CIF: Small: Resonance-Based Signal Analysis: Algorithms and Applications

基于共振的信号分析：算法和应用Ivan Selesick许多来自生理和物理过程的信号不仅是非平稳的，而且具有持续振荡和非振荡瞬变的混合，这是很难用线性方法来分离的。这种信号的例子包括语音、生物医学和地球物理信号。例如，脑电信号包含节律性振荡(阿尔法波等)，但由于测量伪影和非节律性大脑活动，它们也包含瞬变。这项研究计划涉及开发和应用新的算法，旨在将这种信号分解成“共振”分量--高共振分量是由多个同时持续振荡组成的信号；低共振分量是由未指明形状和持续时间的非振荡瞬变信号组成的信号。虽然频率分量被直接定义并且可以通过线性滤波获得，但谐振分量更难定义，并且获得谐振分量的过程必然是非线性的。可以预见，将非平稳多共振信号分解成共振分量将能够更有效地利用专门针对每个分量的现有处理方法。例如，对于主要由持续振荡(高共振信号)组成的信号，语音的正弦建模是最有效和最有效的。另一方面，时间域和小波域方法对于分段平滑信号是最有效的，这些信号主要是由其瞬时或奇异性(低共振信号)定义的。这项研究利用了信号处理的最新发展，包括稀疏信号表示，形态分量分析，变Q因子的常数-Q(小波)变换，L1范数正则化线性逆问题的快速算法，以及相关算法。这项研究包括开发基于共振的信号分解和概括的算法，并评估它们对处理来自几个物理和生理过程的信号的有效性。

Resonance-Based Signal Analysis: Algorithms and Applications Ivan SelesnickMany signals arising from physiological and physical processes are not only non-stationary but also posses a mixture of sustained oscillations and non-oscillatory transients that are difficult to disentangle by linear methods. Examples of such signals include speech, biomedical, and geophysical signals. For example, EEG signals contain rhythmic oscillations (alpha waves, etc) but they also contain transients due to measurement artifacts and non-rhythmic brain activity. This research program involves the development and application of new algorithms designed to decompose such signals into 'resonance' components - a high-resonance component being a signal consisting of multiple simultaneous sustained oscillations; a low-resonance component being a signal consisting of non-oscillatory transients of unspecified shape and duration. While frequency components are straightforwardly defined and can be obtained by linear filtering, resonance components are more difficult to define and procedures to obtain resonance components are necessarily nonlinear. It is envisioned that the decomposition of a non-stationary multi-resonance signal into resonance components will enable the more effective utilization of existing processing methods specialized to each component. For example, sinusoidal modeling of speech is most efficient and effective for signals consisting primarily of sustained oscillations (high-resonance signals). On the other hand, time-domain and wavelet-domain methods are most effective for piecewise smooth signals that are defined primarily by their transients or singularities (low-resonance signals). This research utilizes recent developments in signal processing, including sparse signal representations, morphological component analysis, constant-Q (wavelet) transforms with varying Q-factors, fast algorithms for L1-norm regularized linear inverse problems, and related algorithms. The research consists of developing algorithms for resonance-based signal decomposition and generalizations, and assessing their effectiveness for the processing of signals arising from several physical and physiological processes.