傅立叶变换的收敛性与解析形式探讨

Research on the Convergence and Analytic Form of Fourier Transform

傅立叶变换自提出之日,便受到以严格著称的数学家们诟病。傅立叶变换之所以对近代工程和自然科学产生了深刻的影响,在于傅立叶变换符合实际情况,给工程应用带来了极大的便利。通过分析阶跃信号的傅立叶变换的存在性及数学推导过程,从数学角度和工程角度探讨信号傅立叶变换存在的条件。

Fourier Transform is denounced by the rigorous mathematician when proposed. But the Fourier Transform actually impact on the modern engineering and science deeply, it meet the reality of the real world and has brought great convenience to the application of engineering. Focusing on the FT of the step signal u（t） and the derivation of its FT, discusses the condition of Fourier Transform in the view of engineering and mathematics.