EMD Based Hierarchical Multiresolution Analysis via DCT with Applications to ECG Denoising and QRS Point Enhancement

Abstract

This paper proposes to employ the discrete cosine transform (DCT) to perform the empirical mode decomposition (EMD) based hierarchical multiresolution analysis. This can simplify the implementation because all the signals are real valued. In this paper, the intrinsic mode functions (IMFs) in the first level of decomposition are obtained by applying the conventional EMD to an electrocardiogram (ECG). Then, the first IMF is further decomposed. More precisely, the zeros are inserted to the first IMF in the DCT domain. Then, the conventional EMD is applied to this zero inserted signal to obtain a new set of IMFs. Next, the DCT coefficients of the new set of IMFs where the zeros are inserted before are discarded. To perform the denoising and the QRS point enhancement, the first IMF in the second level of the decomposition is discarded. The rest of the IMFs in the second level of decomposition as well all the IMFs in the first level of decomposition except the first IMF in the first level of decomposition are summed together to obtain the processed signal. The computer numerical simulation results show that our proposed method can achieve significant improvements in terms of the denoising performance and the QRS point enhancement compared to the corresponding single level EMD based processing.