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。相位问题即解决这种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存在限制：它们不是任意的复数，而是来自更受限的字母表。例如，二进制序列仅包含等于$+1$和$-1$的项。我们研究了两个序列成为等自相关序列的充分必要条件，其中考虑了它们的字母表约束。存在由可预测保持自相关的修改产生的平凡等自相关性形式，例如对二进制序列取反或反转其项的顺序。通过对长度不超过$44$的二进制序列进行搜索，我们发现二进制序列间的非平凡等自相关性确实存在，但较为罕见。当存在长度为$n$的非平凡等自相关二进制序列时，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的有限性以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。