A quantitative approach integrating AR modeling and wavelet transform is presented in this paper to analyze the digitized phonocardiogram. The recognition of the first and the second heart sounds (S(1) and S(2)) were facilitated with wavelet transform without referring to the QRS waveform. We found that the Daubechies wavelet is most effective in identifying S(1) and S(2). In addition, the boundaries of S(1), S(2), and the onset and duration of the systolic murmur thus identified within the systole could be marked using the wavelet-filtered signal's strength. Furthermore, quantitative measures derived from a 2(nd) order AR model were used to delineate the configuration and pitch of the systolic murmur found within through piecewise segmentation. The proposed approach was tested and proved effective in delineating a set of clinically diagnosed systolic murmurs. The suggested AR and wavelet transform combined approach can be generalized with minor adjustments to delineate diastolic murmurs as well.
The correlation dimension was used in this paper as a quantifier to describe the chaotic behavior of sleep EEG recorded from the hippocampus of adult rats during vigilance states of quiet-waking, slow-wave sleep, and REM sleep. A modified Grassberger-Procaccia method was implemented to compute the correlation integral using a Euclidean distance normalized by the embedding dimension. The performance of the correlation dimension as a measure to characterize the sleep EEG was compared to the quantitative measures derived from linear autoregressive models. Even though linear and chaotic measures are based on completely different theories and concepts, our experimental results have indicated them both effective in capturing the characteristic differences of sleep EEG during various states. The preliminary results have also shown the correlation dimension being particularly effective in emphasizing the differences in regard to the chaotic behavior between the EEG activity in SWS and QW and REM sleep.
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