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Signal Process."],"abstract":"Abstract<\/jats:title>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 $$\\ell _1$$<\/jats:tex-math>\n \n \u2113<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> Fourier transform and the traditional $$\\ell _2$$<\/jats:tex-math>\n \n \u2113<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> Fourier transform. Numerical examples are presented, and the analysis focuses on ECG signals as a real-world application, comparing the performance of the $$\\ell _1$$<\/jats:tex-math>\n \n \u2113<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and $$\\ell _2$$<\/jats:tex-math>\n \n \u2113<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> Fourier transforms. Our results demonstrate that the $$\\ell _1$$<\/jats:tex-math>\n \n \u2113<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> 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 $$\\ell _1$$<\/jats:tex-math>\n \n \u2113<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> Fourier transform, as opposed to the traditional $$\\ell _2$$<\/jats:tex-math>\n \n \u2113<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> Fourier transform.<\/jats:p>","DOI":"10.1186\/s13634-024-01171-x","type":"journal-article","created":{"date-parts":[[2024,7,19]],"date-time":"2024-07-19T13:02:08Z","timestamp":1721394128000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["ECG signal decomposition using Fourier analysis"],"prefix":"10.1186","volume":"2024","author":[{"given":"Arman","family":"Kheirati Roonizi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roberto","family":"Sassi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,7,19]]},"reference":[{"key":"1171_CR1","series-title":"Student\u2019s Guides","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511762307","volume-title":"A Student\u2019s Guide to Fourier Transforms: With Applications in Physics and Engineering","author":"JF James","year":"2011","unstructured":"J.F. 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