On the similarity between discrete harmonic wavelet and discrete orthonormal S transform
Bibliographic record
Abstract
Two efficient transforms: discrete harmonic wavelet transform (DHWT) and discrete orthonormal S transform (DOST) were developed in the literature. They can be used to analyze, model, and simulate nonstationary signals. Both transforms are efficient and have been used to represent seismic ground motions and wind speeds of high-intensity wind events. The efficiency arises from the fact that they are non-redundant transforms which is similar to Fourier transform but can cope with temporal varying characteristics. DOST originated from the summation of Fourier representation over a frequency band and considers phase shift such that the basis functions are absolutely referenced. DHWT originated from the wavelet concept (i.e., continuous harmonic wavelets). Its basic function is also obtained by considering a frequency band. However, the phase of the basis function is not absolutely referenced. It seems that a detailed discussion of their similarity is never provided in the literature. In fact, papers using DHWT for engineering applications rarely mention DOST and vice versa. In the present study, we provide a detailed comparison of these two transforms in terms of the mathematical derivation of their basis functions, their computer implementation, and their characteristics, including edge effects. In addition, we show their potential use in simulating nonstationary processes. To minimize the edge effects by using DHWT and DOST as well as their variants, we suggest an iterative correction algorithm, which is illustrated by simulating nonstationary processes.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.006 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".