Accession Number:

AD0657404

Title:

LINEAR VERSUS LOGARITHMIC AVERAGING

Descriptive Note:

Final rept

Corporate Author:

DAVID W TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER BETHESDA MD SHIP ACOUSTICS DEPT

Personal Author(s):

Report Date:

1967-06-01

Pagination or Media Count:

7.0

Abstract:

Consider n data samples x1,...,xn such that 0 L or xi or U infinity. Let K UL 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 ln KK -1K to the power 1ln K - 1K-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 in 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.

Subject Categories:

  • Numerical Mathematics
  • Acoustics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE