Scholarlink

<p>Recently, the graph Fourier transform for a signal on a directed graph <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {G}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">G</mi> </math></EquationSource> </InlineEquation> has been defined using the singular value decomposition of the Laplacian matrix of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {G}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">G</mi> </math></EquationSource> </InlineEquation>. Using this definition, in this paper, we define the operation of convolution and introduce translation, modulation and dilation operators. After studying certain important properties of translation, we obtain a necessary and sufficient condition for the Gabor system to form a frame. We also prove that, under certain sufficient conditions, the spectral graph wavelet system forms a frame. We illustrate some of our results with numerical examples using Matlab.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Translation Operator and Frames on Directed Graphs

  • 期刊论文

  • 发表日期：

    2026年6月30日

查看全文
  • Prakash Das,
  • Radha Ramakrishnan

摘要

Recently, the graph Fourier transform for a signal on a directed graph \(\mathcal {G}\) G has been defined using the singular value decomposition of the Laplacian matrix of \(\mathcal {G}\) G . Using this definition, in this paper, we define the operation of convolution and introduce translation, modulation and dilation operators. After studying certain important properties of translation, we obtain a necessary and sufficient condition for the Gabor system to form a frame. We also prove that, under certain sufficient conditions, the spectral graph wavelet system forms a frame. We illustrate some of our results with numerical examples using Matlab.