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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Gaussian filter ： ウィキペディア英語版 Gaussian filter In electronics and signal processing, a Gaussian filter is a filter whose impulse response is a Gaussian function (or an approximation to it). Gaussian filters have the properties of having no overshoot to a step function input while minimizing the rise and fall time. This behavior is closely connected to the fact that the Gaussian filter has the minimum possible group delay. It is considered the ideal time domain filter, just as the sinc is the ideal frequency domain filter.〔Filtering in the Time and Frequency Domains by Herman J. Blinchikoff, Anatol I. Zverev〕 These properties are important in areas such as oscilloscopes〔http://www.radiomuseum.org/forumdata/users/4767/file/Tektronix_VerticalAmplifierCircuits_Part1.pdf〕 and digital telecommunication systems.〔http://www.picosecond.com/objects/AN-7a.pdf〕 Mathematically, a Gaussian filter modifies the input signal by convolution with a Gaussian function; this transformation is also known as the Weierstrass transform. ==Definition== The one-dimensional Gaussian filter has an impulse response given by :$g(x)=\; \backslash sqrt\}\backslash cdot\; e^$ and the frequency response is given by the Fourier transform :$\backslash hat\; g(f)=\; e^\}$ with $f$ the ordinary frequency. These equations can also be expressed with the standard deviation as parameter :$g(x)\; =\; \backslash frac\backslash cdot\; e^\}$ and the frequency response is given by :$\backslash hat\; g(f)\; =\; e^\}$ By writing $a$ as a function of $\backslash sigma$ with the two equations for $g(x)$ and as a function of $\backslash sigma\_f$ with the two equations for $\backslash hat\; g(f)$ it can be shown that the product of the standard deviation and the standard deviation in the frequency domain is given by :$\backslash sigma\backslash cdot\backslash sigma\_f=\backslash frac$, where the standard deviations are expressed in their physical units, e.g. in the case of time and frequency in seconds and Hertz. In two dimensions, it is the product of two such Gaussians, one per direction: :$g(x,y)\; =\; \backslash frac\; \backslash cdot\; e^\}$ 〔R.A. Haddad and A.N. Akansu, "A Class of Fast Gaussian Binomial Filters for Speech and Image Processing," IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 39, pp 723-727, March 1991.〕〔Shapiro, L. G. & Stockman, G. C: "Computer Vision", page 137, 150. Prentence Hall, 2001〕〔Mark S. Nixon and Alberto S. Aguado. ''Feature Extraction and Image Processing''. Academic Press, 2008, p. 88.〕 where ''x'' is the distance from the origin in the horizontal axis, ''y'' is the distance from the origin in the vertical axis, and ''σ'' is the standard deviation of the Gaussian distribution. 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「Gaussian filter」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.