Showing papers on "Time–frequency analysis published in 2010"

Empirical Mode Decomposition for Trivariate Signals

Abstract: An extension of empirical mode decomposition (EMD) is proposed in order to make it suitable for operation on trivariate signals. Estimation of local mean envelope of the input signal, a critical step in EMD, is performed by taking projections along multiple directions in three-dimensional spaces using the rotation property of quaternions. The proposed algorithm thus extracts rotating components embedded within the signal and performs accurate time-frequency analysis, via the Hilbert-Huang transform. Simulations on synthetic trivariate point processes and real-world three-dimensional signals support the analysis.

Time-Frequency Energy Distributions Meet Compressed Sensing

Abstract: In the case of multicomponent signals with amplitude and frequency modulations, the idealized representation which consists of weighted trajectories on the time-frequency (TF) plane, is intrinsically sparse. Recent advances in optimal recovery from sparsity constraints thus suggest to revisit the issue of TF localization by exploiting sparsity, as adapted to the specific context of (quadratic) TF distributions. Based on classical results in TF analysis, it is argued that the relevant information is mostly concentrated in a restricted subset of Fourier coefficients of the Wigner-Ville distribution neighboring the origin of the ambiguity plane. Using this incomplete information as the primary constraint, the desired distribution follows as the minimum -norm solution in the transformed TF domain. Possibilities and limitations of the approach are demonstrated via controlled numerical experiments, its performance is assessed in various configurations and the results are compared with standard techniques. It is shown that improved representations can be obtained, though at a computational cost which is significantly increased.

Time-Frequency Analysis of Power-Quality Disturbances via the Gabor–Wigner Transform

Abstract: Recently, many signal-processing techniques, such as fast Fourier transform, short-time Fourier transform, wavelet transform (WT), and wavelet packet transform (WPT), have been applied to detect, identify, and classify power-quality (PQ) disturbances. For research on PQ analysis, it is critical to apply the appropriate signal-processing techniques to solve PQ problems. In this paper, a new time-frequency analysis method, namely, the Gabor-Wigner transform (GWT), is introduced and applied to detect and identify PQ disturbances. Since GWT is an operational combination of the Gabor transform (GT) and the Wigner distribution function (WDF), it can overcome the disadvantages of both. GWT has two advantages which are that it has fewer cross-term problems than the WDF and higher clarity than the GT. Studies are presented which verify that the merits of GWT make it adequate for PQ analysis. In the case studies considered here, the various PQ disturbances, including voltage swell, voltage sag, harmonics, interharmonics, transients, voltage changes with multiple frequencies and voltage fluctuation, or flicker, will be thoroughly investigated by using this new time-frequency analysis method.

Separation of overlapping linear frequency modulated (LFM) signals using the fractional fourier transform

Abstract: Linear frequency modulated (LFM) excitation combined with pulse compression provides an increase in SNR at the receiver. LFM signals are of longer duration than pulsed signals of the same bandwidth; consequently, in many practical situations, maintaining temporal separation between echoes is not possible. Where analysis is performed on individual LFM signals, a separation technique is required. Time windowing is unable to separate signals overlapping in time. Frequency domain filtering is unable to separate signals with overlapping spectra. This paper describes a method to separate time-overlapping LFM signals through the application of the fractional Fourier transform (FrFT), a transform operating in both time and frequency domains. A short introduction to the FrFT and its operation and calculation are presented. The proposed signal separation method is illustrated by application to a simulated ultrasound signal, created by the summation of multiple time-overlapping LFM signals and the component signals recovered with ±0.6% spectral error. The results of an experimental investigation are presented in which the proposed separation method is applied to time-overlapping LFM signals created by the transmission of a LFM signal through a stainless steel plate and water-filled pipe.

Time-Frequency Representation Based on an Adaptive Short-Time Fourier Transform

Abstract: In this paper, a new concise algorithm about time-frequency representation (TFR) based on an adaptive short-time Fourier transform (ASTFT) is presented. In this algorithm, the analysis window width is equal to the local stationary length which is measured by the instantaneous frequency gradient (IFG) of the signal. And the instantaneous frequency (IF) of the signal is obtained by detecting the ridge of wavelet transform (WT). The ASTFT provides much better performance than conventional TFR algorithms. Furthermore, the algorithm is simpler and more computational efficient than some of other adaptive TFR algorithms proposed previously. Several examples are presented to illustrate its behavior on different kinds of signals and demonstrate its validity.

Micro-Doppler Effect Analysis and Feature Extraction in ISAR Imaging With Stepped-Frequency Chirp Signals

Abstract: The micro-Doppler (m-D) effect induced by the rotating parts or vibrations of the target provides a new approach for target recognition. To obtain high range resolution for the extraction of the fine m-D signatures of an inverse synthetic aperture radar target, the stepped-frequency chirp signal (SFCS) is used to synthesize the ultrabroad bandwidth and reduce the requirement of sample rates. In this paper, the m-D effect in SFCS is analyzed. The analytical expressions of the m-D signatures, which are extracted by an improved Hough transform method associated with time-frequency analysis, are deduced on the range-slow-time plane. The implementation of the algorithm is presented, particularly in those extreme cases of rotating (vibrating) frequencies and radii. The simulations validate the theoretical formulation and robustness of the proposed m-D extraction method.

Diagnosis of Induction Motor Faults in the Fractional Fourier Domain

Abstract: Motor current signature analysis (MCSA) is a well-established method for the diagnosis of induction motor faults. It is based on the analysis of the spectral content of a motor current, which is sampled while a motor runs in steady state, to detect the harmonic components that characterize each type of fault. The Fourier transform (FT) plays a prominent role as a tool for identifying these spectral components. Recently, MCSA has also been applied during the transient regime (TMCSA) using the whole transient speed range to create a unique stamp of each harmonic as it evolves in the time-frequency plane. This method greatly enhances the reliability of the diagnostic process compared with the traditional method, which relies on spectral analysis at a single speed. However, the FT cannot be used in this case because the fault harmonics are not stationary signals. This paper proposes the use of the fractional FT (FrFT) instead of the FT to perform TMCSA. This paper also proposes the optimization of the FrFT to generate a spectrum where the frequency-varying fault harmonics appear as single spectral lines and, therefore, facilitate the diagnostic process. A discrete wavelet transform (DWT) is used as a conditioning tool to filter the motor current prior to its processing by the FrFT. Experimental results that are obtained with a 1.1-kW three-phase squirrel-cage induction motor with broken bars are presented to validate the proposed method.

Time–Frequency Sparsity by Removing Perceptually Irrelevant Components Using a Simple Model of Simultaneous Masking

Abstract: We present an algorithm for removing time-frequency components, found by a standard Gabor transform, of a ldquoreal-worldrdquo sound while causing no audible difference to the original sound after resynthesis. Thus, this representation is made sparser. The selection of removable components is based on a simple model of simultaneous masking in the auditory system. Important goals were the applicability to any real-world music and speech sound, integrating mutual masking effects between time-frequency components, coping with the time-frequency spread of such an operation, and computational efficiency. The proposed algorithm first determines an estimation of the masked threshold within an analysis window. The masked threshold function is then shifted in level by an amount determined experimentally, and all components falling below this function (the irrelevance threshold) are removed. This shift gives a conservative way to deal with uncertainty effects resulting from removing time-frequency components and with inaccuracies in the masking model. The removal of components is described as an adaptive Gabor multiplier. Thirty-six normal hearing subjects participated in an experiment to determine the maximum shift value for which they could not discriminate the irrelevance filtered signal from the original signal. On average across the test stimuli, 32 percent of the time-frequency components fell below the irrelevance threshold.

Selection of Dynamic Features Based on Time–Frequency Representations for Heart Murmur Detection from Phonocardiographic Signals

Abstract: This work discusses a method for the selection of dynamic features, based on the calculation of the spectral power through time applied to the detection of systolic murmurs from phonocardiographic recordings. To investigate the dynamic properties of the spectral power during murmurs, several quadratic energy distributions have been studied, namely Wigner-Ville, Choi-Williams, smoothed pseudo Wigner-Ville, exponential, and hyperbolic T-distribution. The classification performance has been compared with that using a Short Time Fourier Transform and Continuous Wavelet Transform representations. Furthermore, this work discusses a variety of nonparametric techniques to estimate the spectral power contours as dynamic features that characterize the heart sounds (HS): instantaneous energy, eigenvectors, instantaneous frequency, equivalent bandwidth, subband spectral centroids, and Mel cepstral coefficients. In this way, the aforementioned time-frequency representations and their dynamic features were evaluated by means of their ability to detect the presence of murmurs using a simple k-Nearest Neighbors classifier. Moreover, the relevancies of the proposed dynamic features have been evaluated using a time-varying principal component analysis. The work presented is carried out using a database containing 22 phonocardiographic recordings (16 normal and 6 records with murmurs), segmented to extract 402 representative individual beats (201 per class). The results suggest that the smoothing given by the quadratic energy distribution significantly improves the classification performance for the detection of murmurs in HS. Moreover, it is shown that the power dynamic features which give the best overall classification performance are the MFCC contours. As a result, the proposed method can be implemented as a simple diagnostic tool for primary health-care purposes with high accuracy (up to 98%) discriminating between normal and pathologic beats.

Classification of Sleep Stages Using Multi-wavelet Time Frequency Entropy and LDA

Abstract: Background: The process of automatic sleep stage scoring consists of two major parts: feature extraction and classification. Features are normally extracted from the polysomnographic recordings, mainly electroencephalograph (EEG) signals. The EEG is considered a non-stationary signal which increases the complexity of the detection of different waves in it. Objectives: This work presents a new technique for automatic sleep stage scoring based on employing continuous wavelet transform (CWT) and linear discriminant analysis (LDA) using different mother wavelets to detect different waves embedded in the EEG signal. Methods: The use of different mother wavelets increases the ability to detect waves in the EEG signal. The extracted features were formed based on CWT time frequency entropy using three mother wavelets, and the classification was performed using the linear discriminant analysis. Thirty-two data sets from the MIT-BIH database were used to evaluate the performance of the proposed method. Results: Features of a single EEG signal were extracted successfully based on the time frequency entropy using the continuous wavelet transform with three mother wavelets. The proposed method has shown to outperform the classification based on a CWT using a single mother wavelet. The accuracy was found to be 0.84, while the kappa coefficient was 0.78. Conclusions: This work has shown that wavelet time frequency entropy provides a powerful tool for feature extraction for the non-stationary EEG signal; the accuracy of the classification procedure improved when using multiple wavelets compared to the use of single wavelet time frequency entropy.

Sparsity in Time-Frequency Representations

Abstract: We consider signals and operators in finite dimension which have sparse time-frequency representations As main result we show that an S-sparse Gabor representation in ℂ n with respect to a random unimodular window can be recovered by Basis Pursuit with high probability provided that S≤Cn/log (n) Our results are applicable to the channel estimation problem in wireless communications and they establish the usefulness of a class of measurement matrices for compressive sensing

Bivariate Instantaneous Frequency and Bandwidth

Abstract: The generalizations of instantaneous frequency and instantaneous bandwidth to a bivariate signal are derived. These are uniquely defined whether the signal is represented as a pair of real-valued signals or as one analytic and one anti-analytic signal. A nonstationary but oscillatory bivariate signal has a natural representation as an ellipse whose properties evolve in time, and this representation provides a simple geometric interpretation for the bivariate instantaneous moments. The bivariate bandwidth is shown to consist of three terms measuring the degree of instability of the time-varying ellipse: amplitude modulation with fixed eccentricity, eccentricity modulation, and orientation modulation or precession. An application to the analysis of data from a free-drifting oceanographic float is presented and discussed.

Multiwindow S-method for instantaneous frequency estimation and its application in radar signal analysis

Abstract: A new distribution that provides high concentration in the time-frequency domain is proposed. It is based on the S-method and multiwindow approach, where different order Hermite functions are employed as multiple windows. The resulting distribution will be referred to as the multiwindow S-method. It preserves favourable properties of the standard S-method, whereas the distribution concentration is improved by using Hermite functions of just a few first orders. The proposed distribution is appropriate for radar signal analysis, as it will be proven by experimental examples.

The approach to carrier scheme convergence based on 4-weighted fractional fourier transform

Abstract: We propose a new variant of a block transmission based on 4-Weighted Fractional Fourier Transform (4-WFRFT), which contains a compatible process of single-carrier (SC) and multi-carrier (MC) modulation. The 4-WFRFT system has an even and symmetrical bit energy distribution on the timefrequency plane that it could achieve a better performance than or equal to those of SC and MC systems in selective fading channels. The approach of 4-WFRFT may facilitate unification of the two competitive carrier schemes, and improve the distortion resistance capability of communication system.

Null Space Pursuit: An Operator-based Approach to Adaptive Signal Separation

Abstract: The operator-based signal separation approach uses an adaptive operator to separate a signal into additive subcomponents. The approach can be formulated as an optimization problem whose optimal solution can be derived analytically. However, the following issues must still be resolved: estimating the robustness of the operator's parameters and the Lagrangian multipliers, and determining how much of the information in the null space of the operator should be retained in the residual signal. To address these problems, we propose a novel optimization formula for operator-based signal separation and show that the parameters of the problem can be estimated adaptively. We demonstrate the effectiveness of the proposed method by processing several signals, including real-life signals.

Searching for autocoherence in the cortical network with a time-frequency analysis of the local field potential.

Abstract: Gamma-band peaks in the power spectrum of local field potentials (LFP) are found in multiple brain regions. It has been theorized that gamma oscillations may serve as a 'clock' signal for the purposes of precise temporal encoding of information and 'binding' of stimulus features across regions of the brain. Neurons in model networks may exhibit periodic spike firing or synchronized membrane potentials that give rise to a gamma-band oscillation that could operate as a 'clock'. The phase of the oscillation in such models is conserved over the length of the stimulus. We define these types of oscillations to be 'autocoherent'. We investigated the hypothesis that autocoherent oscillations are the basis of the experimentally observed gamma-band peaks: the autocoherent oscillator (ACO) hypothesis. To test the ACO hypothesis, we developed a new technique to analyze the autocoherence of a time-varying signal. This analysis used the continuous Gabor transform to examine the time evolution of the phase of each frequency component in the power spectrum. Using this analysis method, we formulated a statistical test to compare the ACO hypothesis with measurements of the LFP in macaque primary visual cortex, V1. The experimental data were not consistent with the ACO hypothesis. Gamma-band activity recorded in V1 did not have the properties of a 'clock' signal during visual stimulation. We propose instead that the source of the gamma-band spectral peak is the resonant V1 network driven by random inputs.

Generalized Sampling Expansion for Bandlimited Signals Associated With the Fractional Fourier Transform

Abstract: The aim of the generalized sampling expansion (GSE) is the reconstruction of an unknown continuously defined function f(t), from the samples of the responses of M linear time invariant (LTI) systems, each sampled by the 1/M th Nyquist rate. In this letter, we investigate the GSE in the fractional Fourier transform (FRFT) domain. Firstly, the GSE for fractional bandlimited signals with FRFT is proposed based on new linear fractional systems, which is the generalization of classical generalized Papoulis sampling expansion. Then, by designing fractional Fourier filters, we obtain reconstruction method for sampling from the signal and its derivative based on the derived GSE and the property of FRFT. Last, the potential application of the GSE is presented to show the advantage of the theory.

ICI Analysis for FRFT-OFDM Systems to Frequency Offset in Time-Frequency Selective Fading Channels

Abstract: This letter presents the effects of frequency offset to orthogonal frequency division multiplexing systems based on fractional Fourier transform (FRFT-OFDM) in time-frequency selective fading channels. FRFT-OFDM systems generalize the OFDM systems based on discrete Fourier transform by the deployment of FRFT. The expressions of signal-to-interference ratio (SIR) due to ICI are derived in different fading channels. In a flat channel, the performances of both systems are the same. In a frequency selective channel, the FRFT-OFDM systems have superior SIR performances by choosing the optimal fractional factor, when Doppler spread is comparable to the inverse of the symbol duration or carrier offset exists in the system.

On the structure of Gabor and super Gabor spaces

Abstract: We study the structure of Gabor and super Gabor spaces inside \({L^{2}(\mathbb{R}^{2d})}\) and specialize the results to the case where the spaces are generated by vectors of Hermite functions. We then construct an isometric isomorphism between such spaces and Fock spaces of polyanalytic functions and use it in order to obtain structure theorems and orthogonal projections for both spaces at once, including explicit formulas for the reproducing kernels. In particular we recover a structure result obtained by N. Vasilevski using complex analysis and special functions. In contrast, our methods use only time-frequency analysis, exploring a link between time-frequency analysis and the theory of polyanalytic functions, provided by the polyanalytic part of the Gabor transform with a Hermite window, the polyanalytic Bargmann transform.

Bearing fault detection and diagnosis based on order tracking and Teager-Huang transform

Abstract: The vibration signal of the run-up or run-down process is more complex than that of the stationary process. A novel approach to fault diagnosis of roller bearing under run-up condition based on order tracking and Teager-Huang transform (THT) is presented. This method is based on order tracking, empirical mode decomposition (EMD) and Teager Kaiser energy operator (TKEO) technique. The nonstationary vibration signals are transformed from the time domain transient signal to angle domain stationary one using order tracking. EMD can adaptively decompose the vibration signal into a series of zero mean amplitude modulation-frequency modulation (AM-FM) intrinsic mode functions (IMFs). TKEO can track the instantaneous amplitude and instantaneous frequency of the AM-FM component at any instant. Experimental examples are conducted to evaluate the effectiveness of the proposed approach. The experimental results provide strong evidence that the performance of the Teager-Huang transform approach is better to that of the Hilbert-Huang transform approach for bearing fault detection and diagnosis. The Teager-Huang transform has better resolution than that of Hilbert-Huang transform. Teager-Huang transform can effectively diagnose the faults of the bearing, thus providing a viable processing tool for gearbox defect monitoring.

Modeling and Identification of Nonlinear Systems in the Short-Time Fourier Transform Domain

Abstract: In this paper, we introduce a novel approach for improved nonlinear system identification in the short-time Fourier transform (STFT) domain. We first derive explicit representations of discrete-time Volterra filters in the STFT domain. Based on these representations, approximate nonlinear STFT models, which consist of parallel combinations of linear and nonlinear components, are developed. The linear components are represented by cross-band filters between subbands, while the nonlinear components are modeled by multiplicative cross-terms. We consider the identification of quadratically nonlinear systems and show that a significant reduction in computational cost as well as substantial improvement in estimation accuracy can be achieved over a time-domain Volterra model, particularly when long-memory systems are considered. Experimental results validate the theoretical derivations and demonstrate the effectiveness of the proposed approach.

Wavelet transform theory and its application in EMG signal processing

Abstract: Wavelet analysis is often very effective because it provides a simple approach for dealing with local aspects of a signal. The electromyogram (EMG) signals arising from muscle activities have become a useful tool for clinical diagnosis, rehabilitation medicine and sport medicine. In this paper, a time-frequency analysis based on the wavelet transform of the EMG signals is presented with a focus on 2 areas: de-noising and feature extraction.

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.

Time-frequency analysis of acoustic signals in the audio-frequency range generated during Hadfield’s steel friction

Abstract: Time-frequency analysis of sound waves detected by a microphone during the friction of Hadfield’s steel has been performed using wavelet transform and window Fourier transform methods. This approach reveals a relationship between the appearance of quasi-periodic intensity outbursts in the acoustic response signals and the processes responsible for the formation of wear products. It is shown that the time-frequency analysis of acoustic emission in a tribosystem can be applied, along with traditional approaches, to studying features in the wear and friction process.

Scaled Radon-Wigner Transform Imaging and Scaling of Maneuvering Target

Abstract: The use of scaled Radon-Wigner transform (RWT) imaging and simultaneous cross-range scaling is proposed for a maneuvering target using a signal model of a rotating target with uniform acceleration Three steps are needed to realize such a process First, the rotational parameters are calculated via the weighted linear least squares method after obtaining frequency modulation parameters of signals in multirange cells Second, rotational parameters are used to compensate for the slow-time signals Third, inverse synthetic aperture radar imaging of scaled RWT is implemented with cross-range scaling Parameter substitution changes every component signal from a slanting line to a horizontal line in the time-frequency plane, and the horizontal line integral can be expressed as a cross-range profile Compared with conventional RWT imaging methods, this algorithm improves calculation speed greatly and provides more stable imaging performance This method was tested successfully with simulated and experimental radar data

Estimation of micro-motion parameters based on micro-Doppler

Abstract: Micro-Doppler has played an important role in describing the micro-motion of a radar target. After analysing the characteristics of micro-Doppler induced by typical micro-motions, a technique based on time-frequency transform and Hough transform is introduced, to extract the modes and estimate the parameters of multiple frequency modulation components in micro-Doppler simultaneously, which can describe the properties of radial micro-motion. Experiments show the performance of estimation algorithm with simulating radar data.

Feature extraction of EEG signals from epilepsy patients based on Gabor Transform and EMD Decomposition

Abstract: Electroencephalograph (EEG) has been considered as a practical media to explore human brain activities It is believed that EEG signals have lots of information carried still unknown The non-stationary, non-linear traits of EEG signals make the information detection a hard task While time-frequency methods, for their superiority to process such data, were widely studied and applied to this research EEG information detection is very important during the diagnostics process of epilepsy diseases, because doctors detect abnormal brain activities mainly with their experiences on EEG signals and such subjective method is not so reliable Here, we try a time-frequency method (Gabor Transform) on EEG signals The results of Gabor Transform display good performance on both time and frequency scales The Frequency Band Relative Intensity Ratio (FBRIR) can clearly differentiate the epilepsy periods including interictal, preictal and ictal Empirical Mode Decomposition (EMD) is also used to extract patterns from the original EEG signals It shows that EMD can be a valuable practical method for such tasks The results of the two methods can provide doctors with clinical guidelines