Applied Time-frequency Analysis

应用时频分析

• 批准号: RGPIN-2014-05059
• 负责人: Zhu, Hongmei
• 金额: $ 0.8万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=588184
• 关键词: Applied; Time; frequency; Analysis

Abnormalities by their own nature have only extremely weak footprints hidden deeply underneath the vast majority of normal data. In many cases, they reveal themselves as unusual localized structures along a joint time and frequency domain of a large set of non-stationary data. Time-frequency analysis (TFA) by design aims to reveal local features of non-stationary signals with time-varying frequency content. It provides the ability to uncover hidden abnormalities if the original data can be intelligently transformed and represented along the time and frequency domains. For example, irregular heartbeats, abnormal brain activities, or abnormal airplane vibrations that have a sudden onset and occur at a distinct frequency range can all be identified by TFA. Early detection of critical abnormalities allows us to take appropriate action to prevent expensive and fatal damages. Despite of its usefulness, two main issues severely impede the effectiveness of the TFA-based diagnoses. First, as TFA represents a one-dimensional signal as a function of two variables, time and frequency, the computational efforts are often substantial. This is particularly problematic for processing ultra large data set and/or used in a real-time setting. However, in many cases, the intended application has unique features that can be exploited to considerably reduce the computational complexity. Second, many standard TFA techniques require simplifying assumptions or standard characteristics such as that the signals are deterministic, sampled evenly, or fit well to linear models of sinusoidal waveforms. However, in practice, the majority of important applications will violate these assumptions significantly. Nevertheless, current mathematical theories can be extended so that specific TFA techniques can be developed without the reliance of some of the simplifying assumptions. Furthermore, if the actual data has certain characteristics that can be usefully exploit, these “non-standard characteristics” can be incorporated in the theoretical development of the techniques to help increase the effectiveness. The objective of this research program is to fundamentally overcome the critical limitations of the existing TFA techniques, in order to release its full potential for practical applications. More specifically, we aim to generalize the rationale behind the time-frequency analysis 1) to first tackle ultra large data size and then real-time TFA-based signal processing; 2) to investigate a number of “non-standard characteristics” that are regularly presented in the actual data; 3) with the availability of efficient computational schemes and more refined theoretical framework established in 1) and 2), a much broader range of computer-aided diagnostic applications can be explored. This research proposal is interdisciplinary and practical. It integrates mathematics, statistics, computing, and applications development. I expect that the trainees in the program will work closely with engineers and scientists in medical science and industries and make significant original contributions relevant to real-world problems. The success of this program will advance time-frequency analysis field, create sophisticated time-frequency analysis techniques tailored for specific types of signals and lead to the R&D development of computer-assisted monitoring and diagnostic software for various purposes.

异常现象本身的性质非常微弱，隐藏在绝大多数正常数据之下。在许多情况下，它们表现为沿着大量非平稳数据的联合时域和频域的异常局部结构。频率分析 (TFA) 的设计目的是揭示具有时变频率内容的非平稳信号的局部特征，如果原始数据可以沿时域和频域进行智能转换和表示，则它能够发现隐藏的异常。例如，心律不齐、异常的大脑活动或突然发生并在不同频率范围内发生的异常飞机振动都可以通过 TFA 进行识别，尽早发现严重异常使我们能够采取适当的行动来防止昂贵和致命的损害。 尽管它很有用，但两个主要问题严重阻碍了基于 TFA 的诊断的有效性，首先，由于 TFA 表示作为时间和频率两个变量的函数的一维信号，因此计算量通常很大。然而，在许多情况下，预期的应用程序具有可以大大降低计算复杂性的独特功能。其次，许多标准 TFA 技术需要简化假设。或标准特性，例如信号是确定性的、均匀采样的，或者很好地适合正弦波形的线性模型。然而，在实践中，大多数重要的应用都会严重违反这些假设，尽管如此，可以扩展当前的数学理论，以便在不使用 TFA 的情况下开发特定的 TFA 技术。此外，如果实际数据具有某些可以有效利用的特征，则可以将这些“非标准特征”纳入技术的理论开发中，以帮助提高有效性。 本研究计划的目标是从根本上克服现有 TFA 技术的关键局限性，以便充分发挥其在实际应用中的潜力。更具体地说，我们的目标是概括时频分析 1) 背后的基本原理，以首先解决这一问题。超大数据量，然后基于 TFA 的实时信号处理；2）研究实际数据中经常出现的一些“非标准特征”；3）提供高效的计算方案和更精细的理论。 1) 中建立的框架和2），可以探索更广泛的计算机辅助诊断应用。 这项研究计划是跨学科的、实用的，它整合了数学、统计学、计算和应用开发，我希望该项目的学员能够与医学和工业界的工程师和科学家密切合作，并做出与现实世界相关的重大原创贡献。该计划的成功将推动时频分析领域的发展，创建针对特定类型信号的复杂时频分析技术，并促进用于各种目的的计算机辅助监测和诊断软件的研发。