Shiqian Chen

Time-Varying Frequency-Modulated Component Extraction Based on Parameterized Demodulation and Singular Value Decomposition

To analyze the valuable frequency component for time-varying frequency-modulated (FM) signals, component extraction is necessary in most applications. Considering the advantage of parameterized demodulation (PD) in transforming FM signals to be stationary, a novel component extraction method based on PD and singular value decomposition (PD-SVD) for both monocomponent and multicomponent signals is proposed. By extending the idea of PD, the time-varying term of the continuous phase function for the interested FM component can be removed, thus resulting in a highly self-correlated component with constant phase. Then, the extraction of the target component from noise or other components can be realized by SVD. Compared with the existing methods, the proposed algorithm is able to analyze the multicomponent signal with crossed instantaneous frequency trajectories and effectively improve the signal-to-noise ratio of the extracted component. The effectiveness of the proposed method is demonstrated by applying it on several numerical signals and the radial vibration signal of a hydroturbine rotor, indicating the potential of analyzing many practical FM signals.

Intrinsic chirp component decomposition by using Fourier Series representation

We introduce a general model to characterize multi-component chirp signals.The model represents instantaneous frequencies and instantaneous amplitudes of the intrinsic chirp components as Fourier series.We propose a novel chirp component decomposition method based on the model.The method is able to decompose multi-component chirp signals with intersecting IFs. In this paper, we consider the decomposition problem for multi-component chirp signals (MCCSs). We develop a general model to characterize MCCSs, where instantaneous frequencies (IFs) and instantaneous amplitudes (IAs) of the intrinsic chirp components (ICCs) are modeled as Fourier series. The decomposition problem thus boils down to identifying the developed model. The IF estimation is addressed using the framework of the general parameterized time-frequency transform and then the signal can be easily reconstructed by solving a linear system. For the practical implementation of our method, we present a two-step algorithm, which is initiated by an iterative scheme to achieve preliminary separation of the ICCs, followed by a joint-refinement step to get high-resolution ICC reconstructions. Our method acts as a time-varying band-pass filter and can even separate ICCs that cross in the time-frequency domain. The method is applied to analyze several simulated and real signals, which indicates its usefulness in various applications.

Separation of Overlapped Non-Stationary Signals by Ridge Path Regrouping and Intrinsic Chirp Component Decomposition

In some applications, it is necessary to analyze multi-component non-stationary signals whose components severely overlap in the time-frequency (T-F) domain. Separating those signal components is desired but very challenging for existing methods. To address this issue, we propose a novel non-parametric algorithm called ridge path regrouping (RPRG) to extract the instantaneous frequencies (IFs) of the overlapped components from a T-F representation (TFR). The RPRG first detects the ridges of a multi-component signal from a TFR and then extracts the desired IFs by regrouping the ridge curves according to their variation rates at the intersections. After the IFs are obtained, component separation is achieved by using the intrinsic chirp component decomposition (ICCD) method. Different from traditional T-F filter-based methods, the ICCD can accurately reconstruct overlapped components by using a joint-estimation scheme. Finally, applications of separating some simulated and experimental micro-Doppler signals are presented to show the effectiveness of the method.

Nonlinear Chirp Mode Decomposition: A Variational Method

Variational mode decomposition (VMD), a recently introduced method for adaptive data analysis, has aroused much attention in various fields. However, the VMD is formulated based on the assumption of narrow-band property of the signal model. To analyze wide-band nonlinear chirp signals (NCSs), we present an alternative method called variational nonlinear chirp mode decomposition (VNCMD). The VNCMD is developed from the fact that a wideband NCS can be transformed to a narrow-band signal by using demodulation techniques. Our decomposition problem is, thus, formulated as an optimal demodulation problem, which is efficiently solved by the alternating direction method of multipliers. Our method can be viewed as a time–frequency filter bank, which concurrently extracts all the signal modes. Some simulated and real data examples are provided showing the effectiveness of the VNCMD in analyzing NCSs containing close or even crossed modes.

Chirplet Path Fusion for the Analysis of Time-Varying Frequency-Modulated Signals

We propose a novel method, called chirplet path fusion, to analyze nonstationary signals with time-varying frequencies. As opposed to many existing methods that assume the signal persists throughout the whole time, the proposed method can be applied in cases where the signals are only present in short time frames. A demodulation-operator-based method is introduced to estimate the locally matched chirplet atoms which can form a chirplet path in the time-frequency domain. According to the density of the multiple chirplet paths obtained under different scales, the effective time support and the instantaneous frequency (IF) of the target signal can be estimated. Our method is effective in analyzing the nonstationary signal with discontinuous IF curve and works well under heavy noise. Several simulated signals and the vibration signal of a rotor test rig are considered to verify the effectiveness of the proposed method.

Accurate Measurement in Doppler Radar Vital Sign Detection Based on Parameterized Demodulation

Utilizing Doppler radar to conduct noncontact vital sign detection has attracted growing interest in recent years. Aiming to extract the vital sign information from the baseband signal effectively and accurately, a novel signal processing method based on parameterized demodulation (PD) is proposed. To effectively characterize the baseband signal whose phase consists of two oscillating components (i.e., the respiration and heartbeat components), the proposed algorithm defines a demodulation operator with sine kernel functions and formulates the phase demodulation as a parameter optimization problem. To increase the computational efficiency of the algorithm, the parameters corresponding to the respiration and heartbeat components are estimated sequentially. Specifically, the respiration component is first estimated and removed from the phase of the baseband signal, and then, the heartbeat component is extracted from the residual signal. Compared with the existing methods, the proposed algorithm is free of the resolution problem in fast Fourier transform-based methods with a limited data length and can obtain accurate rate tracking in a noisy environment. Both simulated and experimental results are provided to demonstrate the advantages and effectiveness of the proposed method for accurate noncontact vital sign detection.

Frequency-domain intrinsic component decomposition for multimodal signals with nonlinear group delays

Abstract Signals propagated in dispersive systems usually present multimodal and nonlinear group delay (GD) properties. The characterization of GDs and the signal decomposition are still challenging issues. Existing methods are mainly limited to identify monotonous GDs by estimating monotonous instantaneous frequencies. Bandpass filters are usually utilized to separate each mode, but the inherent defects of digital filters will decrease the reconstruction accuracy inevitably. In this paper, we propose the frequency-domain intrinsic component decomposition method (FICD). On one hand, it can characterize nonlinear and non-monotonic GDs in frequency domain by using different kernel functions. On the other hand, the method itself can act as a time-frequency filter to separate and reconstruct each mode simultaneously. One of the advantages of our method is that it can deal with close or overlapped signals with high precision. Finally, simulated examples are provided to verify the effectiveness and efficiency.

Parameterized model based Short-time chirp component decomposition

Abstract As a specific case of chirp component, the short-time chirp component (STCC) only continues a duration in a reference interval with a birth and death. A STCC usually possesses of important information directly related to kinematic or structural characteristics of a target. In this paper, a novel method is developed to decompose a multi-component short-time chirp signal into a series of STCCs. The decomposition method is mainly based on a parameterized mathematical model, which is used to represent the STCC, and a peak tracking approach, which is adopted to extract the instantaneous frequencies (IFs), and corresponding births and deaths for all the STCCs. With the model and the extracted IFs, the decomposition can be conducted by solving a linear system of equations. The effectiveness of the proposed method is demonstrated by two simulated examples and a marine biologic sound.

Nonstationary Signal Denoising Using an Envelope-Tracking Filter

Signal denoising is crucial to condition monitoring of mechanical systems as fault characteristics may be hidden by strong noise in some cases. In this paper, we focus on the denoising of nonstationary vibration signals which contain multiple complex components. To this end, we introduce a time-frequency filter called envelope-tracking filter (ETF). The basic idea of the ETF is to characterize the envelope of a signal using Fourier basis functions and estimate the envelope by solving a least-squares problem. We show that the ETF is similar to the Vold–Kalman filter, but it has several promising advantages, i.e., easier to determine the bandwidth expression, more flexible to handle signals at different noise levels, and less sensitive to errors of instantaneous frequency (IF) estimations. Our denoising method includes two steps: 1) extract IFs of each nonstationary component by optimizing a spectrum concentration index, and 2) recover each component by using the ETF. Our method works very well in heavy noise and is effective for signals with overlapped components. Some examples including simulated and real-life vibration signals are offered to show the validity of the method.

Parameterized model based blind intrinsic chirp source separation

Abstract The blind source separation (BSS) concerns recovering sources from their mixtures. Specifically, the sources in this paper, named intrinsic chirp sources (ICSs), are modeled as the linear combination of non-linear chirp components (NCCs). A novel method is developed here to address the blind separation issue of them. Firstly, all the mixtures at each channel are decomposed into a series of NCCs by a parameterized decomposition approach. It can adapt to NCCs with time-frequency (T-F) distribution suffering from bad T-F concentration and non-disjoint T-F overlapping. Next, the reconstructed NCCs can be clustered into corresponding ICS according to the fact that the NCCs belonging to the identical ICS share the same column in mixing matrix. The source recovery and mixing matrix estimation are finally accomplished based on the clustering consequence. Three simulations demonstrate the capability of our method in dealing with challenging under-determined BSS cases and its potential in practical applications.