Unitary equivalence: a new twist on signal processing
Unitary equivalence: a new twist on signal processing
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DOI：
10.1109/78.469861
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发表时间：
1995-10
期刊：
影响因子：
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通讯作者：
Richard Baraniuk;Douglas L. Jones
中科院分区：
文献类型：
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作者：
Richard Baraniuk;Douglas L. Jones
酉相似性变换提供了一个强大的工具，用于生成无限类的信号分析和处理工具的基础上不同的概念，从时间，频率和规模。这些新工具的实现涉及简单地通过酉变换对信号进行预处理，对变换后的信号执行标准处理，然后（在某些情况下）对结果输出进行变换。由此产生的酉等效系统可以集中在大类信号的关键信号特性，因此，证明有用的表示和处理信号，不匹配的当前技术。作为这个过程的具体例子，我们概括了线性时不变系统，标准正交基和帧分解，以及联合时频和时标分布。这些应用程序说明了效用的统一等价的概念，在文献中提出的看似不同的方法。>
Unitary similarity transformations furnish a powerful vehicle for generating infinite generic classes of signal analysis and processing tools based on concepts different from time, frequency, and scale. Implementation of these new tools involves simply preprocessing the signal by a unitary transformation, performing standard processing on the transformed signal, and then (in some cases) transforming the resulting output. The resulting unitarily equivalent systems can focus on the critical signal characteristics in large classes of signals and, hence, prove useful for representing and processing signals that are not well matched by current techniques. As specific examples of this procedure, we generalize linear time-invariant systems, orthonormal basis and frame decompositions, and joint time-frequency and time-scale distributions. These applications illustrate the utility of the unitary equivalence concept for uniting seemingly disparate approaches proposed in the literature. >