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Elliptic Filter
An elliptic filter (also known as a Cauer filter, named after Wilhelm Cauer, or as a Zolotarev filter, after Yegor Zolotarev) is a filter (signal processing), signal processing filter with equalized ripple (filters), ripple (equiripple) behavior in both the passband and the stopband. The amount of ripple in each band is independently adjustable, and no other filter of equal order can have a faster transition in Gain (electronics), gain between the passband and the stopband, for the given values of ripple (whether the ripple is equalized or not). Alternatively, one may give up the ability to adjust independently the passband and stopband ripple, and instead design a filter which is maximally insensitive to component variations. As the ripple in the stopband approaches zero, the filter becomes a type I Chebyshev filter. As the ripple in the passband approaches zero, the filter becomes a type II Chebyshev filter and finally, as both ripple values approach zero, the filter becomes a B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilhelm Cauer
Wilhelm Cauer (24 June 1900 – 22 April 1945) was a German mathematician and scientist. He is most noted for his work on the analysis and synthesis of electrical filters and his work marked the beginning of the field of network synthesis. Prior to his work, electronic filter design used techniques which accurately predicted filter behaviour only under unrealistic conditions. This required a certain amount of experience on the part of the designer to choose suitable sections to include in the design. Cauer placed the field on a firm mathematical footing, providing tools that could produce exact solutions to a given specification for the design of an electronic filter. Cauer initially specialised in general relativity but soon switched to electrical engineering. His work for a German subsidiary of the Bell Telephone Company brought him into contact with leading American engineers in the field of filters. This proved useful when Cauer was unable to feed his children during the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacobi Elliptic Functions
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum, as well as in the design of electronic elliptic filters. While trigonometric functions are defined with reference to a circle, the Jacobi elliptic functions are a generalization which refer to other conic sections, the ellipse in particular. The relation to trigonometric functions is contained in the notation, for example, by the matching notation \operatorname for \sin. The Jacobi elliptic functions are used more often in practical problems than the Weierstrass elliptic functions as they do not require notions of complex analysis to be defined and/or understood. They were introduced by . Carl Friedrich Gauss had already studied special Jacobi elliptic functions in 1797, the lemniscate elliptic functions in particular, but his work was published much later. Overview There are twelve Jacobi elliptic functions denoted by \operatorna ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-port Network
In electronics, a two-port network (a kind of four-terminal network or quadripole) is an electrical network (i.e. a circuit) or device with two ''pairs'' of Terminal (electronics), terminals to connect to external circuits. Two terminals constitute a port (circuit theory), port if the Electric current, currents applied to them satisfy the essential requirement known as the port condition: the current entering one terminal must equal the current emerging from the other terminal on the same port.Gray, §3.2, p. 172Jaeger, §10.5 §13.5 §13.8 The ports constitute interfaces where the network connects to other networks, the points where signals are applied or outputs are taken. In a two-port network, often port 1 is considered the input port and port 2 is considered the output port. It is commonly used in mathematical Network analysis (electrical circuits), circuit analysis. Application The two-port network model is used in mathematical circuit analysis techniques to isol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Delay And Phase Delay
In signal processing, group delay and phase delay are functions that describe in different ways the delay times experienced by a signal’s various sinusoidal frequency components as they pass through a linear time-invariant (LTI) system (such as a microphone, coaxial cable, amplifier, loudspeaker, communications system, ethernet cable, digital filter, or analog filter). Unfortunately, these delays are sometimes frequency dependent, which means that different sinusoid frequency components experience different time delays. As a result, the signal's waveform experiences distortion as it passes through the system. This distortion can cause problems such as poor fidelity in analog video and analog audio, or a high bit-error rate in a digital bit stream. Background Frequency components of a signal Fourier analysis reveals how signals in time can alternatively be expressed as the sum of sinusoidal frequency components, each based on the trigonometric function \sin(x) with a fixed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Even Modified Elliptic
Even may refer to: General * Even (given name), a Norwegian male personal name * Even (surname), a Breton surname * Even (people), an ethnic group from Siberia and Russian Far East **Even language, a language spoken by the Evens * Odd and Even, a solitaire game which is played with two decks of playing cards *Evening, the period of a day that begins at the end of daylight and overlaps with the beginning of night Science and technology *In mathematics, the term ''even'' is used in several senses related to ''odd'': ** even and odd numbers, an integer is even if dividing by two yields an integer ** even and odd functions, a function is even if ''f''(−''x'') = ''f''(''x'') for all ''x'' ** even and odd permutations, a permutation of a finite set is even if it is composed of an even number of transpositions **Singly even number, an integer divisible by 2 but not divisible by 4 * Even code, if the Hamming weight of all of a binary code's codewords is even Entertainment *E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scattering Matrix
In physics, the ''S''-matrix or scattering matrix is a matrix that relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT). More formally, in the context of QFT, the ''S''-matrix is defined as the unitary matrix connecting sets of asymptotically free particle states (the ''in-states'' and the ''out-states'') in the Hilbert space of physical states: a multi-particle state is said to be ''free'' (or non-interacting) if it transforms under Lorentz transformations as a tensor product, or ''direct product'' in physics parlance, of ''one-particle states'' as prescribed by equation below. ''Asymptotically free'' then means that the state has this appearance in either the distant past or the distant future. While the ''S''-matrix may be defined for any background (spacetime) that is asymptotically solvable and has no event horizons, it has a simple form in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Five Pole Elliptic
5 (five) is a number, numeral and digit. It is the natural number, and cardinal number, following 4 and preceding 6, and is a prime number. Humans, and many other animals, have 5 digits on their limbs. Mathematics 5 is a Fermat prime, a Mersenne prime exponent, as well as a Fibonacci number. 5 is the first congruent number, as well as the length of the hypotenuse of the smallest integer-sided right triangle, making part of the smallest Pythagorean triple ( 3, 4, 5). 5 is the first safe prime and the first good prime. 11 forms the first pair of sexy primes with 5. 5 is the second Fermat prime, of a total of five known Fermat primes. 5 is also the first of three known Wilson primes (5, 13, 563). Geometry A shape with five sides is called a pentagon. The pentagon is the first regular polygon that does not tile the plane with copies of itself. It is the largest face any of the five regular three-dimensional regular Platonic solid can have. A conic is determined ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Root-finding Algorithms
In numerical analysis, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function is a number such that . As, generally, the zeros of a function cannot be computed exactly nor expressed in closed form, root-finding algorithms provide approximations to zeros. For functions from the real numbers to real numbers or from the complex numbers to the complex numbers, these are expressed either as floating-point numbers without error bounds or as floating-point values together with error bounds. The latter, approximations with error bounds, are equivalent to small isolating intervals for real roots or disks for complex roots. Solving an equation is the same as finding the roots of the function . Thus root-finding algorithms can be used to solve any equation of continuous functions. However, most root-finding algorithms do not guarantee that they will find all roots of a function, and if such an algorithm does not fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bozeman, Montana
Bozeman ( ) is a city in and the county seat of Gallatin County, Montana, United States. The 2020 United States census put Bozeman's population at 53,293, making it Montana's fourth-largest city. It is the principal city of the Bozeman, Montana, Metropolitan Statistical Area, consisting of all of Gallatin County, with a population of 118,960. It is the second-largest of Montana's statistical areas. History Early history For many years, indigenous people of the United States, including the Shoshone, Nez Perce, Blackfeet, Flathead, Crow Nation and Sioux traveled through the area, called the "Valley of the Flowers". The Gallatin Valley in particular, in which Bozeman is located, was primarily within the territory of the Crow people. 19th century William Clark visited the area in July 1806 as he traveled east from Three Forks along the Gallatin River. The party camped east of what is now Bozeman, at the mouth of Kelly Canyon. The journal entries from Clark's party bri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transmission Zeroes
Generally, in a two-port network, for a finite input, there exists an output. However, when zero output occurs for finite input, the network is said to have 'zero-transmission'. A transmission zero is a frequency at which the transfer function of a linear two-port network has zero transmission. Transmission zeroes at zero frequency and infinite frequency may be found in high-pass filters and low-pass filters respectively. Transmission zeroes at finite, non-zero frequency may be found in band-stop filters, elliptic filters, and type II Chebyshev filters. Transfer functions with both zero and infinite frequency can be found in band-pass filters. A transfer function may have multiple zeroes at the same frequency. A transfer function may have any number of transmission zeroes at zero frequency and infinite frequency, but transmission zeroes at finite non-zero frequency always come in conjugate pairs. Combination of elements may prevent input from reaching the output by 'shortening ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Filters Order5
Filtration is a physical process that separates solid matter and fluid from a mixture. Filter, filtering, filters or filtration may also refer to: Science and technology Computing * Filter (higher-order function), in functional programming * Filter (software), a computer program to process a data stream * Filter (video), a software component that performs some operation on a multimedia stream * Information filtering system ** Email filtering, the processing of email to organize it according to specified criteria * Content-control software also known as an Internet filter * Wordfilter, a script typically used on Internet forums or chat rooms * Berkeley Packet Filter, filter expression used in the qualification of network data * DSL filter, a low-pass filter installed between analog devices and a telephone line * Helicon Filter, a raster graphics editor * Filter (large eddy simulation), a mathematical operation intended to remove a range of small scales from the solution to the Nav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
