| 戴银云,易华.空间l2(Z×Z)上正交小波基的频域特征刻画与算法[J].井冈山大学自然版,2023,44(4):1-6 |
| 空间l2(Z×Z)上正交小波基的频域特征刻画与算法 |
| CHARACTERIZATION AND ALGORITHMS OF ORTHONORMAL WAVELET BASES OF l2(Z×Z) |
| 投稿时间：2022-09-08 修订日期：2023-04-12 |
| DOI：10.3969/j.issn.1674-8085.2023.04.001 |
| 中文关键词: 正交小波基 卷积 滤波器组 完美重构 |
| 英文关键词: orthonormal wavelet bases convolution filter bank perfect reconstruction |
| 基金项目: |
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| 中文摘要: |
| 小波基的频域特征刻画有助于小波基的构造。首先给出了函数空间l2(Z×Z)上正交小波基的频域特征刻画，再根据正交小波基的频域特征刻画，可以容易验证：一维空间的两个正交小波基的乘积是二维空间的正交小波基。最后还给出了完美重构条件以及快速分解重构算法。 |
| 英文摘要: |
| Frequency domain characterization of wavelet basis makes constructing wavelet bases painless. In this paper, such description is given for function space l2(Z×Z). According to the characterization of orthogonal wavelet bases in frequency domain, it could be verified that the product of two orthogonal wavelet bases in one-dimensional space is orthogonal wavelet bases in two-dimensional space. The conditions of perfect reconstruction and the fast decomposition and reconstruction algorithm are also given. |
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