On the Invariance of Cross-Correlation Peak Positions Under Monotonic Signal Transformations, with Application to Fast Time Difference Estimation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909804310560768 |
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| author | Ueno, Natsuki Sato, Ryotaro Ono, Nobutaka |
| author_facet | Ueno, Natsuki Sato, Ryotaro Ono, Nobutaka |
| contents | We present a theorem concerning the invariance of cross-correlation peak positions, which provides a foundation for a new method for time difference estimation that is potentially faster than the conventional fast Fourier transform (FFT) approach for real/complex sequences. This theoretical result shows that the peak position of the cross-correlation function between two shifted discrete-time signals remains unchanged under arbitrary monotonic transformations of the input signals. By exploiting this property, we design an efficient estimation algorithm based on the cross-correlation function between signals quantized into low-bit integers. The proposed method requires only integer arithmetic instead of real-valued operations, and further computational efficiency can be achieved through number-theoretic algorithms. Numerical experiments demonstrate that the proposed method achieves a shorter processing time than conventional FFT-based approaches. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_19974 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Invariance of Cross-Correlation Peak Positions Under Monotonic Signal Transformations, with Application to Fast Time Difference Estimation Ueno, Natsuki Sato, Ryotaro Ono, Nobutaka Signal Processing Audio and Speech Processing We present a theorem concerning the invariance of cross-correlation peak positions, which provides a foundation for a new method for time difference estimation that is potentially faster than the conventional fast Fourier transform (FFT) approach for real/complex sequences. This theoretical result shows that the peak position of the cross-correlation function between two shifted discrete-time signals remains unchanged under arbitrary monotonic transformations of the input signals. By exploiting this property, we design an efficient estimation algorithm based on the cross-correlation function between signals quantized into low-bit integers. The proposed method requires only integer arithmetic instead of real-valued operations, and further computational efficiency can be achieved through number-theoretic algorithms. Numerical experiments demonstrate that the proposed method achieves a shorter processing time than conventional FFT-based approaches. |
| title | On the Invariance of Cross-Correlation Peak Positions Under Monotonic Signal Transformations, with Application to Fast Time Difference Estimation |
| topic | Signal Processing Audio and Speech Processing |
| url | https://arxiv.org/abs/2509.19974 |