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A technique to remove baseline wander (BW) from electrocardiogram (ECG) signals based on the Hilbert vibration decomposition (HVD) technique is presented. It is proposed that the first component (highest energy component) obtained using the HVD of the ECG signal corresponds to the BW signal in it. The proposed technique is compared with the baseline removal method based on the empirical mode decomposition technique and mathematical morphology in terms of the correlation criterion and signal-to-noise ratio. The simulations were performed using artificial BWs of different amplitudes added in the ECG recordings and it is seen that the proposed technique for BW removal performs better in most of the cases of severe baseline wander distortions.Introduction: Baseline wander (BW) of the electrocardiogram (ECG) is mainly caused by the movement and respiration process of the patient and it mainly appears as low-frequency artefacts in the ECG signals [1][2][3][4]. Removal of BW is necessary for better visual interpretation, and detection of certain patterns in the ECG signal for subsequent automatic processing. The use of highpass filtering for BW removal is not recommended as it can distort the ECG waveform because of variations in the frequency spectrum of the ECG signal [2]. A nonlinear filter bank technique is proposed for BW removal without distorting the ECG signal [3]. The empirical mode decomposition (EMD) technique has also emerged as a tool for time-frequency analysis and is being used in a number of applications [5]. By using the EMD, the ECG signal can be decomposed in a series of intrinsic mode functions (IMFs) [4]. In the method proposed in [4], the higher-order IMFs are used to obtain the BW signal. These higher-order IMFs obtained by the EMD technique are filtered through a lowpass filter to obtain the BW of the ECG signal. A similar technique for BW removal based on the EMD technique is also proposed in [2] where the lowpass filter is designed by averaging two basic morphological operators: opening and closing.Recently the Hilbert vibration decomposition (HVD) technique has attracted the attention of the researchers and it decomposes the nonstationary wideband signals into a sum of components with slowly varying amplitudes and frequencies [6]. In the HVD technique, the first component represents the highest instantaneous amplitude component and the residue signal contains information of the lower amplitude components [6]. In this Letter, an approach for BW removal based on the HVD technique is proposed. The main motivation for using the HVD technique stems from the fact that the BW component in the ECG signal generally has a significant fraction of the total energy of the ECG signal. Thus, the BW signal can be obtained from the highest energy component (first iteration) of the HVD.

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This second part of the paper on an analysis strategy for data acquired using three-dimensional X-ray diffraction (3DXRD) describes the procedure for the determination of the grain characteristics for thousands of grains. The approach developed here is orders of magnitude faster than those presently available for indexing thousands of grains. Using information obtained from the steps described in Part I . J. Appl. Cryst. 45, 693-704], the volume, crystallographic orientation, centre-of-mass position and strain state of grains in the sample can be determined. The algorithms dealing with the determination of the orientation, centre-of-mass position and strain state of the grains are divided into two parts. The first deals with indexing, i.e. it assigns diffraction spots to individual grains assuming an unstrained lattice, and the second deals with the refinement of the crystallographic orientation, centreof-mass position and strain state of the grains using the diffraction spots assigned during indexing. The different approaches to indexing that exist in the literature are presented and compared with the novel approach developed here. Indexing can be run in two modes depending on the number of grains. For large numbers of grains, the approach employs a novel sample 'surface' scanning technique, in combination with a reduced number of search orientations, to achieve high robustness and computation efficiency. For small numbers of grains, the approach neglects the position of the diffracting grains in the sample in order to improve the computation efficiency. For unstrained samples, both modes of indexing and the subsequent process of refinement are validated using simulated data for 60 and 3000 grains. In both cases, the centre-of-mass position of the grains was determined with a mean error of 0.7 mm and the orientation was determined with a mean error of 0.0003 . Furthermore, an experiment was 'mimicked' by introducing experimental errors into the simulation for 3000 grains. The resulting mean errors in the centre-of-mass position (2.1 mm) and orientation (0.008 ) of the grains are higher than those for the ideal simulations, and the errors in an experiment will depend on the 'true' experimental errors. The algorithms dealing with strained samples are validated using a simulation for 3000 grains with mimicked experimental errors. The centre-of-mass position, crystallographic orientation, normal strain tensor components and shear strain tensor components of the grains were determined with mean errors of 8 mm, 0.006 , 5.2 Â 10 À5 and 2.8 Â 10 À5 , respectively. The possibility of obtaining grain-level information for thousands of grains with a high speed of acquisition makes the technique very attractive for in situ studies of thermomechanical processes in polycrystalline materials. research papers J. Appl. Cryst. (2012). 45, 705-718 Hemant Sharma et al. Grain characterization II 707

A fast methodology to determine the characteristics of thousands of grains using three-dimensional X-ray diffraction. I. Overlapping diffraction peaks and parameters of the experimental setup A data-analysis methodology is presented for the characterization of threedimensional microstructures of polycrystalline materials from data acquired using three-dimensional X-ray diffraction (3DXRD). The method is developed for 3DXRD microscopy using a far-field detector and yields information about the centre-of-mass position, crystallographic orientation, volume and strain state for thousands of grains. This first part deals with pre-processing of the diffraction data for input into the algorithms presented in the second part . J. Appl. Cryst. 45, 705-718] for determination of the grain characteristics. An algorithm is presented for accurate identification of overlapping diffraction peaks from X-ray diffraction images, which has been an issue limiting the accuracy of experiments of this type. The algorithm works in two stages, namely the identification of overlapping peaks using a seeded watershed algorithm, and then the fitting of the peaks with a pseudo-Voigt shape function to yield an accurate centre-of-mass position and integrated intensity for the peaks. Regions consisting of up to six overlapping peaks can be successfully fitted. Two simulations and an experiment are used to verify the results of the algorithms. An example of the processing of diffraction images acquired in a 3DXRD experiment with a sample consisting of more than 1600 grains is shown. Furthermore, a procedure for the determination of the parameters of the experimental setup (global parameters) without the need for a calibration sample is presented and validated using simulations. This is immensely beneficial for simplifying experiments and the subsequent data analysis. research papers J. Appl. Cryst. (2012). 45, 693-704 Hemant Sharma et al. Grain characterization I 695

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