Showing papers on "Time–frequency analysis published in 2011"
TL;DR: This paper introduces a precise mathematical definition for a class of functions that can be viewed as a superposition of a reasonably small number of approximately harmonic components, and proves that the method does indeed succeed in decomposing arbitrary functions in this class.
1,704 citations
TL;DR: In this article, the authors extended the method of stationary spiking deconvolution of seismic data to the context of nonstationary signals in which the nonstationarity is due to attenuation processes.
Abstract: We have extended the method of stationary spiking deconvolution of seismic data to the context of nonstationary signals in which the nonstationarity is due to attenuation processes. As in the stationary case, we have assumed a statistically white reflectivity and a minimum-phase source and attenuation process. This extension is based on a nonstationary convolutional model, which we have developed and related to the stationary convolutional model. To facilitate our method, we have devised a simple numerical approach to calculate the discrete Gabor transform, or complex-valued time-frequency decomposition, of any signal. Although the Fourier transform renders stationary convolution into exact, multiplicative factors, the Gabor transform, or windowed Fourier transform, induces only an approximate factorization of the nonstationary convolutional model. This factorization serves as a guide to develop a smoothing process that, when applied to the Gabor transform of the nonstationary seismic trace, estimates the magnitude of the time-frequency attenuation function and the source wavelet. By assuming that both are minimum-phase processes, their phases can be determined. Gabor deconvolution is accomplished by spectral division in the time-frequency domain. The complex-valued Gabor transform of the seismic trace is divided by the complex-valued estimates of attenuation and source wavelet to estimate the Gabor transform of the reflectivity. An inverse Gabor transform recovers the time-domain reflectivity. The technique has applications to synthetic data and real data.
223 citations
TL;DR: An effective IF estimation algorithm is proposed based on the PCT, and the effectiveness of this algorithm is validated by applying it to estimate the IF of a signal with a nonlinear chirp component and seriously contaminated by a Gaussian noise and a vibration signal collected from a rotor test rig.
Abstract: In this paper, a new time-frequency analysis method known as the polynomial chirplet transform (PCT) is developed by extending the conventional chirplet transform (CT). By using a polynomial function instead of the linear chirp kernel in the CT, the PCT can produce a time-frequency distribution with excellent concentration for a wide range of signals with a continuous instantaneous frequency (IF). In addition, an effective IF estimation algorithm is proposed based on the PCT, and the effectiveness of this algorithm is validated by applying it to estimate the IF of a signal with a nonlinear chirp component and seriously contaminated by a Gaussian noise and a vibration signal collected from a rotor test rig.
218 citations
TL;DR: The distribution is demonstrated to be a CFCR representation that is computed without using any searching operation and to generate a new TF representation, called inverse LVD (ILVD), and a new ambiguity function, called Lv's ambiguity function (LVAF), both of which may break through the tradeoff between resolution and cross terms.
Abstract: This paper proposes a novel representation, known as Lv's distribution (LVD), of linear frequency modulated (LFM) signals. It has been well known that a monocomponent LFM signal can be uniquely determined by two important physical quantities, centroid frequency and chirp rate (CFCR). The basic reason for expressing a LFM signal in the CFCR domain is that these two quantities may not be apparent in the time or time-frequency (TF) domain. The goal of the LVD is to naturally and accurately represent a mono- or multicomponent LFM in the CFCR domain. The proposed LVD is simple and only requires a two-dimensional (2-D) Fourier transform of a parametric scaled symmetric instantaneous autocorrelation function. It can be easily implemented by using the complex multiplications and fast Fourier transforms (FFT) based on the scaling principle. The computational complexity, properties, detection performance and representation errors are analyzed for this new distribution. Comparisons with three other popular methods, Radon-Wigner transform (RWT), Radon-Ambiguity transform (RAT), and fractional Fourier transform (FRFT) are performed. With several numerical examples, our distribution is demonstrated to be a CFCR representation that is computed without using any searching operation. The main significance of the LVD is to convert a 1-D LFM into a 2-D single-frequency signal. One of the most important applications of the LVD is to generate a new TF representation, called inverse LVD (ILVD), and a new ambiguity function, called Lv's ambiguity function (LVAF), both of which may break through the tradeoff between resolution and cross terms.
191 citations
TL;DR: It is shown that wavelet transforms, constant-Q transforms and more general filter banks may be modeled in the framework of nonstationary Gabor frames and given the explicit formula for the canonical dual frame for a particular case, the painless case.
149 citations
TL;DR: The results indicate that the proposed probabilistic neural network-based feature selection approach is capable of efficiently eliminating nonessential features to improve the performance of classifiers, even in environments with noise interference.
Abstract: This paper proposes an optimal feature selection approach, namely, probabilistic neural network-based feature selection (PFS), for power-quality disturbances classification. The PFS combines a global optimization algorithm with an adaptive probabilistic neural network (APNN) to gradually remove redundant and irrelevant features in noisy environments. To validate the practicability of the features selected by the proposed PFS approach, we employed three common classifiers: multilayer perceptron, k-nearest neighbor and APNN. The results indicate that this PFS approach is capable of efficiently eliminating nonessential features to improve the performance of classifiers, even in environments with noise interference.
148 citations
TL;DR: In this article, the use of the continuous wavelet transform (CWT) in the study of power system low-frequency electromechanical oscillations (LFEOs) is addressed.
Abstract: This paper addresses the use of the continuous wavelet transform (CWT) in the study of power system low-frequency electromechanical oscillations (LFEOs). Based on a modified complex Morlet mother-wavelet function, an approach is proposed to exploit the relationship between system low-frequency oscillation features and the Morlet CWT of a system ringdown signal for detection of modal parameter changes as well as for modal frequency and damping computation. Also, several guidelines for selecting the center frequency and bandwidth parameters, the scaling factor and the translation factor, are proposed in order to provide reliable modal identification estimates. The efficiency of the proposed approach is confirmed by applying it to synthetic, simulated and measured signals.
137 citations
TL;DR: One of the novelties of this paper is the fact that the diagnosis is carried out via the identification not only of the traditional lower sideband harmonic but also of the upper side band harmonic and four additional fault-related components.
Abstract: In this paper, a new induction motor diagnosis methodology is proposed. The approach is based on obtaining a 2-D time-frequency plot representing the time-frequency evolution of the main components in an electrical machine transient current. The identification of characteristic patterns in the time-frequency plane caused by many of the fault-related components enables a reliable machine diagnosis. Unlike other continuous-wavelet-transform-based methods, this work uses frequency B-spline (FBS) wavelets. It is shown that these wavelets enable an efficient filtering in the region neighboring the main frequency, as well as enable a high level of detail in the time-frequency maps. As a consequence, the evolution of the most important current components is precisely traced. These characteristics make it easy to identify the patterns related to the fault components. The technique is applied to the experimental no-load start-up current of motors in a healthy state and with broken bars; the FBS capabilities are revealed. One of the novelties of this paper is the fact that the diagnosis is carried out via the identification not only of the traditional lower sideband harmonic but also of the upper sideband harmonic and four additional fault-related components.
135 citations
TL;DR: Time-frequency analysis of single pulse electrical stimulation can assist in delineation of the epileptogenic cortex using time-frequency single pulse-evoked fast ripples as a potential new marker.
Abstract: Epilepsy surgery depends on reliable pre-surgical markers of epileptogenic tissue. The current gold standard is the seizure onset zone in ictal, i.e. chronic, electrocorticography recordings. Single pulse electrical stimulation can evoke epileptic, spike-like responses in areas of seizure onset also recorded by electrocorticography. Recently, spontaneous pathological high-frequency oscillations (80–520 Hz) have been observed in the electrocorticogram that are related to epileptic spikes, but seem more specific for epileptogenic cortex. We wanted to see whether a quantitative electroencephalography analysis using time–frequency information including the higher frequency range could be applied to evoked responses by single pulse electrical stimulation, to enhance its specificity and clinical use. Electrocorticography data were recorded at a 2048-Hz sampling rate from 13 patients. Single pulse electrical stimulation (10 stimuli, 1 ms, 8 mA, 0.2 Hz) was performed stimulating pairs of adjacent electrodes. A time–frequency analysis based on Morlet wavelet transformation was performed in a [−1 s : 1 s] time interval around the stimulus and a frequency range of 10–520 Hz. Significant ( P = 0.05) changes in power spectra averaged for 10 epochs were computed, resulting in event-related spectral perturbation images. In these images, time–frequency analysis of single pulse-evoked responses, in the range of 10–80 Hz for spikes, 80–250 Hz for ripples and 250–520 Hz for fast ripples, were scored by two observers independently. Sensitivity, specificity and predictive value of time–frequency single pulse-evoked responses in the three frequency ranges were compared with seizure onset zone and post-surgical outcome. In all patients, evoked responses included spikes, ripples and fast ripples. For the seizure onset zone, the median sensitivity of time–frequency single pulse-evoked responses decreased from 100% for spikes to 67% for fast ripples and the median specificity increased from 17% for spikes to 79% for fast ripples. A median positive predictive value for the evoked responses in the seizure onset zone of 17% was found for spikes, 26% for ripples and 37% for fast ripples. Five out of seven patients with <50% of fast ripples removed by resection had a poor outcome. A wavelet transform-based time–frequency analysis of single pulse electrical stimulation reveals evoked responses in the frequency range of spikes, ripples and fast ripples. We demonstrate that time–frequency analysis of single pulse electrical stimulation can assist in delineation of the epileptogenic cortex using time–frequency single pulse-evoked fast ripples as a potential new marker.
* Abbreviations
: ERSP
: event-related spectral perturbation
PPV
: positive prediction value
SPES
: single pulse electrical stimulation
106 citations
TL;DR: The reassignment method is combined with the LPFT and the robust LPFT to improve the concentration of the signal representation in the time-frequency domain and has its superiority in obtaining improved SNRs, which can be supported by theoretical analysis and computer simulations.
97 citations
TL;DR: In this paper, an iterative generalized demodulation method is used as a preprocessing tool to separate signals into mono-components, so as to satisfy the requirements by energy separation algorithm.
TL;DR: An iterative method for the accurate estimation of amplitude and frequency modulations (AM-FM) in time-varying multi-component quasi-periodic signals such as voiced speech and suggests an adaptive algorithm for nonparametric estimation of AM-FM components in voiced speech.
Abstract: In this paper, we present an iterative method for the accurate estimation of amplitude and frequency modulations (AM-FM) in time-varying multi-component quasi-periodic signals such as voiced speech. Based on a deterministic plus noise representation of speech initially suggested by Laroche (“HNM: A simple, efficient harmonic plus noise model for speech,” Proc. WASPAA, Oct., 1993, pp. 169-172), and focusing on the deterministic representation, we reveal the properties of the model showing that such a representation is equivalent to a time-varying quasi-harmonic representation of voiced speech. Next, we show how this representation can be used for the estimation of amplitude and frequency modulations and provide the conditions under which such an estimation is valid. Finally, we suggest an adaptive algorithm for nonparametric estimation of AM-FM components in voiced speech. Based on the estimated amplitude and frequency components, a high-resolution time-frequency representation is obtained. The suggested approach was evaluated on synthetic AM-FM signals, while using the estimated AM-FM information, speech signal reconstruction was performed, resulting in a high signal-to-reconstruction error ratio (around 30 dB).
TL;DR: A new convolutional neural network architecture that includes the fast Fourier transform between two hidden layers to switch the signal analysis from the time domain to the frequency domain inside the network is presented.
TL;DR: This paper establishes the restricted isometry property for a Gabor system generated by n2 time–frequency shifts of a random window function in n dimensions by establishing the sth order restricted isometric constant of the associated n × n2 Gabor synthesis matrix is small.
Abstract: This paper establishes the restricted isometry property for a Gabor system generated by n2 time–frequency shifts of a random window function in n dimensions. The sth order restricted isometry constant of the associated n × n2 Gabor synthesis matrix is small provided that s ≤ cn2/3 / log2n. This bound provides a qualitative improvement over previous estimates, which achieve only quadratic scaling of the sparsity s with respect to n. The proof depends on an estimate for the expected supremum of a second-order chaos.
TL;DR: A new phase estimation method based on the Rihaczek distribution and Reduced Interference Rihaczen distribution belonging to Cohen's class is proposed which offers phase estimates with uniformly high time-frequency resolution which can be used for defining time and frequency dependent phase synchrony.
Abstract: Time-varying phase synchrony is an important bivariate measure that quantifies the dynamics between nonstationary signals and has been widely used in many applications including chaotic oscillators in physics and multichannel electroencephalography recordings in neuroscience. Current state-of-the-art in time-varying phase estimation uses either the Hilbert transform or the complex wavelet transform of the signals. Both of these methods have some major drawbacks such as the assumption that the signals are narrowband for the Hilbert transform and the nonuniform time-frequency resolution inherent to the wavelet analysis. In this paper, a new phase estimation method based on the Rihaczek distribution and Reduced Interference Rihaczek distribution belonging to Cohen's class is proposed. These distributions offer phase estimates with uniformly high time-frequency resolution which can be used for defining time and frequency dependent phase synchrony. Properties of the phase estimator and the corresponding phase synchrony measure are evaluated both analytically and through simulations showing the effectiveness of the new measures compared to existing methods.
19 Oct 2011
TL;DR: A scheme of non-intrusive load monitoring system is employed by extracting the significant and representative power signatures of voltage and current at utility service entry in identifying loads and analyzing the characteristics of loads, and then finds out the physical behavior of operation of loads to establish the model of loads.
Abstract: This paper proposes a concept of non-intrusive load monitoring system for smart meter to monitor the situation of loads In this study, the user can clearly know the power consumption of loads by observing the operation and time of use of loads, and then improve the habit of consumption to complete the goals of saving energy and reducing carbon This paper employs a scheme of non-intrusive load monitoring system by extracting the significant and representative power signatures of voltage and current at utility service entry in identifying loads and analyzing the characteristics of loads, and then finds out the physical behavior of operation of loads to establish the model of loads This paper uses short-time Fourier transform (STFT) and wavelet transform (WT) of time-frequency domain to analyze and compare different loads in the experiments In the experiments, the results reveal wavelet transform is better than STFT on transient analysis of loads Choice of power signatures affects the results of load recognition and computation time
TL;DR: Experiments show that mel-frequency cepstral coefficients features derived from the delta-phase spectrum can produce broadly similar performance to equivalent magnitude domain features for both voice activity detection and speaker recognition tasks.
Abstract: For several reasons, the Fourier phase domain is less favored than the magnitude domain in signal processing and modeling of speech. To correctly analyze the phase, several factors must be considered and compensated, including the effect of the step size, windowing function and other processing parameters. Building on a review of these factors, this paper investigates a spectral representation based on the Instantaneous Frequency Deviation, but in which the step size between processing frames is used in calculating phase changes, rather than the traditional single sample interval. Reflecting these longer intervals, the term delta-phase spectrum is used to distinguish this from instantaneous derivatives. Experiments show that mel-frequency cepstral coefficients features derived from the delta-phase spectrum (termed Mel-Frequency delta-phase features) can produce broadly similar performance to equivalent magnitude domain features for both voice activity detection and speaker recognition tasks. Further, it is shown that the fusion of the magnitude and phase representations yields performance benefits over either in isolation.
TL;DR: An algorithm based on Hilbert-Huang Transform (HHT) is developed to compute statistically significant time-frequency spectra of T MS-evoked EEG oscillations on a single trial basis and it is found that the HHT-based algorithm outperforms the WT-based one in detecting the time onset of TMS- Evoked oscillations in the classical EEG bands.
TL;DR: The actual data obtained from the practical power systems of Taiwan Power Company is employed to test the effectiveness of the developed noise-suppression method.
Abstract: The wavelet transform (WT) technique has been proposed for detecting and localizing a transient disturbance in power systems. The disturbance is detected by comparing the transformed signal with an empirically given threshold. However, as the signal under analysis contains noises, especially the white noise with flat spectrum, the threshold is difficult to give. Due to the nature of the flat spectrum, a filter cannot just get rid of the noise without removing the significant disturbance signals together. To enhance the WT technique in processing the noise-riding signals, this paper proposes a noise-suppression algorithm. The abilities of the WT in detecting and localizing the disturbances can hence be restored. Finally, this paper employed the actual data obtained from the practical power systems of Taiwan Power Company to test the effectiveness of the developed noise-suppression method.
TL;DR: An efficient method based on 2D signal processing techniques and fractional Fourier transform is presented to suppress interference terms of Wigner distribution and shows that it is more efficient than recent interference suppression techniques of comparable performance.
TL;DR: The polynomial-phase transform is used in radar, sonar, communications, and power systems fields, but this is the first time, to the best knowledge of the authors, that it has been applied to the diagnosis of induction motor faults.
Abstract: Transient motor current signature analysis is a recently developed technique for motor diagnostics using speed transients. The whole speed range is used to create a unique stamp of each fault harmonic in the time-frequency plane. This greatly increases diagnostic reliability when compared with nontransient analysis, which is based on the detection of fault harmonics at a single speed. But this added functionality comes at a price: well-established signal analysis tools used in the permanent regime, mainly the Fourier transform, cannot be applied to the nonstationary currents of a speed transient. In this paper, a new method is proposed to fill this gap. By applying a polynomial-phase transform to the transient current, a new, stationary signal is generated. This signal contains information regarding the fault components along the different regimes covered by the transient, and can be analyzed using the Fourier transform. The polynomial-phase transform is used in radar, sonar, communications, and power systems fields, but this is the first time, to the best knowledge of the authors, that it has been applied to the diagnosis of induction motor faults. Experimental results obtained with two different commercial motors with broken bars are presented to validate the proposed method.
TL;DR: The proposed instantaneous frequency estimator gives superior performance with respect to the state-of-the-art techniques for signals with non-linear instantaneous frequency.
TL;DR: Through this evaluation, the novel adaptation of wavelet thresholding is shown to produce superior reduction of ocular artifacts when compared to regression, principal component analysis, and ICA.
Abstract: The reduction of artifacts in neural data is a key element in improving analysis of brain recordings and the development of effective brain-computer interfaces. This complex problem becomes even more difficult as the number of channels in the neural recording is increased. Here, new techniques based on wavelet thresholding and independent component analysis (ICA) are developed for use in high-dimensional neural data. The wavelet technique uses a discrete wavelet transform with a Haar basis function to localize artifacts in both time and frequency before removing them with thresholding. Wavelet decomposition level is automatically selected based on the smoothness of artifactual wavelet approximation coefficients. The ICA method separates the signal into independent components, detects artifactual components by measuring the offset between the mean and median of each component, and then removing the correct number of components based on the aforementioned offset and the power of the reconstructed signal. A quantitative method for evaluating these techniques is also presented. Through this evaluation, the novel adaptation of wavelet thresholding is shown to produce superior reduction of ocular artifacts when compared to regression, principal component analysis, and ICA.
TL;DR: An open-source virtual instrument for time-frequency analysis is presented to show the correct practical implementation, and the performance, of a number of complex algorithms and of a practical criterion to select the proper algorithm for a given signal.
Abstract: This paper presents an open-source virtual instrument for time-frequency analysis. The purpose is to show the correct practical implementation, and the performance, of a number of complex algorithms and of a practical criterion (the concentration measure) to select the proper algorithm for a given signal. The virtual instrument provides efficient solutions for signals with a highly nonstationary instantaneous frequency. Despite variations of signal phase function, a high concentration can be achieved by a suitable choice of distribution form. The distribution can be chosen manually, or the instrument can perform optimal distribution selection. Namely, a procedure for the automated selection of optimal distribution order is provided. The concentration measure is employed as a selection criterion. A variety of options provides different comparisons for several distributions simultaneously. Efficiency of the proposed instrument is demonstrated on various examples. It is important to emphasize that an extensive and complex theory is implemented as a set of open-source algorithms. All the algorithms can be used “as is” or modified and upgraded (even separately) by researchers and practitioners in the field. The virtual instrument is available at http://www.tfsa.ac.me/Open_source_codes.html,, or upon request to the authors.
TL;DR: Three methods for separating oscillations from transients are compared: finite impulse response (FIR) filtering, wavelet analysis with stationary wavelet transform (SWT), time-frequency sparse decomposition with Matching Pursuit (MP).
TL;DR: A novel signal transform, called a moving band chirp Z-transform, is introduced in order to allow the entire azimuth aperture to be focused simultaneously without any need for temporary unaliasing, which requires upsampling, or subaperture processing.
Abstract: The main operational mode of the European Space Agency's upcoming Sentinel-1 operational satellite will be the Terrain Observation by Progressive Scans (TOPS) imaging mode. This paper presents a very efficient wavenumber domain processor for the processing of TOPS mode data. In particular, a novel signal transform, called a moving band chirp Z-transform, is introduced in order to allow the entire azimuth aperture to be focused simultaneously without any need for temporary unaliasing, which requires upsampling, or subaperture processing.
TL;DR: This paper develops a joint time-frequency approach for appliance event detection based on the time varying power signals obtained from the measured aggregated current and voltage waveforms and demonstrates the superior performance of the proposed algorithm compared to the conventional generalized likelihood ratio detector.
Abstract: Non-intrusive load monitoring is an emerging signal processing and analysis technology that aims to identify individual appliance in residential or commercial buildings or to diagnose shipboard electro-mechanical systems through continuous monitoring of the change of On and Off status of various loads. In this paper, we develop a joint time-frequency approach for appliance event detection based on the time varying power signals obtained from the measured aggregated current and voltage waveforms. The short-time Fourier transform is performed to obtain the spectral components of the non-stationary aggregated power signals of appliances. The proposed event detector utilizes a goodness-of-fit Chi-squared test for detecting load activities using the calculated average power followed by a change point detector for estimating the change point of the transient signals using the first harmonic component of the power signals. Unlike the conventional detectors such as the generalized likelihood ratio test, the proposed event detector allows a closed form calculation of the decision threshold and provides a guideline for choosing the size of the detection data window, thus eliminating the need for extensive training for determining the detection threshold while providing robust detection performance against dynamic load activities. Using the real-world power data collected in two residential building testbeds, we demonstrate the superior performance of the proposed algorithm compared to the conventional generalized likelihood ratio detector.
TL;DR: A new local polynomial modeling method for identification of time-varying autoregressive (TVAR) models and applies it to time-frequency analysis (TFA) of event-related electroencephalogram (ER-EEG).
Abstract: This paper proposes a new local polynomial modeling (LPM) method for identification of time-varying autoregressive (TVAR) models and applies it to time-frequency analysis (TFA) of event-related electroencephalogram (ER-EEG). The LPM method models the TVAR coefficients locally by polynomials and estimates the polynomial coefficients using weighted least-squares with a window having a certain bandwidth. A data-driven variable bandwidth selection method is developed to determine the optimal bandwidth that minimizes the mean squared error. The resultant time-varying power spectral density estimation of the signal is capable of achieving both high time resolution and high frequency resolution in the time-frequency domain, making it a powerful TFA technique for nonstationary biomedical signals like ER-EEG. Experimental results on synthesized signals and real EEG data show that the LPM method can achieve a more accurate and complete time-frequency representation of the signal.
TL;DR: Simulation results show that this algorithm is capable of estimating parameters of multicomponent chirp signals even in the presence of strong intended interference and colored noise.
Abstract: A novel algorithm for parameter estimation of multicomponent chirp signals in complicated noise environment is proposed. By the matching pursuit (MP) algorithm, the signal is decomposed into Gabor atoms which provide sparse information that represents the signal time-frequency signature. The Hough transform (HT) is then directly used to estimate the parameter of chirp components without computing the time-frequency distribution. Simulation results show that this algorithm is capable of estimating parameters of multicomponent chirp signals even in the presence of strong intended interference and colored noise.
TL;DR: A series of desirable properties for the linear transform used in a multichannel source separation scenario: stationary invertibility, relative delay, relative attenuation, and finally delay invariant relative windowed-disjoint orthogonality (DIRWDO).
Abstract: This paper proposes the use of a synchronized linear transform, the synchronized short-time-Fourier-transform (sSTFT), for time-frequency analysis of anechoic mixtures. We address the short comings of the commonly used time-frequency linear transform in multichannel settings, namely the classical short-time-Fourier-transform (cSTFT). We propose a series of desirable properties for the linear transform used in a multichannel source separation scenario: stationary invertibility, relative delay, relative attenuation, and finally delay invariant relative windowed-disjoint orthogonality (DIRWDO). Multisensor source separation techniques which operate in the time-frequency domain, have an inherent error unless consideration is given to the multichannel properties proposed in this paper. The sSTFT preserves these relationships for multichannel data. The crucial innovation of the sSTFT is to locally synchronize the analysis to the observations as opposed to a global clock. Improvement in separation performance can be achieved because assumed properties of the time-frequency transform are satisfied when it is appropriately synchronized. Numerical experiments show the sSTFT improves instantaneous subsample relative parameter estimation in low noise conditions and achieves good synthesis.