ECG signal decomposition using Fourier analysis

This paper explores the Fourier decomposition method to approximate the decomposition of electrocardiogram (ECG) signals into their component waveforms, such as the QRS-complex and T-wave. We compute expansion coefficients using the \(\ell _1\) ${\ell }_1$ Fourier transform and the traditional \(\ell _2\) ${\ell }_2$ Fourier transform. Numerical examples are presented, and the analysis focuses on ECG signals as a real-world application, comparing the performance of the \(\ell _1\) ${\ell }_1$ and \(\ell _2\) ${\ell }_2$ Fourier transforms. Our results demonstrate that the \(\ell _1\) ${\ell }_1$ Fourier transform significantly enhances the separation of ECG signal components, such as the QRS-complex and T-wave. This improvement is attributed to a notable reduction in the Gibbs phenomenon introduced by the Fourier-series expansion when using the \(\ell _1\) ${\ell }_1$ Fourier transform, as opposed to the traditional \(\ell _2\) ${\ell }_2$ Fourier transform.