Polynomial families of isotropic windows and filters for geophysical signal analysis on the sphere
Bibliographic record
Abstract
The study of global-scale geophysical signals requires the modification of conventional spectral analysis and signal processing techniques from the real line to the sphere. These techniques often depend on the use of window functions (e.g., for localized spectral analysis and to improve the detection of periodic constituents). Normalized window functions are also utilized as averaging filters.In this work, we only focus on polynomial window functions. We present some families of polynomial windows that have been used in conventional signal processing, such as the B-spline, Singla-Singh, Kulkarni-type and generalized adaptive polynomial windows. We also demonstrate the possibility of approximating more sophisticated non-polynomial windows, such as the Kaiser, Lanczos and hyperbolic cosine windows, using their Taylor series expansion. The approach followed for their adaptation to the sphere results in isotropic (i.e., rotationally symmetric) window functions. We also examine their related filter kernels and provide expressions for their representation in the spatial domain.Recent advances on the evaluation of spherical harmonic coefficients of polynomial functions also enable us to assess the spectral characteristics of all window functions and filter kernels examined. We compare their main spectral characteristics, such as the main lobe width, first side lobe level and side lobe decay rate. Since all of these windows and filters have not been examined on the sphere before, the present work extends the current methods for localizing and filtering geophysical signals on the sphere.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".