This paper proposes a fractional singular spectrum analysis (SSA)-based method for performing the fractional delay. First, the input sequence is divided into two overlapping sequences with the first sequence being the input sequence without its last point and the second sequence being the input sequence without its first point. Then, the singular value decompositions (SVD) are performed on the trajectory matrices constructed based on these two sequences. Next, the designs of both the right unitary matrix and the left unitary matrix for generating the new trajectory matrix are formulated as the quadratically constrained quadratic programing problems. The analytical solutions of these quadratically constrained quadratic programing problems are derived via the SVD approach. Finally, the fractional SSA components are obtained by performing the diagonal averaging operation, and the fractional delay sequence is obtained by summing up all the fractional SSA components together. Since the fractional SSA operations are nonlinear and adaptive, our proposed method is a kind of nonlinear and adaptive approach for performing the fractional delay. Besides, by discarding some fractional SSA components, the joint fractional delay operation and the denoising operation can be performed simultaneously.

本文提出了一种基于分数奇异谱分析 (SSA) 的方法来执行分数延迟。首先，将输入序列分成两个重叠序列，第一个序列是没有最后一个点的输入序列，第二个序列是没有第一个点的输入序列。然后，对基于这两个序列构建的轨迹矩阵进行奇异值分解（SVD）。接下来，用于生成新轨迹矩阵的右酉矩阵和左酉矩阵的设计被公式化为二次约束二次规划问题。这些二次约束二次规划问题的解析解是通过 SVD 方法推导出来的。最后，分数SSA分量是通过对角线平均运算得到的，分数延迟序列是所有分数SSA分量相加得到的。由于分数 SSA 操作是非线性和自适应的，我们提出的方法是一种非线性和自适应方法来执行分数延迟。此外，通过丢弃一些分数SSA分量，联合分数延迟操作和去噪操作可以同时进行。