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We show in a rigorous mathematical way that information encoding by means of Threshold-Based Representation based on either Leaky Integrate-and-Fire or Send-on-Delta is linked to an analog-to-spike conversion that guarantees maximum sparsity while satisfying an approximation condition based on the Alexiewicz norm.<\/jats:p>","DOI":"10.1088\/2634-4386\/adb884","type":"journal-article","created":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T22:52:44Z","timestamp":1740091964000},"page":"014011","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["On the sampling sparsity of analog-to-spike conversion based on leaky integrate-and-fire"],"prefix":"10.1088","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8373-7523","authenticated-orcid":true,"given":"Bernhard A","family":"Moser","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Lunglmayr","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2025,3,5]]},"reference":[{"key":"nceadb884bib1","doi-asserted-by":"publisher","first-page":"289","DOI":"10.4064\/cm-1-4-289-293","article-title":"Linear functionals on Denjoy-integrable functions","volume":"1","author":"Alexiewicz","year":"1948","journal-title":"Colloq. 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