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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 Bandlimiting ： ウィキペディア英語版 Bandlimiting Bandlimiting is the limiting of a signal's Fourier transform or power spectral density to zero above a certain finite frequency. A band-limited signal is one whose Fourier transform or power spectral density has bounded support. The signal may be either random (stochastic) or non-random (deterministic). In general, infinitely many terms are required in a continuous Fourier series representation, but if a finite number of Fourier series terms can be calculated from that signal, that signal is considered to be band-limited. ==Sampling bandlimited signals== A bandlimited signal can be fully reconstructed from its samples, provided that the sampling rate exceeds twice the maximum frequency in the bandlimited signal. This minimum sampling frequency is called the Nyquist rate. This result, usually attributed to Nyquist and Shannon, is known as the Nyquist–Shannon sampling theorem. An example of a simple deterministic bandlimited signal is a sinusoid of the form $x(t)\; =\; \backslash sin(2\; \backslash pi\; ft\; +\; \backslash theta)\; \backslash$. If this signal is sampled at a rate $f\_s\; =\backslash frac\; >\; 2f$ so that we have the samples $x(nT)\; \backslash$, for all integers $n$, we can recover $x(t)\; \backslash$ completely from these samples. Similarly, sums of sinusoids with different frequencies and phases are also bandlimited to the highest of their frequencies. The signal whose Fourier transform is shown in the figure is also bandlimited. Suppose $x(t)\backslash$ is a signal whose Fourier transform is $X(f)\backslash$, the magnitude of which is shown in the figure. The highest frequency component in $x(t)\backslash$ is $B\; \backslash$. As a result, the Nyquist rate is :$R\_N\; =\; 2B\; \backslash ,$ or twice the highest frequency component in the signal, as shown in the figure. According to the sampling theorem, it is possible to reconstruct $x(t)\backslash$ completely and exactly using the samples :$x()\; \backslash \; \backslash stackrel\backslash \; x(nT)\; =\; x\; \backslash left(\; \backslash right)$ for all integers $n\; \backslash ,$ and $T\; \backslash \; \backslash stackrel\backslash$ as long as :$f\_s\; >\; R\_N\; \backslash ,$ The reconstruction of a signal from its samples can be accomplished using the Whittaker–Shannon interpolation formula. 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「Bandlimiting」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.