Showing papers on "Time–frequency analysis published in 2015"

Second-Order Synchrosqueezing Transform or Invertible Reassignment? Towards Ideal Time-Frequency Representations

Abstract: This paper considers the analysis of multicomponent signals, defined as superpositions of real or complex modulated waves. It introduces two new post-transformations for the short-time Fourier transform that achieve a compact time-frequency representation while allowing for the separation and the reconstruction of the modes. These two new transformations thus benefit from both the synchrosqueezing transform (which allows for reconstruction) and the reassignment method (which achieves a compact time-frequency representation). Numerical experiments on real and synthetic signals demonstrate the efficiency of these new transformations, and illustrate their differences.

Epileptic Seizure Classification of EEG Time-Series Using Rational Discrete Short-Time Fourier Transform

Abstract: A system for epileptic seizure detection in electroencephalography (EEG) is described in this paper. One of the challenges is to distinguish rhythmic discharges from nonstationary patterns occurring during seizures. The proposed approach is based on an adaptive and localized time–frequency representation of EEG signals by means of rational functions. The corresponding rational discrete short-time Fourier transform (DSTFT) is a novel feature extraction technique for epileptic EEG data. A multilayer perceptron classifier is fed by the coefficients of the rational DSTFT in order to separate seizure epochs from seizure-free epochs. The effectiveness of the proposed method is compared with several state-of-art feature extraction algorithms used in offline epileptic seizure detection. The results of the comparative evaluations show that the proposed method outperforms competing techniques in terms of classification accuracy. In addition, it provides a compact representation of EEG time-series.

Histogram of gradients of time-frequency representations for audio scene classification

Abstract: This abstract presents our entry to the Detection and Classification of Acoustic Scenes challenge. The approach we propose for classifying acoustic scenes is based on transforming the audio signal into a time–frequency representation and then in extracting relevant features about shapes and evolutions of time–frequency structures. These features are based on histogram of gradients that are subsequently fed to a multi-class linear support vector machines.

High-Impedance Fault Detection in the Distribution Network Using the Time-Frequency-Based Algorithm

Abstract: A new high-impedance fault (HIF) detection method using time-frequency analysis for feature extraction is proposed. A pattern classifier is trained whose feature set consists of current waveform energy and normalized joint time–frequency moments. The proposed method shows high efficacy in all of the detection criteria defined in this paper. The method is verified using real-world data, acquired from HIF tests on three different materials (concrete, grass, and tree branch) and under two different conditions (wet and dry). Several nonfault events, which often confuse HIF detection systems, were simulated, such as capacitor switching, transformer inrush current, nonlinear loads, and power-electronics sources. A new set of criteria for fault detection is proposed. Using these criteria, the proposed method is evaluated and its performance is compared with the existing methods. These criteria are accuracy, dependability, security, safety, sensibility, cost, objectivity, completeness, and speed. The proposed method is compared with the existing methods, and it is shown to be more reliable and efficient than its existing counterparts. The effect of choice of the pattern classifier on method efficacy is also investigated.

ConceFT: Concentration of Frequency and Time via a multitapered synchrosqueezed transform

Abstract: 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.

Assess Sleep Stage by Modern Signal Processing Techniques

Abstract: In this paper, two modern adaptive signal processing techniques, empirical intrinsic geometry and synchrosqueezing transform, are applied to quantify different dynamical features of the respiratory and electroencephalographic signals. We show that the proposed features are theoretically rigorously supported, as well as capture the sleep information hidden inside the signals. The features are used as input to multiclass support vector machines with the radial basis function to automatically classify sleep stages. The effectiveness of the classification based on the proposed features is shown to be comparable to human expert classification—the proposed classification of awake, REM, N1, N2, and N3 sleeping stages based on the respiratory signal (resp. respiratory and EEG signals) has the overall accuracy $81.7\%$ (resp. $89.3\%$ ) in the relatively normal subject group. In addition, by examining the combination of the respiratory signal with the electroencephalographic signal, we conclude that the respiratory signal consists of ample sleep information, which supplements to the information stored in the electroencephalographic signal.

Time- and Frequency-Varying $K$ -Factor of Non-Stationary Vehicular Channels for Safety-Relevant Scenarios

Abstract: Vehicular communication channels are characterized by a non-stationary time- and frequency-selective fading process due to fast changes in the environment. We characterize the distribution of the envelope of the first delay bin in vehicle-to-vehicle channels by means of its Rician $K$ -factor. We analyze the time–frequency variability of this channel parameter using vehicular channel measurements at 5.6 GHz with a bandwidth of 240 MHz for safety-relevant scenarios in intelligent transportation systems (ITS) . This data enables a frequency-variability analysis from an IEEE 802.11p system point of view, which uses 10 MHz channels. We show that the small-scale fading of the envelope of the first delay bin is Rician distributed with a varying $K$ -factor. The later delay bins are Rayleigh distributed. We demonstrate that the $K$ -factor cannot be assumed to be constant in time and frequency. The causes of these variations are the frequency-varying antenna radiation patterns, as well as the time-varying number of active scatterers, and the effects of vegetation. We also present a simple but accurate bimodal Gaussian mixture model, which allows to capture the $K$ -factor variability in time for safety-relevant ITS scenarios.

GPR Signal Denoising and Target Extraction With the CEEMD Method

Abstract: In this letter, we apply a time and frequency analysis method based on the complete ensemble empirical mode decomposition (CEEMD) method in ground-penetrating radar (GPR) signal processing. It decomposes the GPR signal into a sum of oscillatory components, with guaranteed positive and smoothly varying instantaneous frequencies. The key idea of this method relies on averaging the modes obtained by empirical mode decomposition (EMD) applied to several realizations of Gaussian white noise added to the original signal. It can solve the mode-mixing problem in the EMD method and improve the resolution of ensemble EMD (EEMD) when the signal has a low signal-to-noise ratio. First, we analyze the difference between the basic theory of EMD, EEMD, and CEEMD. Then, we compare the time and frequency analysis with Hilbert–Huang transform to test the results of different methods. The synthetic and real GPR data demonstrate that CEEMD promises higher spectral–spatial resolution than the other two EMD methods in GPR signal denoising and target extraction. Its decomposition is complete, with a numerically negligible error.

New Pattern-Recognition Method for Fault Analysis in Transmission Line With UPFC

Abstract: In this paper, a new set of time-frequency features for fault-type identification, fault-loop status supervision, and fault-zone detection modules in a compensated transmission line with a unified power-flow controller is proposed. Some features are extracted from a one-cycle data window of one side of the compensated line, including 3/16 cycle of postfault data by the fast discrete orthonormal S-Transform (FDOST). The computation burden of the FDOST as a time–frequency decomposition is the same as the fast Fourier transform. The support vector machine is employed for classification of the ranked features by the Gram–Schmidt method. The graphical representations of extracted features and the obtained numerical results under different conditions confirm the efficacy of the proposed scheme.

Radon-fractional ambiguity function-based detection method of low-observable maneuvering target

Abstract: Based on the quadratic frequency modulated (FM) signal of a maneuvering target, a novel long-time coherent integration method, i.e., Radon-fractional ambiguity function (RFRAF), is proposed to compensate the range and Doppler migrations simultaneously. By the long-time instantaneous autocorrelation function and rotating the time-frequency plane, the observation values of a maneuvering target can be well matched and accumulated as a peak in the RFRAF domain. Results of experiments with simulated and real data prove its effectiveness.

Time–Frequency Filtering Based on Spectrogram Zeros

Abstract: For a proper choice of the analysis window, a short-time Fourier transform is known to be completely characterized by its zeros, which coincide with those of the associated spectrogram. A simplified representation of the time-frequency structure of a signal can therefore be given by the Delaunay triangulation attached to spectrogram zeros. In the case of multicomponent nonstationary signals embedded in white Gaussian noise, it turns out that each time–frequency domain attached to a given component can be viewed as the union of adjacent Delaunay triangles whose edge length is an outlier as compared to the distribution in noise-only regions. Identifying such domains offers a new way of disentangling the different components in the time–frequency plane, as well as of reconstructing the corresponding waveforms.

Component Extraction for Non-Stationary Multi-Component Signal Using Parameterized De-chirping and Band-Pass Filter

Abstract: In most applications, component extraction is important when components of non-stationary multi-component signal are key features to be monitored and analyzed. Existing methods are either sensitive to noise or forced to select a proper time-frequency representation for the considered signal. In this paper, we present a novel component extraction method for non-stationary multi-component signal. The proposed method combines parameterized de-chirping and band-pass filter to obtain components of multi-component signal, which avoids dealing with time-frequency representation of the signal and works well under heavy noise. In addition, it is able to analyze the multi-component signal whose components have intersected instantaneous frequency trajectories. Simulation results show that the proposed method is promising in analyzing complicated multi-component signals. Moreover, it works effective in a high noise environment in terms of improving the output signal-to-noise rate for the interested component.

Detection of constant radial acceleration weak target via IAR-FRFT

Abstract: A novel coherent integration algorithm, improved axis rotation fractional Fourier transform (IAR-FRFT), is proposed to detect the weak targets with a constant radial acceleration. IAR-FRFT could eliminate the linear range migration and alleviate the nonlinear range migration via an improved axis rotation transform and realize coherent integration via fractional Fourier transform. Numerical experiments verify the performance of IAR-FRFT on four aspects: coherent integration time, coherent integration gain, computational complexity, and multitarget detection.

IF estimation of FM signals based on time-frequency image

Abstract: This paper addresses the problem of estimating the instantaneous frequency (IF) of multicomponent radar signals, which are assumed to be frequency-modulated (FM). The difficulties lie in that different FM components which overlap in time-frequency (TF) domain have different time-supports, and their spectral contents may present continuous and stepped IF laws. We propose an IF estimation algorithm by exploiting the combination of TF distributions (TFDs) and image processing techniques. Numerical results are provided to demonstrate desirable capabilities of the proposed algorithm.

Optical Time–Frequency Packing: Principles, Design, Implementation, and Experimental Demonstration

Abstract: Time–frequency packing (TFP) transmission provides the highest achievable spectral efficiency with a constrained symbol alphabet and detector complexity. In this paper, the application of the TFP technique to fiber-optic systems is investigated and experimentally demonstrated. The main theoretical aspects, design guidelines, and implementation issues are discussed, focusing on those aspects which are peculiar to TFP systems. In particular, adaptive compensation of propagation impairments, matched filtering, and maximum a posteriori probability detection are obtained by a combination of a two-dimensional equalizer and four eight-state parallel Bahl–Cocke–Jelinek–Raviv (BCJR) detectors. A novel algorithm that ensures adaptive equalization, channel estimation, and a proper distribution of tasks between the equalizer and BCJR detectors is proposed. A set of irregular low-density parity-check codes with different rates is designed to operate at low error rates and approach the spectral efficiency limit achievable by TFP at different signal-to-noise ratios. An experimental demonstration of the designed system is finally provided with five dual-polarization QPSK-modulated optical carriers, densely packed in a 100-GHz bandwidth, employing a recirculating loop to test the performance of the system at different transmission distances.

Phase Estimation in Single Channel Speech Enhancement Using Phase Decomposition

Abstract: Conventional speech enhancement methods typically utilize the noisy phase spectrum for signal reconstruction. This letter presents a novel method to estimate the clean speech phase spectrum, given the noisy speech observation in single-channel speech enhancement. The proposed method relies on the phase decomposition of the instantaneous noisy phase spectrum followed by temporal smoothing in order to reduce the large variance of noisy phase, and consequently reconstructs an enhanced instantaneous phase spectrum for signal reconstruction. The effectiveness of the proposed method is evaluated in two ways: phase enhancement-only and by quantifying the additional improvement on top of the conventional amplitude enhancement scheme where noisy phase is often used in signal reconstruction. The instrumental metrics predict a consistent improvement in perceived speech quality and speech intelligibility when the noisy phase is enhanced using the proposed phase estimation method.

Time-frequency sparsity map on automatic partial discharge sources separation for power transformer condition assessment

Abstract: Partial discharge (PD) measurements can evaluate integrity of transformers’ insulation systems. Current research focuses on multiple PD sources separation to identify the types of insulation defects that may coexist in a transformer. This paper proposes a time-frequency (TF) sparsity map for revealing and separating different PD sources. TF sparsity map is developed based on decomposing signals into time and frequency domains at multiresolutions. Two decomposition methods, conventional wavelet transform-based signal decomposition and novel mathematical morphology (MM)-based signal decomposition are implemented in this paper. After sparsity values are calculated from the decomposed signals in time and frequency domains, sparsity trends are determined to provide unique representation of PD sources. By taking roughness of the trends, an accurate separation of multiple PD sources is obtained on a TF map. A density-based clustering is then evoked to form clusters related to different PD sources. The proposed method has been verified by signals acquired from multiple PD source models and substation transformers. Results show that an accurate representation of PD pulses in the presence of multiple PD sources and subsequently separation of PD sources can be achieved. Comparisons of wavelet transform and MM-based signal decomposition methods on TF sparsity maps construction and multiple PD sources separation are also provided.

Detection of stator incipient faults and identification of faulty phase in three-phase induction motor – simulation and experimental verification

Abstract: Motor current signature analysis is a well-known method for the diagnosis of stator incipient faults on a three-phase induction motor (IM). In classical motor current signature analysis the fault feature is extracted by analysing the frequency spectrum obtained from the Fourier analysis. However, for proper fault diagnosis, time–frequency domain analysis is required. This study proposes an algorithm based on wavelet analysis for detection of stator incipient faults and identification of faulty phase in three-phase IM. A turn level distributed parameter model of a 3-hp IM is considered for the simulation of inter-turn faults. The parameters used in the simulated model are calculated by conducting experiments on a 3-hp IM. This model is validated by comparing the frequency response of the simulated model with the frequency response measured on practical machine. The proposed algorithm uses an adaptive threshold-based logic for detecting the inter-turn faults and identifying the faulty phase. The algorithm is validated with data generated by the specially designed 3-hp IM. The experimental and simulation results show that the proposed algorithm is effective in detecting the inter-turn faults and identifying the faulty phase even in the presence of supply unbalance conditions.

Classification of micro-Doppler signatures of human motions using log-Gabor filters

Abstract: In recent years, Doppler radar has been used as a sensing modality for human gait recognition, due to its ability to operate in adverse weather and penetrate opaque obstacles. Doppler radar captures not only the speed of the target, but also the micro-motions of its moving parts. These micro-motions induce frequency modulations that can be used to characterise the target movements. However, a major challenge in Doppler signal processing is to extract discriminative features from the radar returns for target classification. This study presents a feature extraction method for classification of human motions from the micro-Doppler radar signal. The proposed method applies the log-Gabor filters at multiple spatial frequencies and orientations on a joint time–frequency representation. To achieve invariance to the target speed, features are extracted from local patches along the torso Doppler shift. Then, the (2D)2PCA (two-directional two-dimensional principal component analysis) method is applied to create a compact feature vector. Experimental results based on real radar data obtained from multiple human subjects demonstrate the effectiveness of the proposed approach in classifying arm motions.

Time-frequency relationship between share prices and exchange rates in India: Evidence from continuous wavelets

Abstract: The paper examines the relationship between exchange rates and share prices using the wavelets approach, and more specifically the continuous wavelet power spectrum, cross-wavelet transform, and cross-wavelet coherency. Our results, based on Indian data, lend support to the traditional (Am Econ Rev 70:960–971, 1980) as well as the new portfolio hypothesis (Am Econ Rev 83:1356–1369, 1993), albeit over different time periods and across different time scales. The wavelet approach used in the paper has helped to uncover some interesting economic relationships within the time–frequency domain which have remained hidden thus far.

Discretewavelet Transform: A Signal Processing Approach

Abstract: Provides easy learning and understanding of DWT from a signal processing point of view • Presents DWT from a digital signal processing point of view, in contrast to the usual mathematical approach, making it highly accessible • Offers a comprehensive coverage of related topics, including convolution and correlation, Fourier transform, FIR filter, orthogonal and biorthogonal filters • Organized systematically, starting from the fundamentals of signal processing to the more advanced topics of DWT and Discrete Wavelet Packet Transform. • Written in a clear and concise manner with abundant examples, figures and detailed explanations • Features a companion website that has several MATLAB programs for the implementation of the DWT with commonly used filters “This well-written textbook is an introduction to the theory of discrete wavelet transform (DWT) and its applications in digital signal and image processing.” -Prof. Dr. Manfred Tasche Institut für Mathematik, Uni Rostock