In this paper, a new concept of the resolution map is presented to extract periodic structures that compose the signal. The resolution map is described by using the frequency–time representation of the signal, which is known as the paired transform that provides the frequency-time representation of signals. The sequential calculation of resolution maps over the signal components of large sizes allows for calculating the small periodic structures, or patterns, which can be used for signal processing, for instance filtration, and from which the signal can be reconstructed. The length of the signal is considered to be a power of two, a case that fits well with qubit processing in quantum computing. The following new results are described: (1) the quantum scheme for the 1D discrete paired transform, (2) the quantum circuit for calculating the signal resolution map, (3) the quantum circuit for signal reconstruction from the resolution map, (4) different schemes for resolution maps for processing signals, and (5) the convolution of signals by their periodic patterns.

中文翻译：

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量子计算中的分辨率图：通过周期性模式表示信号

在本文中，提出了分辨率图的新概念以提取组成信号的周期性结构。通过使用信号的频率-时间表示来描述分辨率图，这被称为提供信号的频率-时间表示的成对变换。对大尺寸信号分量进行分辨率映射的顺序计算，可以计算出较小的周期性结构或模式，这些结构或模式可以用于信号处理（例如滤波），并可以从中重构信号。信号的长度被认为是2的幂，这种情况非常适合量子计算中的qubit处理。描述了以下新结果：（1）一维离散成对变换的量子方案，