A fast Fourier transform is a numerical algorithm used in signal processing.
FFT may also refer to:
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain to a representation in the frequency domain and vice versa. The DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields, but computing it directly from the definition is often too slow to be practical. An FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse factors. As a result, it manages to reduce the complexity of computing the DFT from , which arises if one simply applies the definition of DFT, to , where is the data size. The difference in speed can be enormous, especially for long data sets where N may be in the thousands or millions. In the presence of round-off error, many FFT algorithms are much more accurate than evaluating the DFT definition directly or indirectly. There are many different FFT algorithms based on a wide range of published theories, from simple complex-number arithmetic to group theory and number theory.
A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. The DCT, first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression. It is used in most digital media, including digital images, digital video, digital audio, digital television, digital radio, and speech coding. DCTs are also important to numerous other applications in science and engineering, such as digital signal processing, telecommunication devices, reducing network bandwidth usage, and spectral methods for the numerical solution of partial differential equations.
The French Open, also known as Roland-Garros, is a major tennis tournament held over two weeks at the Stade Roland Garros in Paris, France, beginning in late May each year. The tournament and venue are named after the French aviator Roland Garros. The French Open is the premier clay court championship in the world and the only Grand Slam tournament currently held on this surface. It is chronologically the second of the four annual Grand Slam tournaments, occurring after the Australian Open and before Wimbledon and the US Open. Until 1975, the French Open was the only major tournament not played on grass. Between the seven rounds needed for a championship, the clay surface characteristics, and the best-of-five-set men's singles matches, the French Open is widely regarded as the most physically demanding tournament in tennis.
Fourier may refer to:
A spectrum analyzer measures the magnitude of an input signal versus frequency within the full frequency range of the instrument. The primary use is to measure the power of the spectrum of known and unknown signals. The input signal that most common spectrum analyzers measure is electrical; however, spectral compositions of other signals, such as acoustic pressure waves and optical light waves, can be considered through the use of an appropriate transducer. Spectrum analyzers for other types of signals also exist, such as optical spectrum analyzers which use direct optical techniques such as a monochromator to make measurements.
The Cooley–Tukey algorithm, named after J. W. Cooley and John Tukey, is the most common fast Fourier transform (FFT) algorithm. It re-expresses the discrete Fourier transform (DFT) of an arbitrary composite size in terms of N1 smaller DFTs of sizes N2, recursively, to reduce the computation time to O(N log N) for highly composite N (smooth numbers). Because of the algorithm's importance, specific variants and implementation styles have become known by their own names, as described below.
PFA or Pfa may refer to:
The Schönhage–Strassen algorithm is an asymptotically fast multiplication algorithm for large integers, published by Arnold Schönhage and Volker Strassen in 1971. It works by recursively applying number-theoretic transforms over the integers modulo 2n+1. The run-time bit complexity to multiply two n-digit numbers using the algorithm is in big O notation.
Simonne Mathieu was a female tennis player from France, born in Neuilly-sur-Seine, Hauts-de-Seine, who was active in the 1930s.
The Fastest Fourier Transform in the West (FFTW) is a software library for computing discrete Fourier transforms (DFTs) developed by Matteo Frigo and Steven G. Johnson at the Massachusetts Institute of Technology.
Nancy Richey defeated Ann Jones in the final, 5–7, 6–4, 6–1 to win the women's singles tennis title at the 1968 French Open. It was her first French Open title and second major title overall, after the 1967 Australian Championships.
The 1926 French Championships was a tennis tournament that took place on outdoor Clay courts at the Croix-Catelan of the Racing Club de France in Paris, France. The tournament ran from 2 June until 14 June. It was the 31st staging of the French Championships and the second Grand Slam tournament of the year.
The 1932 French Championships was a tennis tournament that took place on the outdoor clay courts at the Stade Roland-Garros in Paris, France. The tournament ran from 22 May until 6 June. It was the 37th staging of the French Championships and the second Grand Slam tournament of the year.
The 1939 French Championships was a tennis tournament that took place on the outdoor clay courts at the Stade Roland-Garros in Paris, France. The tournament ran from 8 June until 17 June. It was the 44th staging of the French Championships and the last one held before a six-year hiatus due to World War II. It was the second of four Grand Slam tennis events of the year.
The Masters France was a professional tennis exhibition round-robin singles-only tournament, played on indoor hard courts, specifically Plexicushion. It was held in December at the Palais des Sports de Toulouse in Toulouse, France, in 2008 and 2009. The eight players qualified for the event were the top seven French players, based on their performance in the four Association of Tennis Professionals (ATP) tournaments held in France, the Marseille Open 13, the Metz Open de Moselle, the Grand Prix de Tennis de Lyon, and the Paris BNP Paribas Masters, and an eighth French player receiving a wild card.
2019 French Open was a major tennis tournament played on outdoor clay courts. It was held at the Stade Roland Garros in Paris, France, from 26 May to 9 June, comprising singles, doubles and mixed doubles play. Junior and wheelchair tournaments were also scheduled. Rafael Nadal was the two-time defending champion in men's singles and won his record 12th French Open singles title. Simona Halep was the defending champion in women's singles, but lost in the quarterfinals; the title was won by Ashleigh Barty.