{"paper":{"title":"Impulse response of a generalized fractional second order filter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.SY","authors_text":"YangQuan Chen, Zhuang Jiao","submitted_at":"2011-06-07T00:16:13Z","abstract_excerpt":"The impulse response of a generalized fractional second order filter of the form ${{({{s}^{2\\alpha}}+a{{s}^{\\alpha}}+b)}^{-\\gamma}}$ is derived, where $0<\\alpha \\le 1$, $0<\\gamma <2$. The asymptotic properties of the impulse responses are obtained for two cases, and the two cases show the similar properties for the changing of $\\gamma$ values. It is shown that only when ${{({{s}^{2\\alpha}}+a{{s}^{\\alpha}}+b)}^{-1}}$ has the critical stability, the generalized fractional second order filter ${{({{s}^{2\\alpha}}+a{{s}^{\\alpha}}+b)}^{-\\gamma}}$ has different properties as we change the value of $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1220","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":""},"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"}