一种多分辨率离散傅里叶变换的快速算法
An algorithm for fast computation of the multiresolution discrete Fourier transform
摘要：
本文提出了一种计算多分辨率离散傅里叶变换（MrDFT）的有效算法。该算法基于Wen和Sandler [10]提出的降低计算复杂性的思想，并在所考虑的变换的每个阶段利用计算过程的向量化。这允许使用计算过程并行化并导致计算时间的减少。在描述算法的计算过程中，我们使用矩阵符号。这种表示法能够充分地表示所实现的计算过程的时空结构，并将这些结构直接映射到高级程序设计语言的结构中或映射到硬件实现空间中。
英文摘要：
The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and Sandler [10] and utilizes the vectorization of calculating process at each stage of the considered transformation. This allows for the use of a computational process parallelization and results in a reduction of computation time. In the description of the computational procedure, which describes the algorithm, we use the matrix notation. This notation enables to represent adequately the space-time structures of the implemented computational process and directly map these structures into the constructions of a high-level programming language or into a hardware realization space.
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