翻訳と辞書 Words near each other ・ Linear script ・ Linear search ・ Linear search problem ・ Linear seismic inversion ・ Linear separability ・ Linear settlement ・ Linear space (geometry) ・ Linear span ・ Linear speedup theorem ・ Linear Sphere ・ Linear stability ・ Linear stage ・ Linear subspace ・ Linear sweep voltammetry ・ Linear syntax ・ Linear system ・ Linear system of divisors ・ Linear Tape File System ・ Linear Tape-Open ・ Linear Technology ・ Linear temporal logic ・ Linear temporal logic to Büchi automaton ・ Linear timecode ・ Linear topology ・ Linear transform model (MRI) ・ Linear transformation in rotating electrical machines ・ Linear transformer driver ・ Linear transport theory ・ Linear trend estimation ・ Linear Unit Grammar Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Linear system ： ウィキペディア英語版 Linear system A linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the general, nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic control theory, signal processing, and telecommunications. For example, the propagation medium for wireless communication systems can often be modeled by linear systems. ==Definition== A general deterministic system can be described by an operator, $H$, that maps an input, $x(t)$, as a function of $t$ to an output, $y(t)$, a type of black box description. Linear systems satisfy the property of superposition. Given two valid inputs :$x\_1(t)\; \backslash ,$ :$x\_2(t)\; \backslash ,$ as well as their respective outputs :$y\_1(t)\; =\; H\; \backslash left\; \backslash$ :$y\_2(t)\; =\; H\; \backslash left\; \backslash$ then a linear system must satisfy :$\backslash alpha\; y\_1(t)\; +\; \backslash beta\; y\_2(t)\; =\; H\; \backslash left\; \backslash$ for any scalar values $\backslash alpha\; \backslash ,$ and $\backslash beta\; \backslash ,$. The system is then defined by the equation $H(x(t))\; =\; y(t)$, where $y(t)$ is some arbitrary function of time, and $x(t)$ is the system state. Given $y(t)$ and $H$, $x(t)$ can be solved for. For example, a simple harmonic oscillator obeys the differential equation: :$m\; \backslash frac\; =\; -kx$. If :$H(x(t))\; =\; m\; \backslash frac\; +\; kx(t)$, then $H$ is a linear operator. Letting $y(t)\; =\; 0$, we can rewrite the differential equation as $H(x(t))\; =\; y(t)$, which shows that a simple harmonic oscillator is a linear system. The behavior of the resulting system subjected to a complex input can be described as a sum of responses to simpler inputs. In nonlinear systems, there is no such relation. This mathematical property makes the solution of modelling equations simpler than many nonlinear systems. For time-invariant systems this is the basis of the impulse response or the frequency response methods (see LTI system theory), which describe a general input function $x(t)$ in terms of unit impulses or frequency components. Typical differential equations of linear time-invariant systems are well adapted to analysis using the Laplace transform in the continuous case, and the Z-transform in the discrete case (especially in computer implementations). Another perspective is that solutions to linear systems comprise a system of functions which act like vectors in the geometric sense. A common use of linear models is to describe a nonlinear system by linearization. This is usually done for mathematical convenience. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Linear system」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.