Harmonic analysis in rough contexts

谐波分析是一组数学技术，旨在将复杂的信号分解为简单的片段，其方式让人联想到将声音分解为谐波。它可以高效地分析均匀介质中的信号，例如无线通信技术的基础--空气中的波传播。然而，通过非均匀介质的波传播，例如医学成像中的人体或地球物理成像中的地球，更难建模。具有随机成分的现象，例如金融领域的现象，也是有问题的。这个项目是一个激烈的国际研究工作的重要组成部分，在这种粗糙的背景下发展谐波分析。

Harmonic analysis is a set of mathematical techniques aimed at decomposing complex signals into simple pieces in a way that is reminiscent of the decomposition of sounds into harmonics. It is highly efficient in analysing signals in homogeneous media such as wave propagation through the air that underpins wireless communication technology. However, wave propagation through inhomogeneous media, such as the human body in medical imaging or the Earth in geophysical imaging, is much harder to model. Phenomena with random components, as considered in finance for instance, are also problematic. This project is an important part of an intense international research effort to develop harmonic analysis in such rough contexts.