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The Cauchy distribution does not have a mean value or a variance, because the integral (15) does not converge.
Therefore, it is not capable of computing the mean value or the DC component of a signal under analysis.
By picking peaks in the differential that are above a certain threshold (e.g., the mean value or a given percentage of the maximum of the differential over a certain time window) some onsets can be located.
The mean value or expectation (mathbb{E}(X)) of the random variable X is defined as the integral mathbb{E}(X) = int_{Omega}X omega),dmathbb{P} omega), if it exists.
Moreover, these derivations could, also, approximate that of the Rician channels when the mean channel matrix is of rank 1; this could be satisfied when all channel vectors have the same mean value or in some other practical scenarios where the line-of-sight (LOS) component of the channel matrix approaches the scaled all-ones matrix [37].
Shock was defined when the systolic blood pressure was measured as <2 standard deviations (SD) of the age related mean value or in the presence of severely decreased peripheral effusion during physical examination.
Similar(37)
Mean values or results of typical experiments are presented, as indicated.
All data are presented as mean values or number of patients.
In the current review meta-analysis did not require imputation of missing mean values or SDs.
All data was presented as mean values or no. of patients.
Mean values or proportions of the established risk factors are shown in Table 1.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com