{"id":"W3121908202","doi":"10.20944/preprints201907.0189.v1","title":"Discrete Two Dimensional Fourier Transform in Polar Coordinates Part II: Numerical Computation and Approximation of the Continuous Transform","year":2019,"lang":"en","type":"preprint","venue":"Preprints.org","topic":"Digital Filter Design and Implementation","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Ottawa; University of Waterloo","funders":"","keywords":"Discrete Fourier transform (general); Discrete Hartley transform; Discrete sine transform; Hartley transform; Fourier transform; Inverse; Convolution (computer science); Discrete-time Fourier transform; Mathematics; Polar coordinate system; Hankel transform; Log-polar coordinates; Circular convolution; Sine and cosine transforms; Mathematical analysis; Fractional Fourier transform; Algorithm; Fourier analysis; Generalized coordinates; Computer science; Geometry","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006066473,0.0002738538,0.0004096178,0.0001342289,0.00009658012,0.00007271886,0.0006263727,0.000122185,0.00002336299],"category_scores_gemma":[0.00003503407,0.0002228038,0.0001521882,0.0002295509,0.00008992836,0.0006315634,0.0007639763,0.0003794567,0.00001692925],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008333362,"about_ca_system_score_gemma":0.0001239137,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001803764,"about_ca_topic_score_gemma":0.00001598249,"domain_scores_codex":[0.9977484,0.0001429742,0.0006874023,0.0006652339,0.0004816583,0.0002743671],"domain_scores_gemma":[0.9988866,0.00009727556,0.0003016082,0.0005370021,0.0001084653,0.0000690684],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0004187936,0.001273681,0.6946768,0.00157472,0.0004904372,0.00001275141,0.02893602,0.05109588,0.008704533,0.0383894,0.0002833771,0.1741436],"study_design_scores_gemma":[0.003377144,0.0002139019,0.3086697,0.0006865984,0.00008180258,0.00002946576,0.0001484464,0.5520269,0.05145292,0.08130041,0.001061371,0.000951323],"study_design_candidate":"observational","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8454436,0.00004540009,0.1477057,0.001967075,0.0005143813,0.001724601,0.00005598171,0.0000637199,0.002479511],"genre_scores_gemma":[0.9968154,0.000008672265,0.002681284,0.0001027211,0.00002439934,0.00007701224,0.00008282204,0.00001649763,0.000191236],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.500931,"threshold_uncertainty_score":0.9085674,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05732597193738363,"score_gpt":0.3166027344762747,"score_spread":0.2592767625388911,"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."}}