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An optimal double inequality between logarithmic and generalized logarithmic means

Jiang Y., Long B., Chu Y.

Journal of Applied Analysis

2013

Vol. 19, nr 2

271--182

In this paper, we answer the question: for any q > 0 with q ≠ 1, what are the greatest value p1= p1(q) and the least value p2= p2(q) such that the double inequality Lp1(a, b) < [L(aq, bq)]1/q < Lp2(a, b) holds for all a, b > 0 with a ≠ b? Here L(a, b) and Lp(a, b) are the logarithmic and pth generalized logarithmic means of a and b, respectively.

Teager–Kaiser Operator improves the accuracy of EMG onset detection independent of signal-to-noise ratio

Solnik S., Devita P., Rider P., Long B., Hortobagyi T.

Acta of Bioengineering and Biomechanics

2008

Vol. 10, nr 2

57-63

A temporal analysis of electromyographic (EMG) activity has widely been used for non-invasive study of muscle activation patterns. Such an analysis requires robust methods to accurately detect EMG onset. We examined whether data conditioning, supplemented with Teager–Kaiser Energy Operator (TKEO), would improve accuracy of the EMG burst onset detection. EMG signals from vastus lateralis, collected during maximal voluntary contractions, performed by seventeen subjects (8 males, 9 females, mean age of 46 yrs), were analyzed. The error of onset detection using enhanced signal conditioning was significantly lower than that of onset detection performed on signals conditioned without the TKEO (40 š99 ms vs. 229 š356 ms, t-test, p = 0.023). The Pearson correlations revealed that neither accuracy after enhanced conditioning nor accuracy after standard conditioning was significantly related to signal-to-noise ratio (SNR) (r = –0.05, p = 0.8 and r = –0.19, p = 0.46, respectively). It is concluded that conditioning of the EMG signals with TKEO significantly improved the accuracy of the threshold-based onset detection methods, regardless of SNR magnitude.