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Barker Code
In telecommunication technology, a Barker code, or Barker sequence, is a finite sequence of digital values with the ideal autocorrelation property. It is used as a synchronising pattern between sender and receiver. Explanation Binary digits have very little meaning unless the significance of the individual digits is known. The transmission of a pre-arranged synchronising pattern of digits can enable a signal to be regenerated by a receiver with a low probability of error. In simple terms it is equivalent to tying a label to one digit after which others may be related by counting. This is achieved by transmitting a special pattern of digits which is unambiguously recognised by the receiver. The longer the pattern the more accurately the data can be synchronised and errors due to distortion omitted. These patterns, called Barker Sequences are better known as Barker code after the inventor Ronald Hugh Barker. The process is “Group Synchronisation of Binary Digital Systems” fir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Wieferich Prime
In number theory, a Wieferich prime is a prime number ''p'' such that ''p''2 divides , therefore connecting these primes with Fermat's little theorem, which states that every odd prime ''p'' divides . Wieferich primes were first described by Arthur Wieferich in 1909 in works pertaining to Fermat's Last Theorem, at which time both of Fermat's theorems were already well known to mathematicians. Since then, connections between Wieferich primes and various other topics in mathematics have been discovered, including other types of numbers and primes, such as Mersenne and Fermat numbers, specific types of pseudoprimes and some types of numbers generalized from the original definition of a Wieferich prime. Over time, those connections discovered have extended to cover more properties of certain prime numbers as well as more general subjects such as number fields and the ''abc'' conjecture. , the only known Wieferich primes are 1093 and 3511 . Equivalent definitions The stronger ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carrier Wave
In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform (usually sinusoidal) that is modulated (modified) with an information-bearing signal for the purpose of conveying information. This carrier wave usually has a much higher frequency than the input signal does. The purpose of the carrier is usually either to transmit the information through space as an electromagnetic wave (as in radio communication), or to allow several carriers at different frequencies to share a common physical transmission medium by frequency division multiplexing (as in a cable television system). The term originated in radio communication, where the carrier wave creates the waves which carry the information (modulation) through the air from the transmitter to the receiver. The term is also used for an unmodulated emission in the absence of any modulating signal. In music production, carrier signals can be controlled by a modulating signal to change the sound property of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Sequences
Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that takes two arguments * Binary relation, a relation involving two elements * Binary-coded decimal, a method for encoding for decimal digits in binary sequences * Finger binary, a system for counting in binary numbers on the fingers of human hands Computing * Binary code, the digital representation of text and data * Bit, or binary digit, the basic unit of information in computers * Binary file, composed of something other than human-readable text ** Executable, a type of binary file that contains machine code for the computer to execute * Binary tree, a computer tree data structure in which each node has at most two children Astronomy * Binary star, a star system with two stars in it * Binary planet, two planetary bodies of compa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Codes
Line most often refers to: * Line (geometry), object with zero thickness and curvature that stretches to infinity * Telephone line, a single-user circuit on a telephone communication system Line, lines, The Line, or LINE may also refer to: Arts, entertainment, and media Films * ''Lines'' (film), a 2016 Greek film * ''The Line'' (2017 film) * ''The Line'' (2009 film) * ''The Line'', a 2009 independent film by Nancy Schwartzman Podcasts * ''The Line'' (podcast), 2021 by Dan Taberski Literature * Line (comics), a term to describe a subset of comic book series by a publisher * ''Line'' (play), by Israel Horovitz, 1967 * Line (poetry), the fundamental unit of poetic composition * "Lines" (poem), an 1837 poem by Emily Brontë * ''The Line'' (memoir), by Arch and Martin Flanagan * ''The Line'' (play), by Timberlake Wertenbaker, 2009 Music Albums * ''Lines'' (The Walker Brothers album), 1976 * ''Lines'' (Pandelis Karayorgis album), 1995 * ''Lines'' (Unthanks album), 201 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wireless Networking
A wireless network is a computer network that uses wireless data connections between network nodes. Wireless networking is a method by which homes, telecommunications networks and business installations avoid the costly process of introducing cables into a building, or as a connection between various equipment locations. Admin telecommunications networks are generally implemented and administered using radio communication. This implementation takes place at the physical level (layer) of the OSI model network structure. Examples of wireless networks include cell phone networks, wireless local area networks (WLANs), wireless sensor networks, satellite communication networks, and terrestrial microwave networks. History Wireless networks The first professional wireless network was developed under the brand ALOHAnet in 1969 at the University of Hawaii and became operational in June 1971. The first commercial wireless network was the WaveLAN product family, developed by NCR i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Length Sequence
A maximum length sequence (MLS) is a type of pseudorandom binary sequence. They are bit sequences generated using maximal linear-feedback shift registers and are so called because they are periodic and reproduce every binary sequence (except the zero vector) that can be represented by the shift registers (i.e., for length-''m'' registers they produce a sequence of length 2''m'' − 1). An MLS is also sometimes called an n-sequence or an m-sequence. MLSs are spectrally flat, with the exception of a near-zero DC term. These sequences may be represented as coefficients of irreducible polynomials in a polynomial ring over Z/2Z. Practical applications for MLS include measuring impulse responses (e.g., of room reverberation or arrival times from towed sources in the ocean). They are also used as a basis for deriving pseudo-random sequences in digital communication systems that employ direct-sequence spread spectrum and frequency-hopping spread spectrum transmission sys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zadoff–Chu Sequence
A Zadoff–Chu (ZC) sequence, also referred to as Chu sequence or Frank–Zadoff–Chu (FZC) sequence, is a complex-valued mathematical sequence which, when applied to a signal, gives rise to a new signal of constant amplitude. When cyclically shifted versions of a Zadoff–Chu sequence are imposed upon a signal the resulting set of signals detected at the receiver are uncorrelated with one another. They are named after Solomon A. Zadoff, David C. Chu and Robert L. Frank. Description Zadoff–Chu sequences exhibit the useful property that cyclically shifted versions of themselves are orthogonal to one another. A generated Zadoff–Chu sequence that has not been shifted is known as a ''root sequence''. The complex value at each position ''n'' of each root Zadoff–Chu sequence parametrised by ''u'' is given by : x_u(n)=\text\left(-j\frac\right), \, where : 0 \le n < N_\text, : and , : |
Legendre Symbol
In number theory, the Legendre symbol is a multiplicative function with values 1, −1, 0 that is a quadratic character modulo an odd prime number ''p'': its value at a (nonzero) quadratic residue mod ''p'' is 1 and at a non-quadratic residue (''non-residue'') is −1. Its value at zero is 0. The Legendre symbol was introduced by Adrien-Marie Legendre in 1798 in the course of his attempts at proving the law of quadratic reciprocity. Generalizations of the symbol include the Jacobi symbol and Dirichlet characters of higher order. The notational convenience of the Legendre symbol inspired introduction of several other "symbols" used in algebraic number theory, such as the Hilbert symbol and the Artin symbol. Definition Let p be an odd prime number. An integer a is a quadratic residue modulo p if it is congruent to a perfect square modulo p and is a quadratic nonresidue modulo p otherwise. The Legendre symbol is a function of a and p defined as :\left(\frac\right) = \begi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complementary Sequence
: ''For complementary sequences in biology, see complementarity (molecular biology). For integer sequences with complementary sets of members see Lambek–Moser theorem.'' In applied mathematics, complementary sequences (CS) are pairs of sequences with the useful property that their out-of-phase aperiodic autocorrelation coefficients sum to zero. Binary complementary sequences were first introduced by Marcel J. E. Golay in 1949. In 1961–1962 Golay gave several methods for constructing sequences of length 2''N'' and gave examples of complementary sequences of lengths 10 and 26. In 1974 R. J. Turyn gave a method for constructing sequences of length ''mn'' from sequences of lengths ''m'' and ''n'' which allows the construction of sequences of any length of the form 2''N''10''K''26''M''. Later the theory of complementary sequences was generalized by other authors to polyphase complementary sequences, multilevel complementary sequences, and arbitrary complex complementary sequences ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Shifting
In physics and mathematics, the phase of a periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is denoted \phi(t) and expressed in such a scale that it varies by one full turn as the variable t goes through each period (and F(t) goes through each complete cycle). It may be measured in any angular unit such as degrees or radians, thus increasing by 360° or 2\pi as the variable t completes a full period. This convention is especially appropriate for a sinusoidal function, since its value at any argument t then can be expressed as \phi(t), the sine of the phase, multiplied by some factor (the amplitude of the sinusoid). (The cosine may be used instead of sine, depending on where one considers each period to start.) Usually, whole turns are ignored when expressing the phase; so that \phi(t) is also a periodic function, with the same period as F, that repeatedly scans the same range of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
