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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.22721 |
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| _version_ | 1866914505228812288 |
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| author | Valdivia-Prado, Jairo M. Chapman, William E. Friedrich, Katja |
| author_facet | Valdivia-Prado, Jairo M. Chapman, William E. Friedrich, Katja |
| contents | This paper presents a method for computing local mean, variance, standard deviation, and effective sample count on incomplete gridded data using boundary-aware spectral operators. The framework combines normalized convolution with explicit boundary-condition modeling: reflective Discrete Cosine Transform (DCT) for non-periodic Cartesian axes and periodic Real Fast Fourier Transform (RFFT) for circular azimuth processing in polar geometry. Stability safeguards (denominator floor, prefill fallback, and variance clamp) are specified for under-supported regions. We evaluate the framework across three targeted scenarios: a Cartesian boundary-condition check demonstrating the mitigation of wrap-around artifacts, a synthetic 3D outlier-identification test, and a real-radar polar application. Results establish bounded, support-aware interpretation of local statistics while preserving a concise reproducibility path through the open-source 'dct\_toolkit' implementation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22721 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral-Domain Local Statistics with Missing-Data Support for Cartesian and Polar Grids Valdivia-Prado, Jairo M. Chapman, William E. Friedrich, Katja Atmospheric and Oceanic Physics Numerical Analysis Data Analysis, Statistics and Probability 65T50, 62H35, 86A22 This paper presents a method for computing local mean, variance, standard deviation, and effective sample count on incomplete gridded data using boundary-aware spectral operators. The framework combines normalized convolution with explicit boundary-condition modeling: reflective Discrete Cosine Transform (DCT) for non-periodic Cartesian axes and periodic Real Fast Fourier Transform (RFFT) for circular azimuth processing in polar geometry. Stability safeguards (denominator floor, prefill fallback, and variance clamp) are specified for under-supported regions. We evaluate the framework across three targeted scenarios: a Cartesian boundary-condition check demonstrating the mitigation of wrap-around artifacts, a synthetic 3D outlier-identification test, and a real-radar polar application. Results establish bounded, support-aware interpretation of local statistics while preserving a concise reproducibility path through the open-source 'dct\_toolkit' implementation. |
| title | Spectral-Domain Local Statistics with Missing-Data Support for Cartesian and Polar Grids |
| topic | Atmospheric and Oceanic Physics Numerical Analysis Data Analysis, Statistics and Probability 65T50, 62H35, 86A22 |
| url | https://arxiv.org/abs/2604.22721 |