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Signal-flow Graph
A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, but often called a Mason graph after Samuel Jefferson Mason who coined the term, is a specialized Flow graph (mathematics), flow graph, a directed graph in which nodes represent system variables, and branches (edges, arcs, or arrows) represent functional connections between pairs of nodes. Thus, signal-flow graph theory builds on that of directed graphs (also called Digraph (mathematics), digraphs), which includes as well that of Orientation (graph theory)#Oriented graphs, oriented graphs. This mathematical theory of digraphs exists, of course, quite apart from its applications. i SFGs are most commonly used to represent signal flow in a physical systems, physical system and its controller(s), forming a cyber-physical system. Among their other uses are the representation of signal flow in various electronic networks and amplifiers, digital filters, state-variable filters and some other types of analog f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, computer scientist, cryptographer and inventor known as the "father of information theory" and the man who laid the foundations of the Information Age. Shannon was the first to describe the use of Boolean algebra—essential to all digital electronic circuits—and helped found artificial intelligence (AI). Roboticist Rodney Brooks declared Shannon the 20th century engineer who contributed the most to 21st century technologies, and mathematician Solomon W. Golomb described his intellectual achievement as "one of the greatest of the twentieth century". At the University of Michigan, Shannon dual degreed, graduating with a Bachelor of Science in electrical engineering and another in mathematics, both in 1936. A 21-year-old master's degree student in electrical engineering at MIT, his thesis, "A Symbolic Analysis of Relay and Switching Circuits", demonstrated that electric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equations
In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in French an ''équation'' is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. Solving an equation containing variables consists of determining which values of the variables make the equality true. The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true for particular values of the variables. The " =" symbol, which appears in every equation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mason's Gain Formula
Mason's gain formula (MGF) is a method for finding the transfer function of a linear signal-flow graph (SFG). The formula was derived by Samuel Jefferson Mason, for whom it is named. MGF is an alternate method to finding the transfer function algebraically by labeling each signal, writing down the equation for how that signal depends on other signals, and then solving the multiple equations for the output signal in terms of the input signal. MGF provides a step by step method to obtain the transfer function from a SFG. Often, MGF can be determined by inspection of the SFG. The method can easily handle SFGs with many variables and loops including loops with inner loops. MGF comes up often in the context of control systems, microwave circuits and digital filters because these are often represented by SFGs. Formula The gain formula is as follows: : G = \frac = \frac : \Delta = 1 - \sum L_i + \sum L_iL_j- \sum L_iL_jL_k + \cdots + (-1)^m \sum \cdots +\cdots where: *Δ = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaussian Elimination
In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of row-wise operations performed on the corresponding matrix of coefficients. This method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse of an invertible matrix. The method is named after Carl Friedrich Gauss (1777–1855). To perform row reduction on a matrix, one uses a sequence of elementary row operations to modify the matrix until the lower left-hand corner of the matrix is filled with zeros, as much as possible. There are three types of elementary row operations: * Swapping two rows, * Multiplying a row by a nonzero number, * Adding a multiple of one row to another row. Using these operations, a matrix can always be transformed into an upper triangular matrix (possibly bordered by rows or columns of zeros), and in fact one that is in row echelon form. Once all of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elements Of A Signal Flow Graph
Element or elements may refer to: Science * Chemical element, a pure substance of one type of atom * Heating element, a device that generates heat by electrical resistance * Orbital elements, parameters required to identify a specific orbit of one body around another * DNA element, a functional region of DNA, including genes and cis-regulatory elements. Mathematics * Element (category theory), one of the constituents in general category theory * Element (mathematics), one of the constituents of set theory in mathematics * Differential element, an infinitesimally small change of a quantity in an integral * Euclid's ''Elements'', a mathematical treatise on geometry and number theory * An entry, or element, of a matrix Philosophy and religion * Classical elements, ancient beliefs about the fundamental types of matter (earth, air, fire, water) * The elements, a religious term referring to the bread and wine of the Eucharist * ''Godai'' (Japanese philosophy), the basis of the un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solving Linear Equations
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Solution may refer to: * Solution (chemistry), a mixture where one substance is dissolved in another * Solution (equation), in mathematics ** Numerical solution, in numerical analysis, approximate solutions within specified error bounds * Solution, in problem solving * A business solution is a method of organizing people and resources that can be sold as a product ** Solution, in solution selling Other uses * V-STOL Solution, an ultralight aircraft * Solution (band), a Dutch rock band ** ''Solution'' (Solution album), 1971 * Solution A.D., an American rock band * ''Solution'' (Cui Jian album), 1991 * ''Solutions'' (album), a 2019 album by K.Flay See also * Nature-based solutions * The Solution (other) The Solution may refer to: *The Solution (Mannafest album), ''The Solution'' (Mannafest album), an album by indie rock band Mannafest *The Solution (Beanie Sigel album), ''The Solution'' (Beanie Sigel album), an album by rapper Beanie Sigel *The So ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplace Transform
In mathematics, the Laplace transform, named after Pierre-Simon Laplace (), is an integral transform that converts a Function (mathematics), function of a Real number, real Variable (mathematics), variable (usually t, in the ''time domain'') to a function of a Complex number, complex variable s (in the complex-valued frequency domain, also known as ''s''-domain, or ''s''-plane). The transform is useful for converting derivative, differentiation and integral, integration in the time domain into much easier multiplication and Division (mathematics), division in the Laplace domain (analogous to how logarithms are useful for simplifying multiplication and division into addition and subtraction). This gives the transform many applications in science and engineering, mostly as a tool for solving linear differential equations and dynamical systems by simplifying ordinary differential equations and integral equations into algebraic equation, algebraic polynomial equations, and by simplifyin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
