标题： 傅里叶分析的新思路 显示英文标题

标题： Refreshing idea on Fourier analysis

摘要： “傅里叶分析中时间-频率分辨率的理论极限”被认为源于某些数学和/或物理限制。 然而，这并不正确。 实际原因来自于用于减少计算时间的数值（技术）方法。 此外，傅里叶分析的理论方程与其数值实现之间存在差距。 了解这些事实给我们带来了实际的好处。 在这种情况下，这些涉及边界条件和复积分。 例如，用复积分代替傅里叶积分可以得到拉普拉斯和傅里叶变换的混合方法，并揭示了时间-频率分析的另一个视角。 我们在这里提出这种视角，并进行简单的演示分析。 显示英文摘要

摘要： The "theoretical limit of time-frequency resolution in Fourier analysis" is thought to originate in certain mathematical and/or physical limitations. This, however, is not true. The actual origin arises from the numerical (technical) method deployed to reduce computation time. In addition, there is a gap between the theoretical equation for Fourier analysis and its numerical implementation. Knowing the facts brings us practical benefits. In this case, these related to boundary conditions, and complex integrals. For example, replacing a Fourier integral with a complex integral brings a hybrid method for the Laplace and Fourier transforms, and reveals another perspective on time-frequency analysis. We present such a perspective here with a simple demonstrative analysis.