Approximation of statistical distribution of magnitude squared coherence estimated with segment overlapping

A Statistical Study of Temporally Smoothed Wavelet Coherence

“…The use of a wavelet coherence measure, WCOH say, in the scale-time (wavelet) domain, continues to be of great interest in many fields of science [2], [12], [13], [17], [22], [26]. The continuous wavelet transform (CWT) at scale , for , and translation or time is defined as (e.g., [21]) (1) where is the wavelet transform of a signal is the analyzing wavelet, and denotes complex conjugation. Given two jointly stationary signals and , and with ' ' representing a smoothing step, a wavelet coherence estimator at a particular scale and time in the time-scale domain can be expressed as (e.g., [22]) (2) Without smoothing this quantity is identically unity [15].…”

“…Then we cast the WOSA estimator into a multitaper-type formulation which allows us to derive highly accurate degrees of freedom estimates. In so doing we are also able to remove assumptions and approximations made by Bortel and Sovka [1] in their recent study of the statistical distribution of magnitude squared coherence estimated with segment overlapping. Since the Morlet wavelet is complex-valued, we derive analytic results for the case of wavelet coherence calculated from complex-valued, jointly stationary and Gaussian time series.…”

System identification and uncertainty quantification using orthogonal excitations and the Semispan Supersonic Transport (S4T) model

“…However, none of these methods appeared any more applicable to sinusoidal data than the two applied below. 20 and utilized by Bortel & Sobka,26 The open loop single excitation data was first analyzed. The coherence and the 95% confidence bounds calculated using Method 1 are shown in requires that the segments be nonoverlapping.…”

Identification of connectivity in human motor control: exciting the afferent pathways

“…All signals were segmented in 1s segments (2048 samples) -the period of the perturbation -with 75% overlap between segments; the use of overlapping segments decreases the bias and variance of the coherence estimates (Bortel and Sovka, 2007;Carter, 1987). The EOG was used to remove segments containing eye blinks.…”

“…Significance of coherence values was determined using the approximation of the confidence limit (CL) by Bortel and Sovka (2007). The confidence level was set to 0.99 (α = 0.01).…”