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Inverse Chebyshev Filter
Chebyshev filters are analog filter, analog or digital filter, digital filters that have a steeper roll-off than Butterworth filters, and have either passband ripple (filters), ripple (type I) or stopband ripple (type II). Chebyshev filters have the property that they minimize the error between the idealized and the actual filter characteristic over the operating frequency range of the filter, but they achieve this with ripples in the frequency response. This type of filter is named after Pafnuty Chebyshev because its mathematical characteristics are derived from Chebyshev polynomials. Type I Chebyshev filters are usually referred to as "Chebyshev filters", while type II filters are usually called "inverse Chebyshev filters". Because of the passband ripple inherent in Chebyshev filters, filters with a smoother response in the passband but a more irregular response in the stopband are preferred for certain applications. Type I Chebyshev filters (Chebyshev filters) Type I Chebys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analog Filter
Analogue Filter (signal processing), filters are a basic building block of signal processing much used in electronics. Amongst their many applications are the separation of an audio signal before application to bass (music), bass, mid-range speaker, mid-range, and tweeter loudspeakers; the combining and later separation of multiple telephone conversations onto a single channel; the selection of a chosen radio station in a radio receiver and rejection of others. Passive linear electronic analogue filters are those filters which can be described with linear differential equations (linear); they are composed of capacitors, inductors and, sometimes, resistors (passive component, passive) and are designed to operate on continuously varying analogue signals. There are many linear filters which are not analogue in implementation (digital filter), and there are many electronic filters which may not have a passive topology – both of which may have the same transfer function of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analog Electronics
Analogue electronics () are electronic systems with a continuously variable signal, in contrast to digital electronics where signals usually take only two levels. The term ''analogue'' describes the proportional relationship between a signal and a voltage or current that represents the signal. The word ''analogue'' is derived from the Greek word meaning ''proportional''. Analogue signals An analogue signal uses some attribute of the medium to convey the signal's information. For example, an aneroid barometer uses the angular position of a needle on top of a contracting and expanding box as the signal to convey the information of changes in atmospheric pressure. Electrical signals may represent information by changing their voltage, current, frequency, or total charge. Information is converted from some other physical form (such as sound, light, temperature, pressure, position) to an electrical signal by a transducer which converts one type of energy into another (e.g. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poles And Zeroes
In complex analysis (a branch of mathematics), a pole is a certain type of singularity of a complex-valued function of a complex variable. It is the simplest type of non-removable singularity of such a function (see essential singularity). Technically, a point is a pole of a function if it is a zero of the function and is holomorphic (i.e. complex differentiable) in some neighbourhood of . A function is meromorphic in an open set if for every point of there is a neighborhood of in which at least one of and is holomorphic. If is meromorphic in , then a zero of is a pole of , and a pole of is a zero of . This induces a duality between ''zeros'' and ''poles'', that is fundamental for the study of meromorphic functions. For example, if a function is meromorphic on the whole complex plane plus the point at infinity, then the sum of the multiplicities of its poles equals the sum of the multiplicities of its zeros. Definitions A function of a complex variable is ho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reflection Coefficient
In physics and electrical engineering the reflection coefficient is a parameter that describes how much of a wave is reflected by an impedance discontinuity in the transmission medium. It is equal to the ratio of the amplitude of the reflected wave to the incident wave, with each expressed as phasors. For example, it is used in optics to calculate the amount of light that is reflected from a surface with a different index of refraction, such as a glass surface, or in an electrical transmission line to calculate how much of the electromagnetic wave is reflected by an impedance discontinuity. The reflection coefficient is closely related to the ''transmission coefficient''. The reflectance of a system is also sometimes called a reflection coefficient. Different disciplines have different applications for the term. Transmission lines In telecommunications and transmission line theory, the reflection coefficient is the ratio of the complex amplitude of the reflected wave to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continued Fractions
A continued fraction is a mathematical expression that can be written as a fraction with a denominator that is a sum that contains another simple or continued fraction. Depending on whether this iteration terminates with a simple fraction or not, the continued fraction is finite or infinite. Different fields of mathematics have different terminology and notation for continued fraction. In number theory the standard unqualified use of the term continued fraction refers to the special case where all numerators are 1, and is treated in the article simple continued fraction. The present article treats the case where numerators and denominators are sequences \,\ of constants or functions. From the perspective of number theory, these are called generalized continued fraction. From the perspective of complex analysis or numerical analysis, however, they are just standard, and in the present article they will simply be called "continued fraction". Formulation A continued fractio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cauer Topology
Electronic filter topology defines electronic filter circuits without taking note of the values of the components used but only the manner in which those components are connected. Filter design characterises filter circuits primarily by their transfer function rather than their topology. Transfer functions may be linear or nonlinear. Common types of linear filter transfer function are; high-pass, low-pass, bandpass, band-reject or notch and all-pass. Once the transfer function for a filter is chosen, the particular topology to implement such a prototype filter can be selected so that, for example, one might choose to design a Butterworth filter using the Sallen–Key topology. Filter topologies may be divided into passive and active types. Passive topologies are composed exclusively of passive components: resistors, capacitors, and inductors. Active topologies also include active components (such as transistors, op amps, and other integrated circuits) that require powe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Even Modified Cheby3
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] |
Chebyshev Nodes
In numerical analysis, Chebyshev nodes (also called Chebyshev points or a Chebyshev grid) are a set of specific algebraic numbers used as nodes for polynomial interpolation and numerical integration. They are the Projection (linear algebra), projection of a set of equispaced points on the unit circle onto the real interval [-1, 1], the circle's diameter. There are two kinds of Chebyshev nodes. The ''Chebyshev nodes of the first kind'', also called the Chebyshev–Gauss nodes or Chebyshev zeros, are the Zero of a function, zeros of a Chebyshev polynomial of the first kind, . The corresponding ''Chebyshev nodes of the second kind'', also called the Chebyshev–Lobatto nodes or Chebyshev extrema, are the Maximum and minimum, extrema of , which are also the zeros of a Chebyshev polynomial of the second kind, , along with the two endpoints of the interval. Both types of numbers are commonly referred to as ''Chebyshev nodes'' or ''Chebyshev points'' in literature. They are named aft ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poles And Zeroes 2
Pole or poles may refer to: People *Poles (people), another term for Polish people, from the country of Poland *Pole (surname), including a list of people with the name *Pole (musician) (Stefan Betke, born 1967), German electronic music artist *Spot Poles (Spottswood Poles, 1887–1962), American baseball player * Pole Atanraoi-Reim (fl. from 1992), a Kiribati lawyer * Pole baronets, three titles in the UK Astronomy and geography *Poles of astronomical bodies **Celestial pole, two points where the axis of rotation intersects the celestial sphere **Orbital pole, two points at the end of the orbital normal **North magnetic pole of Earth ** South magnetic pole of Earth *Geographical pole, two points on Earth where its axis of rotation intersects its surface **North Pole **South Pole Arts and entertainment * ''Pole'' (album), by Pole, 2003 * ''Pole'' (Stockhausen), a 1970 composition by Karlheinz Stockhausen *Pole, a character in the game ''Yie Ar Kung-Fu'' *Jill Pole, a character ... [...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] |
Group 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 fixe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
