{"paper":{"title":"The Entropy Gain of Linear Time-Invariant Filters and Some of its Implications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jan {\\O}stergaard, Mat\\'ias M\\\"uller, Milan S. Derpich","submitted_at":"2015-12-11T14:25:31Z","abstract_excerpt":"We study the increase in per-sample differential entropy rate of random sequences and processes after being passed through a non minimum-phase (NMP) discrete-time, linear time-invariant (LTI) filter G. For such filters and random processes, it has long been established that this entropy gain, Gain(G), equals the integral of log|G(exp(jw))|. It is also known that, if the first sample of the impulse response of G has unit-magnitude, then this integral equals the sum of the logarithm of the magnitudes of the non-minimum phase zeros of G, say B(G). In this note, we begin by showing that existing t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03655","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"}