 1800 while Washington, D.C. was under construction. During the 19th century, Philadelphia became a major industrial center and a railroad hub that grew from an influx of European immigrants. The city's dominant textile industry represented 40 percent of total United States output in 1906. It became a major destination for African Americans during the Great Migration and surpassed 2 million occupants by 1950.

Philadelphia has transitioned from being a manufacturing powerhouse to an information and service-based economy. Financial activities account for the largest sector of the metro economy, and it is one of the largest health education and research centers in the United States. Philadelphia's history attracts many tourists, with the Liberty Bell receiving over 2 million visitors in 2010. The Delaware Valley contains the headquarters of thirteen Fortune 500 corporations, five of which are in Philadelphia proper. With a gross domestic product of $388 billion, Philadelphia ranks ninth among world cities and fourth in the nation. The city is also the nation's fourth-largest consumer media market, as ranked by the Nielsen Media Research.

Philadelphia is known for its arts and culture. The cheesesteak and soft pretzel are emblematic of Philadelphia cuisine, which is heavily influenced by the city's Italian-American population. The city has more outdoor sculptures and murals than any other American city, and Philadelphia's Fairmount Park is the largest landscaped urban park in the world. Gentrification of Philadelphia's neighborhoods continues into the 21st century and the city has reversed its decades-long trend of population loss.