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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 Chebyshev filter ： ウィキペディア英語版 Chebyshev filter Chebyshev filters are analog or digital filters having a steeper roll-off and more passband ripple (type I) or stopband ripple (type II) than Butterworth filters. Chebyshev filters have the property that they minimize the error between the idealized and the actual filter characteristic over the range of the filter, but with ripples in the passband. This type of filter is named after Pafnuty Chebyshev because its mathematical characteristics are derived from Chebyshev polynomials. Because of the passband ripple inherent in Chebyshev filters, the ones that have a smoother response in the passband but a more irregular response in the stopband are preferred for some applications. == Type I Chebyshev filters == Type I Chebyshev filters are the most common types of Chebyshev filters. The gain (or amplitude) response as a function of angular frequency $\backslash omega$ of the ''n''th-order low-pass filter is equal to the absolute value of the transfer function $H\_n(j\; \backslash omega)$: :$G\_n(\backslash omega)\; =\; \backslash left\; |\; H\_n(j\; \backslash omega)\; \backslash right\; |\; =\; \backslash frac\backslash right)\}\}$ where $\backslash varepsilon$ is the ripple factor, $\backslash omega\_0$ is the cutoff frequency and $T\_n$ is a Chebyshev polynomial of the $n$th order. The passband exhibits equiripple behavior, with the ripple determined by the ripple factor $\backslash varepsilon$. In the passband, the Chebyshev polynomial alternates between -1 and 1 so the filter gain alternate between maxima at ''G'' = 1 and minima at $G=1/\backslash sqrt$. At the cutoff frequency $\backslash omega\_0$ the gain again has the value $1/\backslash sqrt$ but continues to drop into the stop band as the frequency increases. This behavior is shown in the diagram on the right. The common practice of defining the cutoff frequency at −3 dB is usually not applied to Chebyshev filters; instead the cutoff is taken as the point at which the gain falls to the value of the ripple for the final time. The order of a Chebyshev filter is equal to the number of reactive components (for example, inductors) needed to realize the filter using analog electronics. The ripple is often given in dB: :Ripple in dB = $10\; \backslash log\_(1+\backslash varepsilon^2)$ so that a ripple amplitude of 3 dB results from $\backslash varepsilon\; =\; 1.$ An even steeper roll-off can be obtained if ripple is allowed in the stop band, by allowing zeroes on the $j\backslash omega$-axis in the complex plane. However, this results in less suppression in the stop band. The result is called an elliptic filter, also known as Cauer filter. 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「Chebyshev 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.