Estimating Time Delays between Signals under Mixed Noise Influence with Novel Cross- and Bispectral Methods
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909627948466176 |
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| author | Jurhar, Tin Pellegrini, Franziska del Toro, Ana I. Nuñes Stephani, Tilman Nolte, Guido Haufe, Stefan |
| author_facet | Jurhar, Tin Pellegrini, Franziska del Toro, Ana I. Nuñes Stephani, Tilman Nolte, Guido Haufe, Stefan |
| contents | A common problem to signal processing are biases introduced by correlated noise. When quantifying time delays between two signals, mixed noise introduces a bias towards zero delay in conventional delay estimates based on the cross- or bispectrum. Here we propose two novel time delay estimators that address these shortcomings: (1) A cross-spectrum based approach that relies on estimating the periodicity of the phase spectrum rather than its slope, and (2) a bispectrum based approach, bispectral antisymmetrization, which removes contributions from not just Gaussian but all independent sources. In a simulation study, we compare conventional and novel TDE approaches and resolve differences in performance with respect to noise Gaussianity and auto-correlation structure. As a proof-of concept, we also perform TDE analysis on a neural stimulation dataset (n=3). We find that antisymmetrization consistently outperforms conventional bispectral methods at low signal-to-noise ratios (SNR) and prevents spurious zero-delay estimates in all mixed-noise environments. Time delay estimation based on phase periodicity also improves signal sensitivity compared to conventional cross-spectral methods. These observations are stable with respect to the magnitude of the delay and the statistical properties of the noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17474 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Estimating Time Delays between Signals under Mixed Noise Influence with Novel Cross- and Bispectral Methods Jurhar, Tin Pellegrini, Franziska del Toro, Ana I. Nuñes Stephani, Tilman Nolte, Guido Haufe, Stefan Signal Processing Statistics Theory Methodology A common problem to signal processing are biases introduced by correlated noise. When quantifying time delays between two signals, mixed noise introduces a bias towards zero delay in conventional delay estimates based on the cross- or bispectrum. Here we propose two novel time delay estimators that address these shortcomings: (1) A cross-spectrum based approach that relies on estimating the periodicity of the phase spectrum rather than its slope, and (2) a bispectrum based approach, bispectral antisymmetrization, which removes contributions from not just Gaussian but all independent sources. In a simulation study, we compare conventional and novel TDE approaches and resolve differences in performance with respect to noise Gaussianity and auto-correlation structure. As a proof-of concept, we also perform TDE analysis on a neural stimulation dataset (n=3). We find that antisymmetrization consistently outperforms conventional bispectral methods at low signal-to-noise ratios (SNR) and prevents spurious zero-delay estimates in all mixed-noise environments. Time delay estimation based on phase periodicity also improves signal sensitivity compared to conventional cross-spectral methods. These observations are stable with respect to the magnitude of the delay and the statistical properties of the noise. |
| title | Estimating Time Delays between Signals under Mixed Noise Influence with Novel Cross- and Bispectral Methods |
| topic | Signal Processing Statistics Theory Methodology |
| url | https://arxiv.org/abs/2502.17474 |