Aperiodic autocorrelation is an important indicator of performance of sequences used in communications, remote sensing, and scientific instrumentation. Knowing a sequence's autocorrelation function, which reports the autocorrelation at every possible translation, is equivalent to knowing the magnitude of the sequence's Fourier transform. The phase problem is the difficulty in resolving this lack of phase information. We say that two sequences are equicorrelational to mean that they have the same aperiodic autocorrelation function. Sequences used in technological applications often have restrictions on their terms: they are not arbitrary complex numbers, but come from a more restricted alphabet. For example, binary sequences involve terms equal to only $+1$ and $-1$. We investigate the necessary and sufficient conditions for two sequences to be equicorrelational, where we take their alphabet into consideration. There are trivial forms of equicorrelationality arising from modifications that predictably preserve the autocorrelation, for example, negating a binary sequence or reversing the order of its terms. By a search of binary sequences up to length $44$, we find that nontrivial equicorrelationality among binary sequences does occur, but is rare. An integer $n$ is said to be equivocal when there are binary sequences of length $n$ that are nontrivially equicorrelational; otherwise $n$ is unequivocal. For $n \leq 44$, we found that the unequivocal lengths are $1$--$8$, $10$, $11$, $13$, $14$, $19$, $22$, $23$, $26$, $29$, $37$, and $38$. We pose open questions about the finitude of unequivocal numbers and the probability of nontrivial equicorrelationality occurring among binary sequences.

翻译：非周期自相关是通信、遥感和科学仪器应用中序列性能的重要指标。已知序列的自相关函数（报告所有可能平移下的自相关值）等价于已知序列傅里叶变换的幅度。相位问题即指解决此类相位信息缺失的困难。我们称两个序列为等自相关序列，意指它们具有相同的非周期自相关函数。技术应用中使用的序列通常对其项值存在限制：这些项值并非任意复数，而是来自受限的字符集。例如，二进制序列仅包含$+1$和$-1$两种项值。本文研究了两个序列成为等自相关序列的充分必要条件，并特别考虑了其字符集约束。存在由可预测保持自相关的修改操作产生的平凡等自相关性，例如对二进制序列取反或反转其项值顺序。通过对长度不超过$44$的二进制序列进行搜索，我们发现非平凡等自相关性在二进制序列中确实存在，但极为罕见。当存在长度为$n$的二进制序列具有非平凡等自相关性时，称整数$n$为模糊长度；否则称$n$为明确长度。对于$n \leq 44$，我们发现的明确长度包括$1$--$8$、$10$、$11$、$13$、$14$、$19$、$22$、$23$、$26$、$29$、$37$和$38$。我们提出了关于明确长度有限性及二进制序列中出现非平凡等自相关性概率的开放性问题。