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 ₁ ℓ 1 Fourier transform and the traditional ₂ ℓ 2 Fourier transform. Numerical examples are presented, and the analysis focuses on ECG signals as a real-world application, comparing the performance of the ₁ ℓ 1 and ₂ ℓ 2 Fourier transforms. Our results demonstrate that the ₁ ℓ 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 ₁ ℓ 1 Fourier transform, as opposed to the traditional ₂ ℓ 2 Fourier transform.