This paper introduces a novel time–frequency analysis method called the Weight Extracting Transform (WET). The primary objective of WET is to enhance the energy concentration in linear time–frequency ...representations for time-varying signals. By aggregating the time–frequency blur produced by the short-time Fourier transform onto the actual instantaneous frequency, WET improves the readability and accuracy of the time–frequency representation. Additionally, the algorithm is extended to a more general linear time–frequency transform known as the chirplet transform, which effectively handles fast-varying signals. The WET method excels at distinguishing components with closely spaced instantaneous frequencies and can reconstruct the original signal from its time–frequency representation. Experimental results using simulated and real-world signals demonstrate that WET achieves superior energy concentration and noise robustness compared to existing methods.
The objective of this paper is to introduce an innovative approach for the recovery of non-stationary signal components with possibly crossover instantaneous frequency (IF) curves from a ...multi-component blind-source signal. The main idea is to incorporate a chirp rate parameter with the time-scale continuous wavelet-like transformation, by considering the quadratic phase representation of the signal components. Hence-forth, even if two IF curves cross, the two corresponding signal components can still be separated and recovered, provided that their chirp rates are different. In other words, signal components with the same IF value at any time instant could still be recovered. To facilitate our presentation, we introduce the notion of time-scale-chirp_rate (TSC_R) recovery transform or TSC_R recovery operator to develop a TSC_R theory for the 3-dimensional space of time, scale, chirp rate. Our theoretical development is based on the approximation of the non-stationary signal components with linear chirps and applying the proposed adaptive TSC_R transform to the multi-component blind-source signal to obtain fairly accurate error bounds of IF estimations and signal components recovery. Several numerical experimental results are presented to demonstrate the out-performance of the proposed method over all existing time-frequency and time-scale approaches in the published literature, particularly for non-stationary source signals with crossover IFs.
In this article, we optimize the kernel of a time-frequency distribution (TFD) for a specific class of signals with some instantaneous frequency (IF) patterns, such as linear frequency modulated ...(LFM) and sinusoidal frequency modulated (SFM) signals. We introduce an IF estimator of such patterns by maximizing the integration of the local signal-to-noise ratio (LSNR) in the time-frequency (TF) domain over the curves of possible patterns by using an initial kernel. We then maximize the integrated LSNR by optimizing the kernel function by using the estimated IF. This approach provides a signal-dependent kernel in the time-delay domain (TDD), which can be used to reestimate the IF more accurately. Our experimental results for linear and sinusoidal frequency modulation reveal that our optimized signal-dependent TFD kernel significantly outperforms well-established TFDs in the IF estimation, while significantly reducing the number and impacts of the cross-terms (CTs), especially for crossing component signals.
In the real world, most signals encountered are nonstationary. It is essential to extract a time-frequency (TF) characteristics in such signals for an accurate description. Two parameters are usually ...applied to quantify the TF characteristics of a nonstationary signal, i.e., instantaneous frequency (IF) and group delay (GD). A post-processing strategy was adopted by two recently developed techniques, the synchrosqueezing transform (SST) and the time-reassigned SST (TSST) to accurately capture the change rules of IF and GD respectively. However, due to the diversity of modes in complex nonstationary signals, no existing technique has been used to effectively estimate both IF and GD simultaneously. To solve this problem, a post-processing analysis technique termed as time-frequency-multisqueezing transform (TFMST) is proposed in this paper where a so-called chirp rate (CR) discrimination criterion is established by considering the Gaussian window in the short-time Fourier transform. The proposed method can accurately categorize nonstationary signals containing harmonic- and impulsive-like components to achieve a concurrent description and ensure the recovery of original signals. The proposed method is validated by numerical simulation and real signal analyses.
The combination of the complex structure and the nonstationary operating pattern makes the measured signal of the machinery a multi-component one with a complex time-varying spectral structure, ...challenging most time–frequency analysis methods in resolution, adaptability, and objectivity. As such, we propose a novel time–frequency analysis method, namely, the adaptive synchronous demodulation transform (ASDT), by adaptively designing a demodulation term according to the spectral structures of the target signals. The proposed demodulation term can make each component of the windowed signal stationary simultaneously without any prior knowledge, such as the number of components and the corresponding estimated instantaneous frequencies. ASDT possesses three main advantages: it can be used to analyze signals with nonlinear instantaneous frequencies; it can obtain the optimum frequency resolution when window width is set; and the demodulation term is flexible, implying that it can be specifically designed according to the frequency structures of different types of signals. Furthermore, ASDT allows for signal recovery. To testify the superiority of the proposed ASDT, two synthetic signals with parallel and proportional IFs structures were built, and several real-life signals, vibration signals collected from a planetary gearbox test rig and water turbine, and an echo signal collected from a brown bat were used. A comparison of the analysis results of ASDT with those of STFT, continuous wavelet transform, and Wigner–Ville distribution demonstrated the superiority of ASDT over conventional methods.
ConceFT: concentration of frequency and time via a multitapered synchrosqueezed transform Daubechies, Ingrid; Wang, Yi (Grace); Wu, Hau-tieng
Philosophical transactions - Royal Society. Mathematical, Physical and engineering sciences/Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences,
04/2016, Letnik:
374, Številka:
2065
Journal Article
Recenzirano
Odprti dostop
A new method is proposed to determine the time-frequency content of time-dependent signals consisting of multiple oscillatory components, with time-varying amplitudes and instantaneous frequencies. ...Numerical experiments as well as a theoretical analysis are presented to assess its effectiveness.
•A novel time–frequency ridge estimation (TFRE) method is proposed.•The TFRE can detect ridges with higher accuracy from more complicated TFRs.•The TFRE executes automatically without parameter ...setting and adjustment.
For a rotary machine vibration signal collected under variable speed conditions, its time–frequency representation (TFR) contains abundant oscillatory components with time-varying amplitudes and frequencies. A single component with a sequence of peaks in the TFR is called a ridge. Accurate ridge detection from TFRs can boost rotary machine health condition assessment without rotation speed measurement. Nowadays, cost function ridge estimation and fast path optimization ridge estimation are the most widely utilized techniques. However, the unreasonable kernel function definitions and inappropriate search region selections significantly restrict the performance of instantaneous frequency estimation of target ridges. To address the deficiencies, this paper proposes a novel time–frequency ridge estimation (TFRE) method. The TFRE integrates a new cost kernel function and an adaptive search region detection principle. For the former, it comprehensively considers the trade-off between seeking peaks and ensuring the smoothness of a ridge. The latter varies the search bandwidth in real-time according to instantaneous signal signatures to effectively isolate interferences and neighboring ridges. A unique advantage of the proposed method is that it dispenses with the tuning of parameters. As a consequence, human intervention is minimized. Experimental gear and bearing vibration signals were analyzed to demonstrate the performance of the TFRE. Results indicated that the proposed TFRE is characterized by superior ridge estimation performance compared to the state-of-the-art methods.
Time–frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture features in these signals, it is necessary for the analysis methods to be local, adaptive ...and stable. In recent years, decomposition based analysis methods, such as the empirical mode decomposition (EMD) technique pioneered by Huang et al., were developed by different research groups. These methods decompose a signal into a finite number of components on which the time–frequency analysis can be applied more effectively.
In this paper we consider the Iterative Filtering (IF) approach as an alternative to EMD. We provide sufficient conditions on the filters that ensure the convergence of IF applied to any L2 signal. Then we propose a new technique, the Adaptive Local Iterative Filtering (ALIF) method, which uses the IF strategy together with an adaptive and data driven filter length selection to achieve the decomposition. Furthermore we design smooth filters with compact support from solutions of Fokker–Planck equations (FP filters) that can be used within both IF and ALIF methods. These filters fulfill the derived sufficient conditions for the convergence of the IF algorithm. Numerical examples are given to demonstrate the performance and stability of IF and ALIF techniques with FP filters. In addition, in order to have a complete and truly local analysis toolbox for non-linear and non-stationary signals, we propose new definitions for the instantaneous frequency and phase which depend exclusively on local properties of a signal.
•The instantaneous frequency-embedded continuous wavelet transform (IFE-CWT) is introduced and its properties are studied.•Based on IFE-CWT, the instantaneous frequency-embedded synchrosqueezing ...transform (IFE-SST) is introduced.•IFE-SST can preserve the IF of a monocomponent signal. To estimate IF of a component of a multicomponent signal, IFE-SST uses a reference IF function associated with that component.•The IFE-SST-based multicomponent signal separation algorithm is proposed. The experimental results also show that IFE-SST works well in the noise environment.
Recently, the synchrosqueezing transform (SST) was developed as an alternative to the empirical mode decomposition scheme to separate a non-stationary signal with time-varying amplitudes and instantaneous frequencies (IFs) into a superposition of frequency components that each have well-defined IFs. The continuous wavelet transform (CWT)-based SST sharpens the time-frequency representation of a non-stationary signal by assigning the scale variable of the signal’s CWT to the frequency variable by a reference IF function. Since the SST method is applied to estimate the IFs of all frequency components of a signal based on one single reference IF function, it may yield not very accurate results. In this paper we introduce the instantaneous frequency-embedded synchrosqueezing wavelet transform (IFE-SST). IFE-SST uses a rough estimation of the IF of a targeted component to produce accurate IF estimation. The reference IF function of IFE-SST is associated with the targeted component. Our numerical experiments show that IFE-SST outperforms the CWT-based SST in IF estimation and separation of multicomponent signals.
Recently, the use of speech processing in a time–frequency domain that handles the phase spectrum in addition to the amplitude one has been increasing because many studies have revealed the ...importance of phase. Inspired by this motivation, this paper presents a new speech signal phase processing. The contributions of this paper include the following two points: a detailed analysis of a speech signal by considering a novel phase feature, a derivative of instantaneous frequency (DIF), and demonstrating a new phase-based voice activity detection (VAD) algorithm as one of the DIF’s applications. These contributions develop on our previous work that briefly introduced the DIF into VAD. In the analysis part, we investigate the DIF from the theoretical aspect and research the statistical distribution of the DIF of speech signals under various conditions. We also propose a new phase-based VAD algorithm via the statistical likelihood ratio, and use the DIF as an auxiliary feature to improve a conventional amplitude-based VAD method. The experimental results confirm the efficacy of the phase feature in the VAD application and the possibility of combining the phase and amplitude for better performance.
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