Some comments on bias/Misalignment effects in the magnitude squared coherence estimate

Kroenert, J. T.

doi:10.1109/tassp.1982.1163896

Cited by 3 publications

(4 citation statements)

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“…When the noise spectra are both zero, the denominator in Equation (22) goes to unity, indicating that the measured coherence is the actual coherence of the input and output However, when either noise source is non denominator is greater than one, and the measured coherence is less that the actual coherence of u and v. presence of random uncorrelated noise, the measured coherence is γ xy 2 (f )…”

Section: Linear System Withmentioning

confidence: 99%

“…If we consider z(t) to be the input to a unity gain noiseless system, the input measurement, and β output measurement, the coherence function can be calculated by Equation (22). Then for this random case,…”

Section: Two Random Signalsmentioning

confidence: 99%

“…Coherence has been used in modeling linear systems [1][2], estimating system time delay [3][4][5][6], and estimating system nonlinearities [7][8][9][10][11]. Its computation [12][13][14][15][16][17][18][19] is based on the standard Fourier Transform and correlation methods, with some additional considerations for discrete computation and various biases in the estimated values [20][21][22][23][24][25]. When frequency resolution in the estimate is limited in time-varying or transient cases, coherence can still be useful with certain nonstationary processes [26].…”

Section: Introductionmentioning

confidence: 99%

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Coherence Function in Noisy Linear System

Thomas¹

2015

IJBSE

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Abstract:The coherence function provides a measure of spectral similarity of two signals, but measurement noise decreases the values of measured coherence. When the two signals are the input and output of a linear system, any system noise also decreases the measured coherence values. In digital computations, useful coherence values require some degree of averaging to increase the degrees of freedom to more than two. These fundamental issues are presented with application to system input-output coherence and two random signals with a common component. Finally, estimated coherence of the two random signals, with varying degrees of freedom, are shown with empirical adjustments that can improve the estimate of coherence. Coherence has a wide range of biomedical applications, but this article focuses on the fundamental properties of the coherence function.

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Section: Linear System Withmentioning

confidence: 99%

Section: Two Random Signalsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Coherence Function in Noisy Linear System

Thomas¹

2015

IJBSE

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“…One has been aware of misalignment effects on coherence since the 1960's [3], and the bias caused by white signals and rectangular time windowing has been given [4]- [6]. This result has also been extended to arbitrary windows [2], [7]. In the white noise case, the phase of the cross spectrum and the location of the peak in the cross correlation are not affected by misalignment [6], [2].…”

Section: Introductionmentioning

confidence: 99%

Bias in the cross spectrum and time delay estimates due to misalignment

Holm¹,

Ottesen²

1986

IEEE Trans. Acoust., Speech, Signal Process.

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Phase errors in the cross spectrum estimate due to misalignment

Holm

ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing

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is the tine delay.When the crose spectrum is estimated where there is a delay between the two input signals, itIn nost practical estimation problems one has is shown that the corresponding misalignment gives a limited, I seconds, long segment of each input both magnitude and phase errors. The existence of signal. The delay, D, then gives a reduced overlap the phase error is a new result. The importance of of the two inputs of T-D seconds. This is referred the errors depend on the algorithms used. It is to as misalignment, and it gives an error in the shown that the misalignment may either be given by cross spectrum estimate. This error was investigathe total observation time or by the section length ted by Carter [4[ and Rroenert Es], but they only in the processor. In the latter case the effect of found the effect on the magnitude of the cross phase errors must be considered when the section spectrum. In this paper the effect on the phase is length is low, that is when the cross spectrum is also found.smooth, requiring little resolution. EXPECTED VALUE OF THE CROSS SPECTRUM INTROOUCTIONThe input signals are s(t) end r(t) = s(t-D) +

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Some comments on bias/Misalignment effects in the magnitude squared coherence estimate

Cited by 3 publications

References 2 publications

Coherence Function in Noisy Linear System

Coherence Function in Noisy Linear System

Bias in the cross spectrum and time delay estimates due to misalignment

Phase errors in the cross spectrum estimate due to misalignment

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