{"id":"W4226413944","doi":"10.1109/access.2022.3157736","title":"Linear Version of Parseval’s Theorem","year":2022,"lang":"en","type":"article","venue":"IEEE Access","topic":"Mathematical Analysis and Transform Methods","field":"Mathematics","cited_by":23,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Windsor","funders":"","keywords":"Parseval's theorem; Invariant (physics); Nonlinear system; Mathematics; Discrete Fourier transform (general); Fourier transform; Signal processing; Linear system; Discrete mathematics; Applied mathematics; Pure mathematics; Computer science; Algorithm; Digital signal processing; Mathematical analysis; Fourier analysis; Fractional Fourier transform; Quantum mechanics; Physics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001857642,0.0008443024,0.0007952197,0.001305378,0.0008745355,0.002096722,0.001117857,0.0009144071,0.0102949],"category_scores_gemma":[0.007522576,0.0003175872,0.001168882,0.001208695,0.002636739,0.003878772,0.001576452,0.003140914,0.003783058],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001136563,"about_ca_system_score_gemma":0.00119985,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002425182,"about_ca_topic_score_gemma":0.001188393,"domain_scores_codex":[0.9983412,0.0003255421,0.00008687223,0.0004040914,0.0006171903,0.0002250646],"domain_scores_gemma":[0.9975808,0.001247416,0.000168714,0.0002933417,0.0006415243,0.00006818237],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00002371141,0.00001219514,0.0002276594,0.00006716431,0.00001548164,0.0001003952,0.0001390728,0.006697486,0.001337068,0.9626039,0.004489854,0.02428604],"study_design_scores_gemma":[0.00002187076,0.00005143947,0.0005239778,0.00003201842,0.00001422026,0.0003658194,0.00005915917,0.1070945,0.003172162,0.8706434,0.01797343,0.00004791249],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01339281,0.0007123412,0.9510221,0.0009535462,0.0002373956,0.00004019521,0.0003957729,0.0002290948,0.0330168],"genre_scores_gemma":[0.6308663,0.003455677,0.3098356,0.002560151,0.00171411,0.0003531538,0.001115677,0.000689603,0.04940967],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.0102949,"threshold_uncertainty_score":0.0344398,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1182989465061821,"score_gpt":0.4183361819041456,"score_spread":0.3000372353979635,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}