| _version_ | 1866902327812685824 |
|---|---|
| author | Perisic, Aleksandar |
| author_facet | Perisic, Aleksandar |
| contents | <p>This article introduces a two‐dimensional <em>phase‐heatmap</em> technique for visualizing and extracting the primary harmonic coupling in both discrete Fourier and Mellin transforms. In the Fourier context, we scan a continuous "time" variable against frequency‐domain phases; in the Mellin context, we scan a real variable $x>0$ against the nontrivial zeros of the Riemann zeta function. By binning phases, isolating the $\ell=1$ harmonic, and displaying a smoothed heatmap, one obtains crystal‐clear ridges precisely marking the underlying discrete spectra. A final section illustrates the method on the primes–zeros duality.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17108225 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | HBP | Observ | 2.1 • Phase-Heatmap Visualization Methods for Discrete Fourier and Mellin Transforms Perisic, Aleksandar <p>This article introduces a two‐dimensional <em>phase‐heatmap</em> technique for visualizing and extracting the primary harmonic coupling in both discrete Fourier and Mellin transforms. In the Fourier context, we scan a continuous "time" variable against frequency‐domain phases; in the Mellin context, we scan a real variable $x>0$ against the nontrivial zeros of the Riemann zeta function. By binning phases, isolating the $\ell=1$ harmonic, and displaying a smoothed heatmap, one obtains crystal‐clear ridges precisely marking the underlying discrete spectra. A final section illustrates the method on the primes–zeros duality.</p> |
| title | HBP | Observ | 2.1 • Phase-Heatmap Visualization Methods for Discrete Fourier and Mellin Transforms |
| url | https://doi.org/10.5281/zenodo.17108225 |