|
Discrete Hartley Transform
A discrete Hartley transform (DHT) is a Fourier-related transform of discrete, periodic data similar to the discrete Fourier transform (DFT), with analogous applications in signal processing and related fields. Its main distinction from the DFT is that it transforms real inputs to real outputs, with no intrinsic involvement of complex numbers. Just as the DFT is the discrete analogue of the continuous Fourier transform (FT), the DHT is the discrete analogue of the continuous Hartley transform (HT), introduced by Ralph V. L. Hartley in 1942. Because there are fast algorithms for the DHT analogous to the fast Fourier transform (FFT), the DHT was originally proposed by Ronald N. Bracewell in 1983 as a more efficient computational tool in the common case where the data are purely real. It was subsequently argued, however, that specialized FFT algorithms for real inputs or outputs can ordinarily be found with slightly fewer operations than any corresponding algorithm for the DHT. D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier-related Transform
This is a list of linear transformations of functions related to Fourier analysis. Such transformations map a function to a set of coefficients of basis functions, where the basis functions are sinusoidal and are therefore strongly localized in the frequency spectrum. (These transforms are generally designed to be invertible.) In the case of the Fourier transform, each basis function corresponds to a single frequency component. Continuous transforms Applied to functions of continuous arguments, Fourier-related transforms include: * Two-sided Laplace transform * Mellin transform, another closely related integral transform * Laplace transform: the Fourier transform may be considered a special case of the imaginary axis of the bilateral Laplace transform * Fourier transform, with special cases: ** Fourier series *** When the input function/waveform is periodic, the Fourier transform output is a Dirac comb function, modulated by a discrete sequence of finite-valued coefficients th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Big O Notation
Big ''O'' notation is a mathematical notation that describes the asymptotic analysis, limiting behavior of a function (mathematics), function when the Argument of a function, argument tends towards a particular value or infinity. Big O is a member of a #Related asymptotic notations, family of notations invented by German mathematicians Paul Gustav Heinrich Bachmann, Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation. The letter O was chosen by Bachmann to stand for '':wikt:Ordnung#German, Ordnung'', meaning the order of approximation. In computer science, big O notation is used to Computational complexity theory, classify algorithms according to how their run time or space requirements grow as the input size grows. In analytic number theory, big O notation is often used to express a bound on the difference between an arithmetic function, arithmetical function and a better understood approximation; one well-known exam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorization, factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow primality test, method of checking the primality of a given number , called trial division, tests whether is a multiple of any integer between 2 and . Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intel
Intel Corporation is an American multinational corporation and technology company headquartered in Santa Clara, California, and Delaware General Corporation Law, incorporated in Delaware. Intel designs, manufactures, and sells computer components such as central processing units (CPUs) and related products for business and consumer markets. It is one of the world's List of largest semiconductor chip manufacturers, largest semiconductor chip manufacturers by revenue, and ranked in the Fortune 500, ''Fortune'' 500 list of the List of largest companies in the United States by revenue, largest United States corporations by revenue for nearly a decade, from 2007 to 2016 Fiscal year, fiscal years, until it was removed from the ranking in 2018. In 2020, it was reinstated and ranked 45th, being the List of Fortune 500 computer software and information companies, 7th-largest technology company in the ranking. It was one of the first companies listed on Nasdaq. Intel supplies List of I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CPU Pipeline
In computing, a pipeline, also known as a data pipeline, is a set of data processing elements connected in series, where the output of one element is the input of the next one. The elements of a pipeline are often executed in parallel or in time-sliced fashion. Some amount of buffer storage is often inserted between elements. Concept and motivation Pipelining is a commonly used concept in everyday life. For example, in the assembly line of a car factory, each specific task—such as installing the engine, installing the hood, and installing the wheels—is often done by a separate work station. The stations carry out their tasks in parallel, each on a different car. Once a car has had one task performed, it moves to the next station. Variations in the time needed to complete the tasks can be accommodated by "buffering" (holding one or more cars in a space between the stations) and/or by "stalling" (temporarily halting the upstream stations), until the next station becomes avail ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CPU Cache
A CPU cache is a hardware cache used by the central processing unit (CPU) of a computer to reduce the average cost (time or energy) to access data from the main memory. A cache is a smaller, faster memory, located closer to a processor core, which stores copies of the data from frequently used main memory locations. Most CPUs have a hierarchy of multiple cache levels (L1, L2, often L3, and rarely even L4), with different instruction-specific and data-specific caches at level 1. The cache memory is typically implemented with static random-access memory (SRAM), in modern CPUs by far the largest part of them by chip area, but SRAM is not always used for all levels (of I- or D-cache), or even any level, sometimes some latter or all levels are implemented with eDRAM. Other types of caches exist (that are not counted towards the "cache size" of the most important caches mentioned above), such as the translation lookaside buffer (TLB) which is part of the memory management unit (M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Split-radix FFT Algorithm
The split-radix FFT is a fast Fourier transform (FFT) algorithm for computing the discrete Fourier transform (DFT), and was first described in an initially little-appreciated paper by R. Yavne (196and subsequently rediscovered simultaneously by various authors in 1984. (The name "split radix" was coined by two of these reinventors, Pierre Duhamel, P. Duhamel and H. Hollmann.) In particular, split radix is a variant of the Cooley–Tukey FFT algorithm that uses a blend of radices 2 and 4: it recursively expresses a DFT of length ''N'' in terms of one smaller DFT of length ''N''/2 and two smaller DFTs of length ''N''/4. The split-radix FFT, along with its variations, long had the distinction of achieving the lowest published arithmetic operation count (total exact number of required real additions and multiplications) to compute a DFT of power-of-two sizes ''N''. The arithmetic count of the original split-radix algorithm was improved upon in 2004 (with the initial gains made i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Vetterli
Martin Vetterli is a professor of engineering of École polytechnique fédérale de Lausanne (EPFL) in Switzerland, and was the former president of EPFL between 2017 and 2024. He was also formerly the president of the National Research Council of the Swiss National Science Foundation. Martin Vetterli has made numerous research contributions in the general area of digital signal processing and is best known for his work on wavelets. He has also contributed to other areas, including sampling (signal processing), computational complexity theory, signal processing for communications, digital video processing and joint source/channel coding. His work has led to over 150 journal publications and to two dozen of patents. Career Martin Vetterli received his electrical engineering degree from ETH Zurich in 1981, and then completed a Master of Science degree in electrical engineering at Stanford University in 1982. He later pursued his PhD at EPFL in 1986. After his dissertation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floating-point
In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a ''significand'' (a Sign (mathematics), signed sequence of a fixed number of digits in some Radix, base) multiplied by an integer power of that base. Numbers of this form are called floating-point numbers. For example, the number 2469/200 is a floating-point number in base ten with five digits: 2469/200 = 12.345 = \! \underbrace_\text \! \times \! \underbrace_\text\!\!\!\!\!\!\!\overbrace^ However, 7716/625 = 12.3456 is not a floating-point number in base ten with five digits—it needs six digits. The nearest floating-point number with only five digits is 12.346. And 1/3 = 0.3333… is not a floating-point number in base ten with any finite number of digits. In practice, most floating-point systems use Binary number, base two, though base ten (decimal floating point) is also common. Floating-point arithmetic operations, such as addition and division, approximate the correspond ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanford University
Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth List of governors of California, governor of and then-incumbent List of United States senators from California, United States senator representing California) and his wife, Jane Stanford, Jane, in memory of their only child, Leland Stanford Jr., Leland Jr. The university admitted its first students in 1891, opening as a Mixed-sex education, coeducational and non-denominational institution. It struggled financially after Leland died in 1893 and again after much of the campus was damaged by the 1906 San Francisco earthquake. Following World War II, university Provost (education), provost Frederick Terman inspired an entrepreneurship, entrepreneurial culture to build a self-sufficient local industry (later Silicon Valley). In 1951, Stanfor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Software Patent
A software patent is a patent on a piece of software, such as a computer program, library, user interface, or algorithm. The validity of these patents can be difficult to evaluate, as software is often at once a product of engineering, something typically eligible for patents, and an abstract concept, which is typically not. This gray area, along with the difficulty of patent evaluation for intangible, technical works such as libraries and algorithms, makes software patents a frequent subject of controversy and litigation. Different jurisdictions have radically different policies concerning software patents, including a blanket ban, no restrictions, or attempts to distinguish between purely mathematical constructs and "embodiments" of these constructs. For example, an algorithm itself may be judged unpatentable, but its use in software judged patentable. Background A patent is a set of exclusionary rights granted by a state to a patent holder for a limited period of time, usual ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Of Two
A power of two is a number of the form where is an integer, that is, the result of exponentiation with number 2, two as the Base (exponentiation), base and integer as the exponent. In the fast-growing hierarchy, is exactly equal to f_1^n(1). In the Hardy hierarchy, is exactly equal to H_(1). Powers of two with Sign (mathematics)#Terminology for signs, non-negative exponents are integers: , , and is two multiplication, multiplied by itself times. The first ten powers of 2 for non-negative values of are: :1, 2, 4, 8, 16 (number), 16, 32 (number), 32, 64 (number), 64, 128 (number), 128, 256 (number), 256, 512 (number), 512, ... By comparison, powers of two with negative exponents are fractions: for positive integer , is one half multiplied by itself times. Thus the first few negative powers of 2 are , , , , etc. Sometimes these are called ''inverse powers of two'' because each is the multiplicative inverse of a positive power of two. Base of the binary numeral sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
