{"paper":{"title":"The Hilbert spectrum and the Energy Preserving Empirical Mode Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.NA"],"primary_cat":"cs.IT","authors_text":"Kaushik Saha, Pushpendra Singh, Rakesh Kumar Patney, Shiv Dutt Joshi","submitted_at":"2015-04-16T06:08:54Z","abstract_excerpt":"In this paper, we propose algorithms which preserve energy in empirical mode decomposition (EMD), generating finite $n$ number of band limited Intrinsic Mode Functions (IMFs). In the first energy preserving EMD (EPEMD) algorithm, a signal is decomposed into linearly independent (LI), non orthogonal yet energy preserving (LINOEP) IMFs and residue (EPIMFs). It is shown that a vector in an inner product space can be represented as a sum of LI and non orthogonal vectors in such a way that Parseval's type property is satisfied. From the set of $n$ IMFs, through Gram-Schmidt orthogonalization method"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04104","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}