Time-delay estimation using the Wigner-Ville distribution
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arXiv
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| Format: | Preprint |
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2026
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| author | Gurgel, L. de A. de Araújo, J. M. Machado, L. D. de Lima, P. D. S. |
| author_facet | Gurgel, L. de A. de Araújo, J. M. Machado, L. D. de Lima, P. D. S. |
| contents | Accurately calculating time delays between signals is pivotal in many modern physics applications. One approach to estimating these delays is computing the cross-spectrum in the time-frequency domain. Linear time-frequency representations, such as the continuous wavelet transform (CWT), are widely used to construct these cross-spectra. However, it is well known that the frequency resolution is inherently limited by the localized nature of the convolving wavelet. Moreover, the functional form of the CWT cross-spectrum is not a proper correlation measure and typically requires post-processing smoothing. Conversely, quadratic representations achieve joint time-frequency resolution approaching the Gabor-Heisenberg limit while also providing an adequate measure of similarity between the signals. Motivated by these advantages, we propose a time-delay estimation method based on the Wigner-Ville Distribution (WVD). Considering nonstationary signals arising from two typical wave-physics scenarios, we show that the WVD yields more accurate time-delay estimates with lower uncertainty, particularly in the most energetic frequency bands. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20058 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Time-delay estimation using the Wigner-Ville distribution Gurgel, L. de A. de Araújo, J. M. Machado, L. D. de Lima, P. D. S. Computational Physics Accurately calculating time delays between signals is pivotal in many modern physics applications. One approach to estimating these delays is computing the cross-spectrum in the time-frequency domain. Linear time-frequency representations, such as the continuous wavelet transform (CWT), are widely used to construct these cross-spectra. However, it is well known that the frequency resolution is inherently limited by the localized nature of the convolving wavelet. Moreover, the functional form of the CWT cross-spectrum is not a proper correlation measure and typically requires post-processing smoothing. Conversely, quadratic representations achieve joint time-frequency resolution approaching the Gabor-Heisenberg limit while also providing an adequate measure of similarity between the signals. Motivated by these advantages, we propose a time-delay estimation method based on the Wigner-Ville Distribution (WVD). Considering nonstationary signals arising from two typical wave-physics scenarios, we show that the WVD yields more accurate time-delay estimates with lower uncertainty, particularly in the most energetic frequency bands. |
| title | Time-delay estimation using the Wigner-Ville distribution |
| topic | Computational Physics |
| url | https://arxiv.org/abs/2603.20058 |