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<p>The octonion Fourier transform (OFT) plays a very important role in signal processing. In this paper, new convolution operators are defined, they can be viewed as the general forms of the classical convolution operators. And then according to the definition of the OFT, convolution theorems of the OFT are obtained. In some conditions, the convolution theorems of the OFT can be expressed as the form of the sum of the multiplications associated with their OFTs. Finally, based on Gaussian signals, the applications of convolution theorems for the 3-D OFT are explored by different kinds of equations and graphical visualization.</p>

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Convolution Theorems and Applications for the Octonion Fourier Transform

  • 期刊论文

  • 发表日期：

    2025年11月2日

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  • Wen-Biao Gao

摘要

The octonion Fourier transform (OFT) plays a very important role in signal processing. In this paper, new convolution operators are defined, they can be viewed as the general forms of the classical convolution operators. And then according to the definition of the OFT, convolution theorems of the OFT are obtained. In some conditions, the convolution theorems of the OFT can be expressed as the form of the sum of the multiplications associated with their OFTs. Finally, based on Gaussian signals, the applications of convolution theorems for the 3-D OFT are explored by different kinds of equations and graphical visualization.