The Fourier transform decomposes a function into its constituent frequencies. A special case is the expression of a musical chord in terms of the volumes and frequencies of its constituent notes; the term Fourier transform refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of time. The Fourier transform of a function of time is itself a complex-valued function of frequency, whose magnitude represents the amount of that frequency present in the original function, whose argument is the phase offset of the basic sinusoid in that frequency; the Fourier transform is not limited to functions of time, but the domain of the original function is referred to as the time domain. There is an inverse Fourier transform that mathematically synthesizes the original function from its frequency domain representation. Linear operations performed in one domain have corresponding operations in the other domain, which are sometimes easier to perform.

The operation of differentiation in the time domain corresponds to multiplication by the frequency, so some differential equations are easier to analyze in the frequency domain. Convolution in the time domain corresponds to ordinary multiplication in the frequency domain. After performing the desired operations, transformation of the result can be made back to the time domain. Harmonic analysis is the systematic study of the relationship between the frequency and time domains, including the kinds of functions or operations that are "simpler" in one or the other, has deep connections to many areas of modern mathematics. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle; the critical case for this principle is the Gaussian function, of substantial importance in probability theory and statistics as well as in the study of physical phenomena exhibiting normal distribution.

The Fourier transform of a Gaussian function is another Gaussian function. Joseph Fourier introduced the transform in his study of heat transfer, where Gaussian functions appear as solutions of the heat equation; the Fourier transform can be formally defined as an improper Riemann integral, making it an integral transform, although this definition is not suitable for many applications requiring a more sophisticated integration theory. For example, many simple applications use the Dirac delta function, which can be treated formally as if it were a function, but the justification requires a mathematically more sophisticated viewpoint; the Fourier transform can be generalized to functions of several variables on Euclidean space, sending a function of 3-dimensional'position space' to a function of 3-dimensional momentum. This idea makes the spatial Fourier transform natural in the study of waves, as well as in quantum mechanics, where it is important to be able to represent wave solutions as functions of either position or momentum and sometimes both.

In general, functions to which Fourier methods are applicable are complex-valued, vector-valued. Still further generalization is possible to functions on groups, besides the original Fourier transform on ℝ or ℝn, notably includes the discrete-time Fourier transform, the discrete Fourier transform and the Fourier series or circular Fourier transform; the latter is employed to handle periodic functions. The fast Fourier transform is an algorithm for computing the DFT; the Fourier transform of a function f is traditionally denoted f ^, by adding a circumflex to the symbol of the function. There are several common conventions for defining the Fourier transform of an integrable function f: R → C. One of them is for any real number ξ. A reason for the negative sign in the exponent is that it is common in electrical engineering to represent by f = e 2 π i ξ 0 x a signal with zero initial phase and frequency ξ 0; the negative sign convention causes the product e 2 π i ξ 0 x e − 2 π i ξ x to be 1 when ξ = ξ 0, causing the integral to diverge.

The result is a Dirac delta function at ξ = ξ 0, the only frequency component of the sinusoidal signal e 2 π i ξ 0 x. When the independent variable x represents time, the transform variable ξ represents frequency. Under suitable conditions, f is determined by f ^ via the inverse transform: for any real

The Netherlands national baseball team is the national baseball team of the Kingdom of the Netherlands, representing the country in international men's baseball. They are ranked as the best team in the Confederation of European Baseball, the team is ranked seventh in the WBSC World Rankings; the Netherlands participated in the Summer Olympic Games in 1996, 2000, 2004, 2008. The team has participated in both of the other major international baseball tournaments recognised by the International Baseball Federation: the World Baseball Classic and the Baseball World Cup. In 2011, the team won the World Cup after beating 25-time champion Cuba in the finals; the team is controlled by the Koninklijke Nederlandse Baseball en Softball Bond, represented in the Confederation of European Baseball. The team is made up of players from the Netherlands in Europe, from Dutch territories and islands in the Caribbean that are part of the Kingdom of the Netherlands, such as Aruba and Curaçao, where baseball is popular.

Some foreigners of Dutch descent have been members of the team. While baseball only maintains a niche following throughout Europe, the Netherlands, along with Italy, are the two European countries where the sport's popularity is strongest; the team played in the 2017 World Baseball Classic, finished in 4th place. It won the 2019 European Baseball Championship, it competed at the Africa/Europe 2020 Olympic Qualification tournament, in Italy in September 2019, taking second place behind Team Israel. The team will next try to qualify for the 2020 Olympics at the six-team Final Qualifying Tournament in Taipei City in April 2020; the Netherlands has competed in all four of the World Baseball Classic tournaments held. All 16 teams that played in the 2006 edition were invited to compete in the second in 2009; the team was an automatic qualifier for the 2017 tournaments. The Netherlands has progressed to the second round of competition in 2009, achieved its highest finish, 4th, in both the 2013 and 2017 tournaments.

Unusual for international competition in baseball, the squads selected in the World Baseball Classic tournaments featured players active in Major League Baseball in addition to Minor League, Nippon Professional Baseball, local players. Players in the Major Leagues are unavailable due to their contracts with the respective clubs; the Netherlands team in the World Baseball Classic has featured several Major Leaguers: Andruw Jones, Sidney Ponson, Randall Simon, Roger Bernadina, Shairon Martis, Jonathan Schoop, Xander Bogaerts, Andrelton Simmons, Didi Gregorius, Jurickson Profar, Kenley Jansen, all born in the Caribbean in either Aruba or Curaçao. Prior to the 2006 World Baseball Classic, the Netherlands played four exhibition games, they lost two games, against a college team from the University of Tampa and an Atlanta Braves squad, at Cracker Jack Stadium in Kissimmee, Florida. The Netherlands competed in Pool C—along with world champion Cuba and Puerto Rico—in the first round at the Hiram Bithorn Stadium in San Juan, Puerto Rico.

Having failed to win against Cuba and Puerto Rico in their round-robin pool games, they finished third in their pool, were eliminated along with Panama. Prior to the 2009 World Baseball Classic, the Netherlands played seven exhibition games, including three games against the Pittsburgh Pirates, Cincinnati Reds, Minnesota Twins; the Netherlands team lost all three games against these MLB opponents. The Netherlands competed in Pool D, along with 2006 WBC semi-finalist Dominican Republic and Puerto Rico, in the first round at Hiram Bithorn Stadium in San Juan, Puerto Rico; the team won both games against the strong Dominican Republic team. As result, the team made it through the first double-elimination round along with Puerto Rico. In the second round the Dutch lost both their games against the United States. Therefore, the team finished 7th in the final standings; the Netherlands competed in Pool B against Chinese Taipei, South Korea, Australia at the Taichung Intercontinental Baseball Stadium in Taichung, Taiwan.

The Dutch team won their first game against South Korea 5-0, but lost to the Chinese Taipei 8-3. However, the Netherlands won against Australia 4-1, thus securing their position for Round 1 in Tokyo Dome to face off against Japan and Cuba; the Dutch team defeated the Cuban team 6-2 before facing two-time defending champion Japan and earned a humiliating loss 16-4 at the end of 7th inning due to mercy rule and faced off against Cuba once again. They narrowly clinched their win against the Cuban team 7-6 to secure their position in the semi-finals where they lost against the Japanese team again 10-6, they faced off against the Dominican Republic where they lost 4-1. The Netherlands finished 4th overall. Team Netherlands, ranked 9th in the world, included major league stars, many of whom were raised in islands in the Caribbean that are part of the Kingdom of the Netherlands; the players included All Star shortstop Xander Bogaerts, 20-home-run-hitter shortstop Didi Gregorius, 20-home-run-hitter second baseman Jonathan Schoop, Gold-Glover shortstop Andrelton Simmons, infielder/outfielder Jurickson Profar.

Sports Illustrated opined that the Dutch team "boasts arguably the most talented infield i

The Q-code is a standardized collection of three-letter codes all of which start with the letter "Q". It is an operating signal developed for commercial radiotelegraph communication and adopted by other radio services amateur radio. To distinguish the use of a Q-code transmitted as a question from the same Q-code transmitted as a statement, operators either prefixed it with the military network question marker "INT" or suffixed it with the standard Morse question mark UD. Although Q-codes were created when radio used Morse code they continued to be employed after the introduction of voice transmissions. To avoid confusion, transmitter call signs are restricted. Codes in the range QAA–QNZ are reserved for aeronautical use. "Q" has no official meaning, but it is sometimes assigned with a word with mnemonic value, such as "Queen's", "Query", "Question", or "reQuest". The original Q-codes were created, circa 1909, by the British government as a "list of abbreviations... prepared for the use of British ships and coast stations licensed by the Postmaster General".

The Q-codes facilitated communication between maritime radio operators speaking different languages, so they were soon adopted internationally. A total of forty-five Q-codes appeared in the "List of Abbreviations to be used in Radio Communications", included in the Service Regulations affixed to the Third International Radiotelegraph Convention in London The following table reviews a sample of the all-services Q-codes adopted by the 1912 Convention: Over the years the original Q-codes were modified to reflect changes in radio practice. For example, QSW / QSX stood for, "Shall I increase / decrease my spark frequency?", but in the 1920s spark-gap transmitters were being banned from land stations, making that meaning obsolete. By the 1970s, the Post Office Handbook for Radio Operators listed over a hundred Q-codes, covering a wide range of subjects including radio procedures, radio direction finding, search and rescue; some Q-codes are used in aviation, in particular QNE, QNH and QFE, referring to certain altimeter settings.

These codes are used in radiotelephone conversations with air traffic control as unambiguous shorthand, where safety and efficiency are of vital importance. A subset of Q-codes is used by the Miami-Dade County, Florida local government for law enforcement and fire rescue communications, one of the few instances where Q-codes are used in ground voice communication; the QAA–QNZ code range includes phrases applicable to the aeronautical service, as defined by the International Civil Aviation Organization. The QOA–QQZ code range is reserved for the maritime service; the QRA–QUZ code range includes phrases applicable to all services and is allocated to the International Telecommunications Union. QVA–QZZ are not allocated. Many codes have no immediate applicability outside one individual service, such as maritime operation or radioteletype operation. Many military and other organizations that use Morse code have adopted additional codes, including the Z code used by most European and NATO countries.

The Z code adds commands and questions adapted for military radio transmissions, for example, "ZBW 2", which means "change to backup frequency number 2", "ZNB abc", which means "my checksum is abc, what is yours?"Used in their formal question / answer sense, the meaning of a Q-code varies depending on whether the individual Q-code is sent as a question or an answer. For example, the message "QRP?" Means "Shall I decrease transmitter power?", a reply of "QRP" means "Yes, decrease your transmitter power", whereas an unprompted statement "QRP" means "Please decrease your transmitter power". This structured use of Q-codes is rare and now limited to amateur radio and military Morse code traffic networks. QAA to QNZ – Assigned by the International Civil Aviation Organization. QNA to QNZ – The American Radio Relay League has developed its own QN Signals for message handling located in this range. Though they overlap with other signals, the ARRL determined that their exclusive use in NTS nets limits confusion.

QOA to QQZ – For the Maritime Mobile Service. QRA to QUZ – Assigned by the International Telecommunications Union Radiocommunication Sector. First defined in ICAO publication "Doc 6100-COM/504/1" and in "ICAO Procedures for Air Navigation Services and Codes", the majority of the Q-codes have fallen out of common use, but several remain part of the standard ICAO radiotelephony phraseology in aviation. These are part of ACP131, which lists all ITU-R Q-codes, without grouping them by aeronautical/marine/general use; this assignment is specified in RECOMMENDATION ITU-R M.1172. Q signals are not used in the maritime service. Morse code is now rarely used for maritime communications, but in isolated maritime regions like Antarctica and the South Pacific the use of Q-codes continues. Q-codes still work when HF voice circuits are not possible due to atmospherics and the nearest vessel is one ionospheric hop away. First defined by the Washington 1927 ITU Radio Regulations. Defined by ITU-R in Appendix 9 to the Radio Regulations Annex to the International Telecommunications Convention 1947.

The current callsig