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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.