Scale‐space filtering is one of the hierarchical representations of the waveform in which the given waveform is observed in multiscale measurement. Scale‐space filtering using the Gaussian filter, whose bandwidth varies with the scale, continuously blurs the waveform. It has a property that the number of zero crossings of the waveform decreases monotonically while increasing the scale. This property is called monotonicity. The relations among intervals sectioned by zero crossings are represented by a tree structure. Thus, most of the past studies on the scale‐space filtering can be viewed as the studies of the waveforms in (‐∞, ∞). However, there has been no adequate discussion on the scale‐space filtering of the periodic waveform. This paper describes a method to construct scale‐space filtering so that the monotonicity of the zero crossings applies also to the periodic waveform. By analyzing the zero crossings of the waveform, essential differences between the ordinary scale‐space filtering and the periodic scale‐space filtering are indicated. An example is presented for the structural analysis of the speech waveform, and the difference between the hierarchical structures derived by those scale‐space filters is discussed.
Background: Patients with Tic Disorders (TD) usually comorbid with Obsessive-compulsive disorder (OCD). The severity of obsessive-compulsive symptoms (OCS) in TD is widely evaluated via the Children’s Yale-Brown Obsessive-Compulsive Scale (CY-BOCS). However, the reliability and validity of CY-BOCS in TD patients are still unclear. Methods: In this study, we examined the psychometric properties of the Chinese version of the CY-BOCS in patients with tic disorders. Results: We examined the psychometric properties of the CY-BOCS in 367 patients with TD in China. We performed reliability and validity analyses on the CY-BOCS and found that the Cronbach’s Alpha and the test-retest reliability of CY-BOCS were 0.809 and 0.821 respectively. The CY-BOCS showed good consistency in the two-factor structure, namely the “obsession” and the “compulsive” factors (the comparative fit index was 0.84). Conclusion: The CY-BOCS has good psychometric properties in children and adolescents with TD. It suggests that the CY-BOCS could be widely used in Chinese children and adolescents with TD, especially for the TS patients.
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