ECG signal decomposition using Fourier analysis

Abstract

Abstract 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 $$\ell _1$$ ℓ 1 Fourier transform and the traditional $$\ell _2$$ 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 $$\ell _1$$ ℓ 1 and $$\ell _2$$ ℓ 2 Fourier transforms. Our results demonstrate that the $$\ell _1$$ 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 $$\ell _1$$ ℓ 1 Fourier transform, as opposed to the traditional $$\ell _2$$ ℓ 2 Fourier transform.

Keywords

• $$\ell _1$$ ℓ 1 Fourier analysis
• $$\ell _1$$ ℓ 1 Fourier analysis
• Signal decomposition
• ECG components