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Nyquist–Shannon sampling theorem

In the field of digital signal processing, the sampling theorem is a fundamental bridge between continuous-time signals and discrete-time signals. It establishes a sufficient condition for a sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of finite bandwidth. Speaking, the theorem only applies to a class of mathematical functions having a Fourier transform, zero outside of a finite region of frequencies. Intuitively we expect that when one reduces a continuous function to a discrete sequence and interpolates back to a continuous function, the fidelity of the result depends on the density of the original samples; the sampling theorem introduces the concept of a sample rate, sufficient for perfect fidelity for the class of functions that are bandlimited to a given bandwidth, such that no actual information is lost in the sampling process. It expresses the sufficient sample rate in terms of the bandwidth for the class of functions.

The theorem leads to a formula for reconstructing the original continuous-time function from the samples. Perfect reconstruction may still be possible when the sample-rate criterion is not satisfied, provided other constraints on the signal are known. In some cases, utilizing additional constraints allows for approximate reconstructions; the fidelity of these reconstructions can be quantified utilizing Bochner's theorem. The name Nyquist–Shannon sampling theorem honours Harry Nyquist and Claude Shannon although it had been discovered in 1933 by Vladimir Kotelnikov; the theorem was discovered independently by E. T. Whittaker and by others, it is thus known by the names Nyquist–Shannon–Kotelnikov, Whittaker–Shannon–Kotelnikov, Whittaker–Nyquist–Kotelnikov–Shannon, cardinal theorem of interpolation. Sampling is a process of converting a signal into a sequence of values. Shannon's version of the theorem states: If a function x contains no frequencies higher than B hertz, it is determined by giving its ordinates at a series of points spaced 1 / seconds apart.

A sufficient sample-rate is therefore anything larger than 2 B samples per second. Equivalently, for a given sample rate f s, perfect reconstruction is guaranteed possible for a bandlimit B < f s / 2. When the bandlimit is too high, the reconstruction exhibits imperfections known as aliasing. Modern statements of the theorem are sometimes careful to explicitly state that x must contain no sinusoidal component at frequency B, or that B must be less than ½ the sample rate; the threshold 2 B is called the Nyquist rate and is an attribute of the continuous-time input x to be sampled. The sample rate must exceed the Nyquist rate for the samples to suffice to represent x; the threshold fs/2 is an attribute of the sampling equipment. All meaningful frequency components of the properly sampled x exist below the Nyquist frequency; the condition described by these inequalities is called the Nyquist criterion, or sometimes the Raabe condition. The theorem is applicable to functions of other domains, such as space, in the case of a digitized image.

The only change, in the case of other domains, is the units of measure applied to t, fs, B. The symbol T = 1/fs is customarily used to represent the interval between samples and is called the sample period or sampling interval, and the samples of function x are denoted by x = x, for all integer values of n. A mathematically ideal way to interpolate the sequence involves the use of sinc functions; each sample in the sequence is replaced by a sinc function, centered on the time axis at the original location of the sample, nT, with the amplitude of the sinc function scaled to the sample value, x. Subsequently, the sinc functions are summed into a continuous function. A mathematically equivalent method is to convolve one sinc function with a series of Dirac delta pulses, weighted by the sample values. Neither method is numerically practical. Instead, some type of approximation of the sinc functions, finite in length, is used; the imperfections attributable to the approximation are known as interpolation error.

Practical digital-to-analog converters produce neither scaled and delayed sinc functions, nor ideal Dirac pulses. Instead they produce a piecewise-constant sequence of scaled and delayed rectangular pulses followed by a lowpass filter to remove spurious high-frequency replicas of the original baseband signal; when x is a function with a Fourier transform X: X ≜ ∫ − ∞ ∞ x e − i 2 π f t d

The Dreamers (novel series)

The Dreamers is the title of a fantasy book series by American writer David Eddings and his wife Leigh Eddings. The story revolves around four beings known as The Elder Gods residing in the land of Dhrall: Dahlaine of the North, Veltan of the South, Zelana of the West and Aracia of the East, they must recruit the help of outlanders to destroy the fiendish Vlagh and prevent its attempt at world conquest. The Vlagh is a creature whose more remarkable power is the ability to consciously direct the evolution of its minions, adapting them to the situation as required. Most of Vlagh's creations are vaguely insect-like and violent, although some creatures have been bred human-like enough to pass as humans; the creatures share an Overmind, through which each of them knows and sees what the others do. Despite these major advantages, the Vlagh and the creatures of the Vlagh are not intelligent, they can't understand the meaning of death which causes many defeats early on but as they fight more they begin to avoid simple traps like arrows and poisoned spikes that the protagonists use.

As the Vlagh realizes this, the heroes have designed new traps and strategies to confuse their enemy. However, the Elder Gods are not permitted to use their powers to kill, but the young Dreamers, infant forms of the Younger Gods: Eleria, Yaltar and Ashad, can use the powers of their dreams to foresee visions of the future as a warning to an attack and cause great natural disasters capable of mass destruction and killing; the books are written in sections each with about 4-6 chapters and each time a new one is started, it gives background information on a specific character and tells the story from their perspective. On occasions, it will have a new character in every chapter, such as in the section titled "Many Voices" in The Treasured One; the series includes four titles: The Elder Gods The Treasured One Crystal Gorge The Younger Gods The first volume of the series, The Elder Gods, is about the invasion of the unsuspecting Zelana's Domain by the hordes of the Vlagh inhabiting the Wasteland center of the Land of Dhrall.

The Elder Gods are each given an infant told to be a Dreamer and are supposed to save the world and defeat the Vlagh. When Eleria, Zelana's child, has the first dream, the Elder Gods go out in search of mercenaries to hire with gold. Zelana takes to the west of Dhrall to the land of Maag where she forces a storm to bring the ship and crew of Sorgan Hook-Beak to her domain. Hook-Beak is shown that she will pay a large quantity of gold to hire an army from Maag and fight a war, he takes the native archers Longbow and Red-Beard as well as Zelana with her child Eleria to Maag in search of more crews. They find much success but when the Vlagh sends an agent out to convince a crew to destroy Sorgan Hook-Beak and steal the gold, they are stopped thanks to a vision of Eleria; the night they came to attack and the small Maag smith of Hook-Beak's crew, destroy the enemy fleet and the Vlagh agent responsible. A tight friendship is made by Longbow. Meanwhile, in the Trogite Empire, south of Dhrall, Veltan has managed to hire a retired army general and his companions Padan, Gunda and Jalkan.

The two armies meet in the western domain in surprise due to their extreme dislike for one another but Hook-Beak and Narasan become friends as they plan to stop the foreseen attack in the Ravine above the Dhrall village of Lattash, the home of Red-Beard. Yaltar, the Dreamer of Veltan, foresees that the Vlagh would attack there and that there would be much killing on both sides; as the armies of Maag and the Trogite Empire build their barricades and planned their assault after the warm ocean air, created by Eleria, melts the snow where the Vlagh's servants are waiting, thus creating flooding and winning most of the war then. While Eleria dreams up the flood and Kesselo are informed about the true nature of the gods, what they are, told to keep it a secret from the other outlanders. Sure enough, Eleria's dream brings forth an warm wind and many servants die in the flood; the native archers dip the arrows in the venom of the dead servants washed down to Lattash to ensure their victory, but the venom was used with spears and wooden stakes.

The remaining creatures of the Vlagh in the ravine met their ends with their own poison. After the Vlagh's first wave of minions were obliterated, the outlander armies moved north to the top of the ravine and built a fort to prevent the continuous coming of the servants. However, as the fort was finished and the domain of Zelana was impregnable, the Vlagh's servants revealed their clever trick, they were using creatures to climb the mountain to the fort as decoys so that the bulk of their army would walk through tunnels in the mountain to end up far down in the ravine. The Vlagh had trapped the outlanders as the earth began to shake. Veltan came and warned the outlanders to reach safe ground as Yaltan was having a dream, about to unleash a behemoth; the outlanders evacuated as two volcanoes of massive power eradicated the Vlagh's creatures by filling up the tunnels and burrows with molten rock. The war had been won by the outlanders. Zelana was afraid of the capabilities of the Dreams and fled but when she returned, Lattash had to be moved due to the twin volcanoes and the chief of the people of Lattash passed on his title to Red-Beard as the natives and outlanders pondered the next location of the Vlagh's attack.

The T

Alexa D.M. Fujise

Alexa Denise Mariko Fujise is a Judge of the Hawaii Intermediate Court of Appeals. Fuise received her bachelor's and law degrees from the University of Hawaii, she served as Reference Support Division of the Prosecutor's Office. She served as appellate research branch chief and deputy prosecutor. Fujise served as an assistant disciplinary counsel for the Office of Disciplinary Counsel and as a law clerk for then-Associate Justice Herman Lum, she was nominated to the court by former Governor Linda Lingle in March 2004 and assumed office on June 10, 2004. She has taught appellate practice seminars for the National District Attorneys Association and the William S. Richardson School of Law, she has been on the Board of the William S. Richardson School of Law Alumni Association since 1980 and was the recipient of the Dean's Distinguished Alumni Award in 2005. Alexa Fujise at Ballotpedia Official Biography on Court of Appeals website

Martha (band)

Martha are a rock band from Pity Me, a village in County Durham in the North East of England. After singles on their own Discount Horse label and Odd Box Records, their debut album Courting Strong, was released on Fortuna Pop! and Salinas Records in 2014. As of 2019 they have released three full length albums on cult UK and US based independent record labels, they have described themselves as queer, straight edge and anarchist. They have no designated frontperson and all contribute vocals. Two members of Martha founded the band ONSIND, another leads the band No Ditching, they have variously cited The Housemartins, Billy Bragg, The Thermals, Ted Leo, power pop, The Replacements, The Marked Men, Big Star and The Exploding Hearts as influences. Martha formed in the village of a suburb of Durham in the North East of England. Formed by J. C. Cairns, Daniel Ellis, Naomi Griffin, Nathan Stephens-Griffin in the early 2010s, they released their self-titled debut EP in February 2012. A year they released the "Sycamore"/"Lost Without You" single on their own Discount Horse label.

The band played Indietracks festival for the first time in 2013. After releasing a split single with American artist Spoonboy Martha headed to the studio with MJ of Hookworms to record their first album. Courting Strong was released by Fortuna Pop! in the U. K. and Salinas Records in the U. S, they followed it with more split singles with American bands Benny "The Jet" Rodriguez and Radiator Hospital, a repeat visit to Indietracks and an appearance at Glastonbury Festival. Their next album Blisters in the Pit of My Heart produced by MJ, was issued in mid-2016 by Dirtnap Records in the U. S. and Fortuna Pop! once again in the U. K, they toured the UK with Radiator Hospital in late 2015, played a tour of the UK and Ireland with Joyce Manor in July 2017. In mid to late April and early May 2018 they, along with Bad Moves of Washington, D. C. supported Jeff Rosenstock for the Midwestern leg of his US tour. On 17 April 2018 Martha, filling in last minute for Yo La Tengo, were the guest band on an episode of The Chris Gethard Show on truTV.

On 13 December 2018 the band released single "Heart Is Healing". On 28 January 2019 the band unveiled; the video for, the second directed for the band by friends Ben Epstein and David Combs of The Max Levine Ensemble. The band's third album, Love Keeps Kicking, was released on 5 April 2019. Courting Strong – Fortuna Pop! / Salinas, 12" LP, CD, MP3 Blisters in the Pit of My Heart – Fortuna Pop! / Dirtnap, 12" LP, CD, MP3 Love Keeps Kicking – Big Scary Monsters / Dirtnap, 12" LP, CD, MP3 Martha EP – Discount Horse/Win Htein/Odd Box, Cassette, MP3 and Tuff Enuff reissue, 7", MP3 "Sycamore"/"Lost Without You" – Discount Horse, 7", MP3 "The Winter Fuel Allowance Ineligibility Blues"/"Fix My Brain" - Fortuna Pop!, 7", MP3 "Heart is Healing" – Big Scary Monsters / Dirtnap, MP3 "Love Keeps Kicking" – Big Scary Monsters / Dirtnap, MP3 "Into This" – Big Scary Monsters / Dirtnap, MP3 Split EP with Spoonboy – Nervous Nelly, 7", MP3 Split EP with Radiator Hospital – Specialist Subject, 7", MP3 Split EP with Benny the Jet Rodriguez – Drunken Sailor, 7", MP3 Martha Bandcamp Discount Horse Records

GENDEX

GENDEX File is a specification to export the index of a genealogical home page to a global name index service. Developed by Eugene W. Stark as a feature of his GEDCOM to HTML translator software, GED2HTML. Stark's GENDEX site accepted the GENDEX files until that site was retired in 2004, since other sites have continued to support the format including the GenDex Network which became publicly available on 4 Apr 2013; the GenDex Network is the direct successor to the TNG Network created by Darrin Lythgoe and is based in part on the code used in the TNG Network. Each line in a GENDEX file represents the reference to a person record; each GENDEX record has the following fields, each terminated by a'|' character: Reference|SURNAME|given name /SURNAME/|date of birth|place of birth|date of death|place of death| Field 1: file name of web page referring to the individual Field 2: surname of the individual Field 3: full name of the individual Field 4: date of birth or christening Field 5: place of birth or christening Field 6: date of death or burial Field 7: place of death or burial The full name field and the date fields have the format as it appears in the GEDCOM NAME and DATE record.

E.g. the URL to a genealogical person record is http://domain.com/index.php?individual=I0001. The first part including the'=' is the static base URL, constant for each person record. The'I 0001' is the variable part; the GENDEX file could look like this: I0001|MILLER|Jhon A. /MILLER/|30 JUN 1899|Berlin|20 SEP 1905|Hamburg| I0002|SMITH|Ann /SMITH/||England|||... GenDex Network: GenDex GENealogical inDEX GenDex Network: GenDex registration GenDex Network: GenDex Advanced Search What is a GENDEX file? FAQ at FamilyTreeSeeker.com FamilyTreeSeeker.com: GENDEX search FamilyTreeSeeker.com: GENDEX file registration

List of games played between NBA and international teams

The following is a history of the list of games played between NBA and international teams. Teams from the National Basketball Association have played numerous basketball games against various international teams from around the world. NBA teams, from both the United States and Canada, have played many games against international clubs from various different basketball leagues, as well as against some league all-star teams and national teams; some of these games have been played under NBA rules, while some of them have been played under a mixture of both NBA and FIBA rules. Since 2003, games played against EuroLeague and EuroCup teams are played under NBA rules, with either 3 NBA referees, or 2 NBA referees and one EuroLeague ref, depending on whether the games take place in the United States/Canada, or in Europe. One of the first basketball games between an NBA and a FIBA team was held in 1978, in Tel Aviv, Israel. Maccabi Tel Aviv of the EuroLeague and Israeli League beat the defending NBA champion Washington Bullets, by a score of 98–97.

Since 6 other EuroLeague teams have defeated an NBA franchise: Barcelona, Málaga and Real Madrid from the Spanish League, CSKA Moscow of the Russian Championship, Fenerbahçe from the Turkish League, Alba Berlin from the German League. In addition to defeating the Washington Bullets in 1978, Maccabi Tel Aviv beat the New Jersey Nets and Phoenix Suns in 1984, in Israel, beat the Toronto Raptors, 103–105, in Toronto in 2005; this was the first loss of an NBA team in North American soil. The first Barcelona and CSKA wins came during the 2006 NBA Europe Live Tour, where Barcelona beat the Philadelphia 76ers 104–99, the Moscow team won by 19 over the Los Angeles Clippers, being the widest victory so far of any international team. During the 2007 NBA Europe Live Tour, Málaga defeated Memphis Grizzlies 102–99, Real Madrid overcame Toronto by a narrow 104–103. In 2010, Barcelona and CSKA Moscow again, beat NBA teams, by narrow margins. More recent EuroLeague victories came during the 2012 NBA Europe Live Tour, when Fenerbahçe Ülker defeated the Boston Celtics, by a score of 97–91, Barcelona beat the Dallas Mavericks, by a score of 99–85.

In 2013, CSKA beat the Minnesota Timberwolves by a score of 108–106, in 2014, Alba Berlin beat the San Antonio Spurs by a score of 94–93. In 2016, Real Madrid beat the Oklahoma City Thunder in overtime, by a score of 142–137; these games were played as part of the now-defunct McDonald's Championship, where NBA teams won all of the games. Since 2006, they are played during the NBA Europe Live Tour and the EuroLeague American Tour. In addition to that, one senior men's national team, the Soviet Union, beat the Atlanta Hawks, by a score of 132–123, in an exhibition game in Moscow, in 1988. NBA Global Games NBA Canada Series NBA versus EuroLeague games McDonald's Championship EuroLeague American Tour Naismith Cup History of Games Played by NBA Teams in Europe Previous exhibition games European clubs vs. NBA History of the NBA Global Games List of games at Spanish League forums