分数傅里叶余弦-拉普拉斯混合加权卷积及其应用

Fractional Fourier Cosine-Laplace Mixed Weighted Convolution and Its Applications

由于不同的卷积运算具有不同的性质,在实际应用中可以对不同的复杂应用场景进行建模,因此,进一步研究分数域卷积运算及其性质,对揭示非平稳信号分析和处理的内在规律,具有重要的理论意义和实际应用价值.首先定义了两类分数傅里叶余弦-拉普拉斯混合加权卷积运算,推导了相应的卷积定理;其次研究了混合加权卷积运算性质,最后将所得卷积运算应用于卷积积分方程组,给出了相应的显式解.

Because different convolution operations have different properties,they can be used to model different complex application scenarios in practical applications.Therefore,further study of fractional convolution operation and its properties has important theoretical significance and practical application value to reveal the internal law of non-stationary signal analysis and processing.Firstly,two classes of fractional Fourier cosine-Laplace mixed weighted convolution are defined based on the existing fractional Fourier-Laplace weighted convolution,and the corresponding convolution theorem is derived.Secondly,the properties of mixed weighted convolution are studied.Finally,based on these kind of convolution,solution of the system of convolution integral equations is studied,and the explicit solutions are obtained.