Time–frequency analysis

About: Time–frequency analysis is a research topic. Over the lifetime, 5407 publications have been published within this topic receiving 104346 citations.

High-Resolution Multiple Wideband and Nonstationary Source Localization With Unknown Number of Sources

Abstract: In this paper, a new algorithm for high-resolution multiple wideband and nonstationary source localization using a sensor array is proposed. The received signals of the sensor array are first converted into the time-frequency domain via short-time Fourier transform (STFT) and we find that a set of short-time power spectrum matrices at different time instants have the joint diagonalization structure in each frequency bin. Based on such joint diagonalization structure, a novel cost function is designed and a new spatial spectrum for direction-of-arrival (DOA) estimation at hand is derived. Compared to the maximum-likelihood (ML) method with high computational complexity, the proposed algorithm obtains the DOA estimates via one-dimensional (1-D) search instead of multidimensional search. Therefore its computational complexity is much lower than the ML method. Unlike the subspace-based high-resolution DOA estimation techniques, it is not necessary to determine the number of sources in advance for the proposed algorithm. Moreover, the proposed method is robust to the effects of reverberation caused by multipath reflections. Hence it is suitable for multiple acoustic source localization in a reverberant room. The results of numerical simulations and experiments in a real room with a moderate reverberation are provided to demonstrate the good performance of the proposed approach.

Sparse Signal Reconstruction Based on Time–Frequency Manifold for Rolling Element Bearing Fault Signature Enhancement

Abstract: Denoising based on signal reconstruction has been one of the most important tasks in signal processing for rolling element bearing fault diagnosis. This paper proposes a sparse signal reconstruction method combining time–frequency manifold (TFM) and sparse reconstruction for fault signature enhancement of rolling element bearings. TFM has good denoising performance for analyzing the defective bearing vibration signals. However, the amplitude information will be influenced by its nonlinear processing. This paper proposes employment of the sparse decomposition method to overcome this problem. The sparse decomposition is first conducted to process the TFM-based result on a designed overcomplete dictionary. Furthermore, the coefficients of the achieved sparse atoms are obtained by projecting the raw signal on the atoms to realize reconstruction of the bearing fault signature. The TFM-based sparse signal reconstruction method takes advantage of both TFM in denoising and the atomic decomposition in sparse reconstruction. The proposed method has a valuable theoretical contribution on explicit expression of nonlinear signal processing results. The results verified by experimental analysis indicate the value in fault signature enhancement of rolling element bearings and other mechanical movements.

The Use of a Multilabel Classification Framework for the Detection of Broken Bars and Mixed Eccentricity Faults Based on the Start-Up Transient

Abstract: In this paper, a data-driven approach for the classification of simultaneously occurring faults in an induction motor is presented. The problem is treated as a multilabel classification problem, with each label corresponding to one specific fault. The faulty conditions examined include the existence of a broken bar fault and the presence of mixed eccentricity with various degrees of static and dynamic eccentricity, while three “problem transformation” methods are tested and compared. For the feature extraction stage, the start-up current is exploited using two well-known time–frequency (scale) transformations. This is the first time that a multilabel framework is used for the diagnosis of co-occurring fault conditions using information coming from the start-up current of induction motors. The efficiency of the proposed approach is validated using simulation data with promising results irrespective of the selected time–frequency transformation.

Multi-Dimensional Signal Processin Using an Algebraically Extended Signal Representation

Abstract: Many concepts that are used in multi-dimensional signal processing are derived from one-dimensional signal processing. As a consequence, they are only suited to multi-dimensional signals which are intrinsically one-dimensional. We claim that this restriction is due to the restricted algebraic frame used in signal processing, especially to the use of the complex numbers in the frequency domain. We propose a generalization of the two-dimensional Fourier transform which yields a quaternionic signal representation. We call this transform quaternionic Fourier transform (QFT). Based on the QFT, we generalize the conceptions of the analytic signal, Gabor filters, instantaneous and local phase to two dimensions in a novel way which is intrinsically two-dimensional. Experimental results are presented.