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Network Synthesis Filters
In signal processing, network synthesis filters are filters designed by the network synthesis method. The method has produced several important classes of filter including the Butterworth filter, the Chebyshev filter and the Elliptic filter. It was originally intended to be applied to the design of passive linear analogue filters but its results can also be applied to implementations in active filters and digital filters. The essence of the method is to obtain the component values of the filter from a given rational function representing the desired transfer function. Description of method The method can be viewed as the inverse problem of network analysis. Network analysis starts with a network and by applying the various electric circuit theorems predicts the response of the network. Network synthesis on the other hand, starts with a desired response and its methods produce a network that outputs, or approximates to, that response. Network synthesis was originally int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signal Processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, Scalar potential, potential fields, Seismic tomography, seismic signals, Altimeter, altimetry processing, and scientific measurements. Signal processing techniques are used to optimize transmissions, Data storage, digital storage efficiency, correcting distorted signals, improve subjective video quality, and to detect or pinpoint components of interest in a measured signal. History According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was publis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Filter Design
Filter design is the process of designing a signal processing filter that satisfies a set of requirements, some of which may be conflicting. The purpose is to find a realization of the filter that meets each of the requirements to an acceptable degree. The filter design process can be described as an optimization problem. Certain parts of the design process can be automated, but an experienced designer may be needed to get a good result. The design of digital filters is a complex topic. Although filters are easily understood and calculated, the practical challenges of their design and implementation are significant and are the subject of advanced research. Typical design requirements Typical requirements which may be considered in the design process are: * Frequency response * Phase shift or group delay * impulse response * Causal filter required? * Stable filter required? * Finite (in duration) impulse response required? * Computational complexity * Technology The f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Continued Fraction
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 fraction is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic Rational Function
In mathematics the elliptic rational functions are a sequence of rational functions with real coefficients. Elliptic rational functions are extensively used in the design of elliptic electronic filters. (These functions are sometimes called Chebyshev rational functions, not to be confused with certain other functions of the same name). Rational elliptic functions are identified by a positive integer order ''n'' and include a parameter ξ ≥ 1 called the selectivity factor. A rational elliptic function of degree ''n'' in ''x'' with selectivity factor ξ is generally defined as: :R_n(\xi,x)\equiv \mathrm\left(n\frac\,\mathrm^(x,1/\xi),1/L_n(\xi)\right) where * cd(u,k) is the Jacobi elliptic cosine function. * K() is a complete elliptic integral of the first kind. * L_n(\xi)=R_n(\xi,\xi) is the discrimination factor, equal to the minimum value of the magnitude of R_n(\xi,x) for , x, \ge\xi. For many cases, in particular for orders of the form ''n'' = 2'' ... [...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] |
Chebyshev Polynomial
The Chebyshev polynomials are two sequences of orthogonal polynomials related to the trigonometric functions, cosine and sine functions, notated as T_n(x) and U_n(x). They can be defined in several equivalent ways, one of which starts with trigonometric functions: The Chebyshev polynomials of the first kind T_n are defined by T_n(\cos \theta) = \cos(n\theta). Similarly, the Chebyshev polynomials of the second kind U_n are defined by U_n(\cos \theta) \sin \theta = \sin\big((n + 1)\theta\big). That these expressions define polynomials in \cos\theta is not obvious at first sight but can be shown using de Moivre's formula (see #Trigonometric definition, below). The Chebyshev polynomials are polynomials with the largest possible leading coefficient whose absolute value on the interval (mathematics), interval is bounded by 1. They are also the "extremal" polynomials for many other properties. In 1952, Cornelius Lanczos showed that the Chebyshev polynomials are important in a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pafnuty Chebyshev
Pafnuty Lvovich Chebyshev ( rus, Пафну́тий Льво́вич Чебышёв, p=pɐfˈnutʲɪj ˈlʲvovʲɪtɕ tɕɪbɨˈʂof) ( – ) was a Russian mathematician and considered to be the founding father of Russian mathematics. Chebyshev is known for his fundamental contributions to the fields of probability, statistics, mechanics, and number theory. A number of important mathematical concepts are named after him, including the Chebyshev inequality (which can be used to prove the weak law of large numbers), the Bertrand–Chebyshev theorem, Chebyshev polynomials, Chebyshev linkage, and Chebyshev bias. Transcription The surname Chebyshev has been transliterated in several different ways, like Tchebichef, Tchebychev, Tchebycheff, Tschebyschev, Tschebyschef, Tschebyscheff, Čebyčev, Čebyšev, Chebysheff, Chebychov, Chebyshov (according to native Russian speakers, this one provides the closest pronunciation in English to the correct pronunciation in old Russian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ripple (filters)
Ripple (specifically ripple voltage) in electronics is the residual periodic variation of the DC voltage within a power supply which has been derived from an alternating current (AC) source. This ripple is due to incomplete suppression of the alternating waveform after rectification. Ripple voltage originates as the output of a rectifier or from generation and commutation of DC power. Ripple (specifically ripple current or surge current) may also refer to the pulsed current consumption of non-linear devices like capacitor-input rectifiers. As well as these time-varying phenomena, there is a frequency domain ripple that arises in some classes of filter and other signal processing networks. In this case the periodic variation is a variation in the insertion loss of the network against increasing frequency. The variation may not be strictly linearly periodic. In this meaning also, ripple is usually to be considered an incidental effect, its existence being a compromise between th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stephen Butterworth
Stephen Butterworth (1885–1958) was a British physicist who invented the filter that bears his name, a class of electrical circuits that separates electrical signals of different frequencies. Biography Stephen Butterworth was born on 11 August 1885 in Rochdale, Lancashire, England (a town located about 10 miles north of the city of Manchester). He was the son of Alexander Butterworth, a postman, and Elizabeth (maiden name Wynn). He was the second of four children. In 1904, he entered the Victoria University of Manchester, from which he received, in 1907, both a Bachelor of Science degree in physics (first class) and a teacher's certificate (first class). In 1908 he received a Master of Science degree in physics. For the next 11 years he was a physics lecturer at the Manchester Municipal College of Technology. He subsequently worked for several years at the National Physical Laboratory, where he did theoretical and experimental work for the determination of standards of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prototype Filter
Prototype filters are electronic filter designs that are used as a template to produce a modified filter design for a particular application. They are an example of a nondimensionalised design from which the desired filter can be scaled or transformed. They are most often seen in regard to electronic filters and especially linear analogue passive filters. However, in principle, the method can be applied to any kind of linear filter or signal processing, including mechanical, acoustic and optical filters. Filters are required to operate at many different frequencies, impedances and bandwidths. The utility of a prototype filter comes from the property that all these other filters can be derived from it by applying a scaling factor to the components of the prototype. The filter design need thus only be carried out once in full, with other filters being obtained by simply applying a scaling factor. Especially useful is the ability to transform from one bandform to another. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Impedance
Image impedance is a concept used in electronic network design and analysis and most especially in filter design. The term ''image impedance'' applies to the impedance seen looking into a Port (circuit theory), port of a network. Usually a two-port network is implied but the concept can be extended to networks with more than two ports. The definition of image impedance for a two-port network is the impedance, ''Z''i 1, seen looking into port 1 when port 2 is terminated with the image impedance, ''Z''i 2, for port 2. In general, the image impedances of ports 1 and 2 will not be equal unless the network is symmetrical (or anti-symmetrical) with respect to the ports. __TOC__ Derivation As an example, the derivation of the image impedances of a simple 'L' network is given below. The 'L' network consists of a series Electrical impedance, impedance, , and a shunt admittance, . The difficulty here is that in order to find i 1 it is first necessary to termina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Composite Image Filters
A composite image filter is an electronic filter consisting of multiple image filter sections of two or more different types. The image method of filter design determines the properties of filter sections by calculating the properties they would have in an infinite chain of identical sections. In this, the analysis parallels transmission line theory on which it is based. Filters designed by this method are called ''image parameter filters'', or just ''image filters''. An important parameter of image filters is their image impedance, the impedance of an infinite chain of identical sections. The basic sections are arranged into a ladder network of several sections, the number of sections required is mostly determined by the amount of stopband rejection required. In its simplest form, the filter can consist entirely of identical sections. However, it is more usual to use a composite filter of two or three different types of section to improve different parameters best addressed by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
