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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 Signal averaging ： ウィキペディア英語版 Signal averaging Signal averaging is a signal processing technique applied in the time domain, intended to increase the strength of a signal relative to noise that is obscuring it. By averaging a set of replicate measurements, the signal-to-noise ratio, S/N, will be increased, ideally in proportion to the square root of the number of measurements. == Deriving the SNR for averaged signals == Assumed that * Signal $s(t)$ is uncorrelated to noise, and noise $z(t)$ is uncorrelated : $E()\; =\; 0\; =\; E()\backslash forall\; t,\backslash tau$. * Signal power $S=\backslash int\_0^T$ is constant in the replicate measurements. * Noise is random, with a mean of zero and constant variance in the replicate measurements: $E()\; =\; 0\; =\; \backslash mu$ and . * We (canonically) define Signal-to-Noise ratio as $SNR=\backslash frac$. === Noise power for sampled signals === Assuming we sample the noise, we get a per-sample variance of $\backslash mathrm(z)=E()\; =\; \backslash sigma^2$. Averaging a random variable leads to the following variance: $\backslash mathrm\backslash left(\backslash frac\; 1n\; \backslash sum\_^n\; z\_n\backslash right)\; =\; \backslash frac\; 1\; \backslash mathrm\backslash left(\backslash sum\_^n\; z\_n\backslash right)=\; \backslash frac\; 1\; \backslash sum\_^n\backslash mathrm\backslash left(\; z\_n\backslash right)$. Since noise variance is constant $\backslash sigma^2$: $N\_\backslash text\; =\; \backslash mathrm\backslash left(\backslash frac\; 1n\; \backslash sum\_^n\; z\_n\backslash right)\; =\; \backslash frac\; 1\; n\; \backslash sigma^2\; =\; \backslash frac\; 1n\; \backslash sigma^2$, demonstrating that averaging $n$ realizations of the same, uncorrelated noise reduces noise power by a factor of $n$. 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「Signal averaging」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.