Influences of the signal border extension in the discrete wavelet transform in EEG spike detection

Abstract Introduction The discrete wavelet transform is used in many studies as signal preprocessor for EEG spike detection. An inherent process of this mathematical tool is the recursive wavelet convolution over the signal that is decomposed into detail and approximation coefficients. To perform these convolutions, firstly it is necessary to extend signal borders. The selection of an unsuitable border extension algorithm may increase the false positive rate of an EEG spike detector. Methods In this study we analyzed nine different border extensions used for convolution and 19 mother wavelets commonly seen in other EEG spike detectors in the literature. Results The border extension may degrade an EEG spike detector up to 44.11%. Furthermore, results behave differently for distinct number of wavelet coefficients. Conclusion There is not a best border extension to be used with any EEG spike detector based on the discrete wavelet transform, but the selection of the most adequate border extension is related to the number of coefficients of a mother wavelet.

Pulmonary crackle characterization: approaches in the use of discrete wavelet transform regarding border effect, mother-wavelet selection, and subband reduction

Introduction Crackles are discontinuous, non-stationary respiratory sounds and can be characterized by their duration and frequency. In the literature, many techniques of filtering, feature extraction, and classification were presented. Although the discrete wavelet transform (DWT) is a well-known tool in this area, issues like signal border extension, mother-wavelet selection, and its subbands were not properly discussed. Methods In this work, 30 different mother-wavelets 8 subbands were assessed, and 9 border extension modes were evaluated. The evaluations were done based on the energy representation of the crackle considering the mother-wavelet and the border extension, allowing a reduction of not representative subbands. Results Tests revealed that the border extension mode considered during the DWT affects crackle characterization, whereas SP1 (Smooth-Padding of order 1) and ASYMW (Antisymmetric-Padding (whole-point)) modes shall not be used. After DWT, only 3 subbands (D3, D4, and D5) were needed to characterize crackles. Finally, from the group of mother-wavelets tested, Daubechies 7 and Symlet 7 were found to be the most adequate for crackle characterization. Discussion DWT can be used to characterize crackles when proper border extension mode, mother-wavelet, and subbands are taken into account.