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<p>In this paper, <i>v</i>-generalised frequency shift is presented, which leads to the formulation of a fractional convolution operator in frequency domain. The standard Fourier Transform’s convolution in the frequency domain being a specific instance. This new operator satisfies the generalised convolution theorem related to the fractional Fourier Transform and preserves the commutative property. Finally, this operator is applied to filter spam(unwanted) frequencies to achieve the original signal <i>f</i>(<i>t</i>).</p>

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Analysis of Convolution Theorem in Frequency Domain by Fractional Fourier Transform

  • 期刊论文

  • 发表日期：

    2025年11月25日

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  • Pankaj Sharma,
  • V. Abisha

摘要

In this paper, v-generalised frequency shift is presented, which leads to the formulation of a fractional convolution operator in frequency domain. The standard Fourier Transform’s convolution in the frequency domain being a specific instance. This new operator satisfies the generalised convolution theorem related to the fractional Fourier Transform and preserves the commutative property. Finally, this operator is applied to filter spam(unwanted) frequencies to achieve the original signal f(t).