Iterative filtering methods were introduced around 2010 to improve definitions and measurements of structural features in signal processing. Like many applied techniques, they present considerable challenges for mathematicians to theorize their effectiveness and limitations in commercial and scientific usages. In this paper we recast iterative filtering methods in a mathematical abstraction more conducive to their understanding and applications. We also introduce a new visualization of simultaneous local frequencies and amplitudes. By combining a theoretical and practical exposition, we hope to stimulate efforts to understand better these methods. Our approach acknowledges the influence of Ciprian Foia\c{s}, who was passionate about pure, applied, and applications of mathematics.
翻译:2010年前后,为改进信号处理结构特征的定义和测量,引入了循环过滤方法,以改进信号处理中结构特征的定义和测量,与许多应用技术一样,这些方法给数学家提出了相当大的挑战,使他们在商业和科学用途方面如何解释其有效性和局限性。在本文中,我们用更有利于其理解和应用的数学抽象学重新塑造了迭代过滤方法。我们还引入了同步本地频率和振幅的新视觉化。通过将理论和实践的论述结合起来,我们希望激发人们努力更好地了解这些方法。我们的方法承认热衷于纯洁、应用和应用数学的Ciprian Foia\c{s}的影响力。