{"ID":2866504,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.19974","arxiv_id":"2509.19974","title":"On the Invariance of Cross-Correlation Peak Positions Under Monotonic Signal Transformations, with Application to Fast Time Difference Estimation","abstract":"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.","short_abstract":"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 p...","url_abs":"https://arxiv.org/abs/2509.19974","url_pdf":"https://arxiv.org/pdf/2509.19974v1","authors":"[\"Natsuki Ueno\",\"Ryotaro Sato\",\"Nobutaka Ono\"]","published":"2025-09-24T10:29:54Z","proceeding":"eess.SP","tasks":"[\"eess.SP\",\"eess.AS\"]","methods":"[]","has_code":false}