Wavelet coherence

If the covariance is restricted to the dominant oscillations of the underlying processes and only the time resolved phase relation but no amplitude and scale information is desired, another method might be superior to wavelet coherency analysis An instantanious phase relation might be derived by Hilbert phase analyis. This method originated from synchronization analysis [14,16]. We combined this approach with a geometrically motivated filtering [13] and successfully utilized it for the analysis of the coupling between El Nino/Southern Oscillation (ENSO) and the Indian monsoon [12]. 

A Hybrid Trial to Trial Wavelet Coherence and Novelty Detection Scheme for a Fast and Clear Notification of Habituation An Objective Uncomfortable Loudness... 

Objective To determine an uncomfortable loudness (UCL) level is not an easy task, especially in children. A need to objectively measure this level is crucial as the age of hearing devices candidates is getting younger. Previous studies have shown that the feasibility of habituation correlates in late auditory evoked potentials for a measurement technique of UCL identification is promising. Nevertheless, a scheme that could provide a fast and clear notification of an UCL level is reached is desirable. The present study has introduced a hybrid trial to trial wavelet coherence and novelty detection scheme to extract and to notify objectively the habituation correlates in late auditory evoked potentials. 

Keywords— habituation, wavelet coherence, novelty detection, late auditory evoked potential... 

Lets (q is the wavelet cross spectrum between signal a and b, where (p and t represent the wavelet and window to calculate wavelet coherence, respectively. With... 

Habituation is defined as reduction of response over repeatable stimulations. Hence, should habituation occurs at present trial in comparison to immediately previous trial, the obtained coherence in between trials is towards zero as both trials are not correlated. See [5] for details explanation of trial to trial wavelet coherence and references therein. 

Trial to trial provides informative features that describe habituate response or non-habituate response. In order to extract the moment of the habituation presence, we further analyze the wavelet coherence results with novelty detection. We have observed in [5] that reduction of wavelet coherence (habituation) occurs after several trials after the experiment began. Therefore, we take these first q trials (training set) to train a classifier. This classifier is generated by all information of q trials and forms a hypothetical sphere with center c and radius K. To minimize this sphere so that the learning machine free from false negative errors, the problem is solved by... 

In previous results as in [5], we could see that habituate responses (low sound) produce a continuous reduction of wavelet coherence in comparison to response of higher sound (insignificant changes of wavelet coherence over time), see [5] for details implementation of trial to trial wavelet coherence and the obtain results. 

In the present study, we further analyze the results in [5] in order to achieve a fast and rehable identification of habituate response. With a combination of trial to trial wavelet coherence and novelty detection schemes, identification of habituation moment is clearly highlighted. Trial to trial wavelet coherence is a reliable method to extract habituation and novelty detection analysis is able to highlight the abnormality in a train of data which provide a suitable method for identifying a reduction of response in real time. 

In the present study, we improved post processing technique to extract habituation in LAEPs by combining trial to trial wavelet coherence with novelty detection. The identification of habituation presence is faster and clearly hig-hhghted in comparison to previous study. These findings, give a promising technique for objectively determine UCL procedure and analysis. 

Wavelet coherence was first introduced by [21] and has been commonly used in evaluating synchronization in EEG... 

Eurthermore, it has recently been used for a reliable detection of auditory habituation [25]. It is noted that the wavelet coherence measure that we applied here is adopted from [25], which is similar to [21],... 

For x,y (IR), the wavelet coherence of two signals x and y, u - (-,-)with a fixed smoothing parameter 5 E M > 0 and wavelet is defined as the cross-wavelet spectrum of the two signals normalized by their corresponding autospectra ... 

Finally, we defined the moving mean wavelet coherence in a similar way to the moving mean wavelet-phase stability ... 

We have presented a performance study of using the WPS in identifying neural correlates of auditory selective attention that reflected in single sweeps ALRs. It is shown that the method requires fewer response sweeps to perform the discrimination of the attentional conditions (attended versus unattended) compared to the widely-used wavelet coherence coefficient methods. It is concluded that the WPS is feasible to be used in an objective evaluation of large-scale neural correlates of auditory selective attention as a synchronization measure. 

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