Experimental Investigation of Bias and Confidence of the Ordinary Coherence Function


Experimental Investigation of Bias and Confidence of the Ordinary Coherence Function

Schumann, P.

The ordinary coherence function 2( ) defined by
Sxy( ) 2
2( ) = (1)
Sxx( ) * Syy( )

is of squared type with a positive bias depending on the number N of accumulated estimations. If the analyzed signals x(t), y(t) as well as the correlated contribution inside x(t), y(t) are normally distributed the power spectral densities Sxx, Syy are 2-distributed. Then the product as well as the quotient in equ. 1 are not of a classical distribution type and the determination of the concrete type becomes difficult.
Therefore the bias and the corresponding standard deviation are investigated experimentally using uncorrelated normally distributed white noise. The result shows for estimation numbers N > 5, that the bias of 2 corresponds to the amount of 1/N. The belonging positive standard deviation
sigma ( OVERLINE { gamma SUP 2 } (f SUB i)) ~ = ~ SQRT { { Sum from { i = 1} TO M { ( OVERLINE { gamma SUP 2 } (f SUB i) ~ - ~ OVERLINE { gamma SUP 2 } ) } SUP 2 } OVER {M -1 } }


(2)

for N > 5 t is in the same order of magnitude as the bias itself. That means: For the evaluation of coherences a confidence band of +(4...5) * should be used to select values of significant statistical accuracy. Only for these selected values one can be sure, that the phase values belonging the same frequency point are useful for system identification.

  • Lecture (Conference)
    IMORN-24 (Informal Meeting on Rector Noise), Oybin / Germany, 23 - 25 June 1993

Permalink: https://www.hzdr.de/publications/Publ-1876
Publ.-Id: 1876