信号单调变换下互相关峰值位置不变，可用于快速时差估计
On the Invariance of Cross-Correlation Peak Positions Under Monotonic Signal Transformations, with Application to Fast Time Difference Estimation
- 利用信号单调变换后互相关峰值位置不变的性质
- 通过低比特整数量化实现仅用整数运算的高效算法
- 相比FFT方法在特定信号长度下更快，适合实时系统
本文提出一个关于互相关峰值位置不变性的定理。该理论表明，两个经平移的离散时间信号之间的互相关函数峰值位置，在输入信号任意单调变换下保持不变。基于此性质，我们设计了一种新的时差估计算法，该算法使用量化为低比特整数的信号进行互相关计算。所提方法仅需整数运算，无需实数操作，并可通过数论算法进一步提升计算效率。数值实验表明，在特定信号长度范围内，该方法的处理时间短于传统的基于快速傅里叶变换（FFT）的方法。
原文摘要 · Abstract (English)
We present a theorem concerning the invariance of cross-correlation peak positions. This theoretical result provides the 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. Specifically, it 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 within a specific range of signal lengths.
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