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Specifically, we prove that functions in <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$ L^2(K) $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msup>\n                      <mml:mi>L<\/mml:mi>\n                      <mml:mn>2<\/mml:mn>\n                    <\/mml:msup>\n                    <mml:mrow>\n                      <mml:mo>(<\/mml:mo>\n                      <mml:mi>K<\/mml:mi>\n                      <mml:mo>)<\/mml:mo>\n                    <\/mml:mrow>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> with <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$ K \\subseteq {{\\mathbb {R}}^d}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>K<\/mml:mi>\n                    <mml:mo>\u2286<\/mml:mo>\n                    <mml:msup>\n                      <mml:mrow>\n                        <mml:mi>R<\/mml:mi>\n                      <\/mml:mrow>\n                      <mml:mi>d<\/mml:mi>\n                    <\/mml:msup>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> compact, are uniquely determined by phaseless lattice-samples of its short-time Fourier transform with window function <jats:italic>g<\/jats:italic>, provided that specific density properties of translates of <jats:italic>g<\/jats:italic> are met. By proving completeness statements for systems of discrete translates in Banach function spaces on compact sets, we obtain new uniqueness statements for phaseless sampling on lattices beyond the known Gaussian window regime. Our results apply to a large class of window functions which are relevant in time-frequency analysis and applications.<\/jats:p>","DOI":"10.1007\/s10444-025-10236-w","type":"journal-article","created":{"date-parts":[[2025,6,13]],"date-time":"2025-06-13T10:37:05Z","timestamp":1749811025000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["From completeness of discrete translates to phaseless sampling of the short-time Fourier transform"],"prefix":"10.1007","volume":"51","author":[{"given":"Philipp","family":"Grohs","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9186-4896","authenticated-orcid":false,"given":"Lukas","family":"Liehr","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Irina","family":"Shafkulovska","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,6,13]]},"reference":[{"issue":"1","key":"10236_CR1","first-page":"179","volume":"83","author":"EJ Akutowicz","year":"1956","unstructured":"Akutowicz, E.J.: On the Determination of the Phase of a Fourier Integral. 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