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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] |
Pseudorandom Binary Sequence
A pseudorandom binary sequence (PRBS), pseudorandom binary code or pseudorandom bitstream is a binary sequence that, while generated with a deterministic algorithm, is difficult to predict and exhibits statistical behavior similar to a truly random sequence. PRBS generators are used in telecommunication, such as in analog-to-information conversion, but also in encryption, simulation, correlation technique and time-of-flight spectroscopy. The most common example is the maximum length sequence generated by a (maximal) linear feedback shift register (LFSR). Other examples are Gold sequences (used in CDMA and GPS), Kasami sequences and JPL sequences, all based on LFSRs. In telecommunications, pseudorandom binary sequences are known as pseudorandom noise codes (PN or PRN codes) due to their application as pseudorandom noise. Details A binary sequence (BS) is a sequence a_0,\ldots, a_ of N bits, i.e. :a_j\in \ for j=0,1,...,N-1. A BS consists of m=\sum a_j ones and N-m zeros. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Primitive Polynomial (field Theory)
In finite field theory, a branch of mathematics, a primitive polynomial is the minimal polynomial of a primitive element of the finite field . This means that a polynomial of degree with coefficients in is a ''primitive polynomial'' if it has a root in such that is the entire field . This implies that is a primitive ()-root of unity in . Properties * Because all minimal polynomials are irreducible, all primitive polynomials are also irreducible. * A primitive polynomial must have a non-zero constant term, for otherwise it will be divisible by ''x''. Over GF(2), is a primitive polynomial and all other primitive polynomials have an odd number of terms, since any polynomial mod 2 with an even number of terms is divisible by (it has 1 as a root). * An irreducible polynomial ''F''(''x'') of degree ''m'' over GF(''p''), where ''p'' is prime, is a primitive polynomial if the smallest positive integer ''n'' such that ''F''(''x'') divides is . * Over GF(''p''''m'') t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complementary Sequences
: ''For complementary sequences in biology, see complementarity (molecular biology) In molecular biology, complementarity describes a relationship between two structures each following the lock-and-key principle. In nature complementarity is the base principle of DNA replication and transcription as it is a property shared b .... 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 sequ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Fast Fourier Transform
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 (often time or space) 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 (mostly zero) factors. As a result, it manages to reduce the complexity of computing the DFT from O\left(N^2\right), which arises if one simply applies the definition of DFT, to O(N \log N), where N 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 algorithm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Correlation
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are ''linearly'' related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling. However ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hadamard Transform
The Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an example of a generalized class of Fourier transforms. It performs an orthogonal, symmetric, involutive, linear operation on real numbers (or complex, or hypercomplex numbers, although the Hadamard matrices themselves are purely real). The Hadamard transform can be regarded as being built out of size-2 discrete Fourier transforms (DFTs), and is in fact equivalent to a multidimensional DFT of size . It decomposes an arbitrary input vector into a superposition of Walsh functions. The transform is named for the French mathematician Jacques Hadamard (), the German-American mathematician Hans Rademacher, and the American mathematician Joseph L. Walsh. Definition The Hadamard transform ''H''''m'' is a 2''m'' × 2''m'' matrix, the Hadamard matrix (scaled by a normalization factor), that transforms 2''m'' re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital-to-analog Converter
In electronics, a digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function. There are several DAC architectures; the suitability of a DAC for a particular application is determined by figures of merit including: resolution, maximum sampling frequency and others. Digital-to-analog conversion can degrade a signal, so a DAC should be specified that has insignificant errors in terms of the application. DACs are commonly used in music players to convert digital data streams into analog audio signals. They are also used in televisions and mobile phones to convert digital video data into analog video signals. These two applications use DACs at opposite ends of the frequency/resolution trade-off. The audio DAC is a low-frequency, high-resolution type while the video DAC is a high-frequency low- to medium-resolution type. Due to the complexity a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signal-to-noise Ratio
Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power, often expressed in decibels. A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise. SNR, bandwidth, and channel capacity of a communication channel are connected by the Shannon–Hartley theorem. Definition Signal-to-noise ratio is defined as the ratio of the power of a signal (meaningful input) to the power of background noise (meaningless or unwanted input): : \mathrm = \frac, where is average power. Both signal and noise power must be measured at the same or equivalent points in a system, and within the same system bandwidth. Depending on whether the signal is a constant () or a random variable (), the signal-to-noise ratio for random noise becomes: : \mathrm = \frac where E refers to the expected value, i.e. in this case ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crest Factor
Crest or CREST may refer to: Buildings *The Crest (Huntington, New York), a historic house in Suffolk County, New York *"The Crest", an alternate name for 63 Wall Street, in Manhattan, New York *Crest Castle (Château Du Crest), Jussy, Switzerland *Crest House, a building, now in ruins, at the summit of Mount Evans in Colorado *Crest Theatre, a historic theatre in downtown Sacramento, California *Crest Theatre, formerly Majestic Crest Theatre, Los Angeles, California *Crest Theatre, in Old School Square, Delray Beach, Florida Business or commerce *Crest (toothpaste), a brand of toothpaste *Crest Audio, an American manufacturer of power amplifiers and mixing consoles *Crest Animation Productions, an animation studio in Burbank, California * Crest Animation Studios, an animation studio in India *Crest Books, an imprint of now defunct Fawcett Publications *Crest Hotels, a defunct hotel chain in the UK * Crest Manufacturing Company, producer of the Crestmobile automobile in the 19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LTI System Theory
LTI can refer to: * ''LTI – Lingua Tertii Imperii'', a book by Victor Klemperer * Language Technologies Institute, a division of Carnegie Mellon University * Linear time-invariant system, an engineering theory that investigates the response of a linear, time-invariant system to an arbitrary input signal * ''Licensed to Ill'', the 1986 debut album by the Beastie Boys * Lost Time Incident or industrial injury or Occupational injury * Learning Tools Interoperability * Louisiana Training Institute-East Baton Rouge, later known as the Jetson Center for Youth (JCY), a juvenile prison in Louisiana Companies * London Taxis International * Larsen & Toubro Infotech Biology and medicine * Lymphoid tissue-inducer cell, see innate lymphoid cell Innate lymphoid cells (ILCs) are the most recently discovered family of innate immune cells, derived from common lymphoid progenitors (CLPs). In response to pathogenic tissue damage, ILCs contribute to immunity via the secretion of signalling ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circular Shift
In combinatorial mathematics, a circular shift is the operation of rearranging the entries in a tuple, either by moving the final entry to the first position, while shifting all other entries to the next position, or by performing the inverse operation. A circular shift is a special kind of cyclic permutation, which in turn is a special kind of permutation. Formally, a circular shift is a permutation σ of the ''n'' entries in the tuple such that either :\sigma(i)\equiv (i+1) modulo ''n'', for all entries ''i'' = 1, ..., ''n'' or :\sigma(i)\equiv (i-1) modulo ''n'', for all entries ''i'' = 1, ..., ''n''. The result of repeatedly applying circular shifts to a given tuple are also called the circular shifts of the tuple. For example, repeatedly applying circular shifts to the four-tuple (''a'', ''b'', ''c'', ''d'') successively gives * (''d'', ''a'', ''b'', ''c''), * (''c'', ''d'', ''a'', ''b''), * (''b'', ''c'', ''d'', ''a''), * (''a'', ''b'', ''c'', ''d'') (the original four- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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