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It has rarely been used in radio pulsar searches, having been historically supplanted by the less computationally expensive fast fourier transform (FFT) with incoherent harmonic summing (IHS). Here, we derive from first principles that an FFA search closely approaches the theoretical optimum sensitivity to all periodic signals; it is analytically shown to be significantly more sensitive than the standard FFT+IHS method, regardless of pulse period and duty cycle. A portion of the pulsar phase space has thus been systematically underexplored for decades; pulsar surveys aiming to fully sample the pulsar population should include an FFA search as part of their data analysis. We have developed an FFA software package, riptide, fast enough to process radio observations on a large scale; riptide has already discovered sources undetectable using existing FFT+IHS implementations. Our sensitivity comparison between search techniques also shows that a more realistic radiometer equation is needed, which includes an additional term: the search efficiency. We derive the theoretical efficiencies of both the FFA and the FFT+IHS methods and discuss how excluding this term has consequences for pulsar population synthesis studies.<\/jats:p>","DOI":"10.1093\/mnras\/staa2291","type":"journal-article","created":{"date-parts":[[2020,8,3]],"date-time":"2020-08-03T11:52:07Z","timestamp":1596455527000},"page":"4654-4671","source":"Crossref","is-referenced-by-count":89,"title":["Optimal periodicity searching: revisiting the fast folding algorithm for large-scale pulsar surveys"],"prefix":"10.1093","volume":"497","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0767-6022","authenticated-orcid":false,"given":"V","family":"Morello","sequence":"first","affiliation":[{"name":"Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8715-9628","authenticated-orcid":false,"given":"E D","family":"Barr","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Radioastronomie, Auf dem H\u00fcgel 69, D-53121 Bonn, Germany"}]},{"given":"B W","family":"Stappers","sequence":"additional","affiliation":[{"name":"Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4553-655X","authenticated-orcid":false,"given":"E F","family":"Keane","sequence":"additional","affiliation":[{"name":"Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK"},{"name":"SKA Organisation, Jodrell Bank, Macclesfield SK11 9FT, UK"}]},{"given":"A G","family":"Lyne","sequence":"additional","affiliation":[{"name":"Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK"}]}],"member":"286","published-online":{"date-parts":[[2020,8,6]]},"reference":[{"key":"2020082506272483100_bib1","first-page":"280","volume":"2","author":"Burns","year":"1969","journal-title":"A&A"},{"key":"2020082506272483100_bib2","doi-asserted-by":"publisher","first-page":"1994","DOI":"10.1093\/mnras\/stx589","volume":"468","author":"Cameron","year":"2017","journal-title":"MNRAS"},{"key":"2020082506272483100_bib3","author":"Casella","year":"2002","journal-title":"Statistical Inference"},{"key":"2020082506272483100_bib4","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1090\/S0025-5718-1965-0178586-1","volume":"19","author":"Cooley","year":"1965","journal-title":"Math. 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