In nature and engineering world, the acquired signals are usually affected by multiple complicated factors and appear as multicomponent nonstationary modes. In such and many other situations, it is necessary to separate these signals into a finite number of monocomponents to represent the intrinsic modes and underlying dynamics implicated in the source signals. In this paper, we consider the mode retrieval of a multicomponent signal which has crossing instantaneous frequencies (IFs), meaning that some of the components of the signal overlap in the time-frequency domain. We use the chirplet transform (CT) to represent a multicomponent signal in the three-dimensional space of time, frequency and chirp rate and introduce a CT-based signal separation scheme (CT3S) to retrieve modes. In addition, we analyze the error bounds for IF estimation and component recovery with this scheme. We also propose a matched-filter along certain specific time-frequency lines with respect to the chirp rate to make nonstationary signals be further separated and more concentrated in the three-dimensional space of CT. Furthermore, based on the approximation of source signals with linear chirps at any local time, we propose an innovative signal reconstruction algorithm, called the group filter-matched CT3S (GFCT3S), which also takes a group of components into consideration simultaneously. GFCT3S is suitable for signals with crossing IFs. It also decreases component recovery errors when the IFs curves of different components are not crossover, but fast-varying and close to one and other. Numerical experiments on synthetic and real signals show our method is more accurate and consistent in signal separation than the empirical mode decomposition, synchrosqueezing transform, and other approaches
翻译:在自然和工程界,获得的信号通常受到多种复杂因素的影响,并看起来是多构非静止模式。在这样和许多其他情况下,有必要将这些信号分离成数量有限的单构件,以代表源信号所涉及的内在模式和内在动态。在本文中,我们考虑多构件信号的恢复模式,该多构件跨越了瞬时频率,这意味着信号在时频域内的某些部分重叠会进一步分离,并更加集中于三维空域。我们使用正构件变换(CT)代表时间、频率和恰普率三维空间的多构件信号,并采用基于CT的信号分解方法(CT3S)检索模式。此外,我们还要分析IFS估算和组件恢复的误差范围。 我们还提议,与某些特定的时速率相匹配的过滤器,以使非静态信号进一步分离,更集中于CT的三维空间。此外,根据源信号与直线焦点、频率和调速速率之间的近,我们提议采用一种基于CFFS的信号再转换方法,同时将一个信号转换为FFS的精确分解。