LINEAR VERSUS LOGARITHMIC AVERAGING
LINEAR VERSUS LOGARITHMIC AVERAGING
复制标题
线性平均与对数平均
DOI：
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发表时间：
1966
期刊：
影响因子：
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通讯作者：
H. Cox
中科院分区：
文献类型：
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作者：
H. Cox
考虑n个数据样本{x1，x2，xn}，使得o<L <$xi <$U < ∞。设K = U/L;然后，它表明，独立于n的数据样本的几何平均值与算术平均值之比的下限由[lnK/（K − 1）]K{（1/lnK）−1/（K−1）}给出。该界限在声学信号处理中很有用，因为它限制了可归因于平均对数而不是取数据样本平均值的对数的偏差量。这两种方法目前都在专门处理声学数据的设施中使用。例如，对于10 dB的K，几何平均值比算术平均值低不到1.5 dB。
Consider n data samples {x1, ⋯, xn} such that o<L⩽xi⩽U < ∞. Let K = U/L; then it is shown that independent of n a lower bound on the ratio of the geometric mean to the arithmetic mean of the data samples is given by [lnK/(K − 1)]K{(1/lnK)−1/(K−1)}. This bound is useful in acoustic signal processing since it limits the amount of deviation that can be attributed to averaging logarithms vice taking the logarithm of the average of data samples. Both methods are currently in use at facilities specializing the processing of acoustic data. For a K of 10 dB, for example, the geometric mean is less than 1.5 dB below the arithmetic mean.