{"paper":{"title":"Correcting for the alias effect when measuring the power spectrum using FFT","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"Y.P. Jing","submitted_at":"2004-09-10T06:51:49Z","abstract_excerpt":"Because of mass assignment onto grid points in the measurement of the power spectrum using the Fast Fourier Transform (FFT), the raw power spectrum $\\la |\\delta^f(k)|^2\\ra$ estimated with FFT is not the same as the true power spectrum $P(k)$. In this paper, we derive the formula which relates $\\la |\\delta^f(k)|^2\\ra$ to $P(k)$. For a sample of $N$ discrete objects, the formula reads: $\\la |\\delta^f(k)|^2\\ra=\\sum_{\\vec n} [|W(\\kalias)|^2P(\\kalias)+1/N|W(\\kalias)|^2]$, where $W(\\vec k)$ is the Fourier transform of the mass assignment function $W(\\vec r)$, $k_N$ is the Nyquist wavenumber, and $\\v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0409240","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/astro-ph/0409240/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}