Showing papers on "Time–frequency analysis published in 2008"

Micro-Doppler-based target detection and feature extraction in indoor and outdoor environments

Abstract: In many cases, a target or a structure on a target may have micro-motions, such as vibrations or rotations. Micro-motions of structures on a target may introduce frequency modulation on the returned radar signal and generate sidebands on the Doppler frequency shift of the target's body. The modulation due to micro-motion is called the micro-Doppler (m-D) phenomenon. In this paper, we present an effective quadratic time–frequency S-method-based approach in conjunction with the Viterbi algorithm to extract m-D features. For target recognition applications, mainly those in military surveillance and reconnaissance operations, m-D features have to be extracted quickly so that they can be used for real-time target identification. The S-method is computationally simple, requiring only slight modifications to the existing Fourier transform-based algorithm. The effectiveness of the S-method in extracting m-D features is demonstrated through the application to indoor and outdoor experimental data sets such as rotating fan and human gait. The Viterbi algorithm for the instantaneous frequency estimation is used to enhance the weak human m-D features in relatively high noise environments. As such, this paper contributes additional experimental m-D data and analysis, which should help in developing a better picture of the human gait m-D research and its applications to indoor and outdoor imaging and automatic gait recognition systems.

Frequency-based window width optimization for S-transform

Abstract: The S-transform combines properties of the short-time Fourier (STFT) and wavelet transforms. It preserves the phase information of a signal as in the STFT, while providing the variable resolution as in the wavelet transform. However, the S-transform suffers from poor energy concentration for some classes of signals. A modification to the existing S-transform is proposed in this paper to enhance the energy concentration in the time–frequency domain. An improvement is achieved by introducing an additional parameter which can be used to optimize the window width. The optimization is performed over frequency and the proposed modification keeps the frequency marginal of the S-transform. The proposed scheme is tested on a set of synthetic signals. The results show that the proposed algorithm produces enhanced energy concentration in comparison to the standard S-transform. Also, the results show that for various signal types the proposed algorithm achieves higher signal concentration in comparison to other standard time–frequency transforms, such as, STFT and pseudo Wigner–Ville distribution (PWVD). Furthermore, it is concluded by numerical study that the proposed algorithm provides more accurate estimation of the instantaneous frequency than the standard S-transform. 2007 Elsevier GmbH. All rights reserved.

Ultrasonic guided-waves characterization with Warped Frequency Transforms

Abstract: Guided wave (GW) dispersion curves can be extracted from a time-transient measurement by means of time-frequency representations (TFRs). Unfortunately, any TFR is subject to the time-frequency uncertainty principle. This, in general, limits the capability of TFRs to characterize closely spaced guided modes over a wide frequency range. To overcome this limitation, we implemented a new warped frequency transform that presents enhanced mode extraction capabilities because of a more flexible tiling of the time-frequency domain. The tiling is designed to match the dispersive spectro-temporal structure of a GW by selecting an appropriate map of the time-frequency plane. The proposed transformation is fast, invertible, and covariant to group delay shifts. An application to Lamb waves propagating in an aluminum plate is presented. Time-transient GWs propagation events obtained both numerically and experimentally are considered. The results show that the proposed warped frequency transform limits the interference patterns which appear with other TFRs and produces a sparse representation of the Lamb wave pattern that can be suitable for identification and characterization purposes.

Fractional Power Spectrum

Abstract: In this paper, by investigating the definitions of the fractional power spectrum and the fractional correlation for the deterministic process, we consider the case associated with the random process in an explicit manner. The fractional power spectral relations for the fractional Fourier domain filter are derived, and the expression for the fractional power spectrum in terms of the fractional correlation is obtained. In addition, the definitions and the properties of the fractional white noise and the chirp-stationary process are presented. Simulation results verify the theoretical derivations and demonstrate the potential applications, such as detection and parameter estimation of chirp signals, fractional power spectral estimation and system identification in the fractional Fourier domain.

Numerical implementation of matching pursuit for the analysis of complex ultrasonic signals

Abstract: Matching pursuit has typically been applied to ultrasonic signal analysis for the purpose of identifying or estimating discrete echoes. In this paper, a specific numerical implementation of matching pursuit designed for ultrasonic signal decomposition is proposed, consisting of the selection of a coarse set of basis functions, the search method for finding the best matching basis function, and interpolation of the basis function parameters to achieve high resolution. In addition, the use of matching pursuit is applied to the analysis of complex ultrasonic signals by interpreting the matching basis functions as characteristic wavelets. Changes in parameters of these wavelets are related to changes in the structure. The efficiency of the numerical implementation method is evaluated, and the capability of the feature extraction method for complex ultrasonic signals is demonstrated on experimental data from an aluminum plate in the context of structural health monitoring.

Parameter Estimation for Locally Linear FM Signals Using a Time-Frequency Hough Transform

Abstract: An estimator for the phase parameters of mono- and multicomponent FM signals, with both good numerical properties and statistical performance is proposed. The proposed approach is based on the Hough transform of the pseudo-Wigner-Ville time-frequency distribution (PWVD). It is shown that the numerical properties of the estimator can be improved by varying the PWVD window length. The effect of the window time extent on the statistical performance of the estimator is delineated. Experimental data is used for validation of the statistical properties.

A fast discrete S-transform for biomedical signal processing

Abstract: Determining the frequency content of a signal is a basic operation in signal and image processing. The S-transform provides both the true frequency and globally referenced phase measurements characteristic of the Fourier transform and also generates local spectra, as does the wavelet transform. Due to this combination, the S-transform has been successfully demonstrated in a variety of biomedical signal and image processing tasks. However, the computational demands of the S-transform have limited its application in medicine to this point in time. This abstract introduces the fast S-transform, a more efficient discrete implementation of the classic S-transform with dramatically reduced computational requirements.

Dispersion extraction for acoustic data using time frequency analysis

Abstract: This invention pertains to the extraction of the slowness dispersion characteristics of acoustic waves received by an array of two or more sensors by the application of a continuous wavelet transform on the received array waveforms (data). This produces a time-frequency map of the data for each sensor that facilitates the separation of the propagating components thereon. Two different methods are described to achieve the dispersion extraction by exploiting the time frequency localization of the propagating mode and the continuity of the dispersion curve as a function of frequency. The first method uses some features on the modulus map such as the peak to determine the time locus of the energy of each mode as a function of frequency. The second method uses a new modified Radon transform applied to the coefficients of the time frequency representation of the waveform traces received by the aforementioned sensors. Both methods are appropriate for automated extraction of the dispersion estimates from the data without the need for expert user input or supervision

Instantaneous Frequency Estimation Using the ${\rm S}$ -Transform

Abstract: Instantaneous frequency (IF) is a fundamental concept that can be found in many disciplines such as communications, speech, and music processing. In this letter, analysis of an IF estimator, based on a time-frequency technique known as S-transform, is performed. The performance analysis is carried out in a white Gaussian noise environment, and expressions for the bias and the variance of the estimator are determined. The results show that the bias and the variance are signal dependent. This has been statistically confirmed through numerical simulations of several signal classes.

Multiple Time-Domain Diffraction for UWB Signals

Abstract: The time-domain (TD) solution of the two-dimensional multiple-diffraction case is investigated. The proposed TD solution is based on the representation of the inverse Fourier transform of the corresponding frequency-domain (FD) solution in closed form, as it is given by the uniform theory of diffraction (UTD), and it incorporates the TD representation of the higher-order diffraction coefficients. An algorithm to predict the TD diffracted field after an arbitrary number of objects is also presented. In the proposed algorithm, different types of objects along the propagation path can be applied as well, such as absorbing knife-edges and metallic or nonperfectly conducting wedges. The comparison between the TD solution and the numerical inverse fast Fourier transform of the FD solution proves the validity of the proposed solution.

Time-Frequency Method for Nonlinear System Identification and Damage Detection:

Abstract: This paper presents a method for extracting system nonlinearities and time-localized transient response to impulsive loading by processing stationary/transient responses using the Hilbert—Huang tra...

Estimation of Frequency for AM/FM Models Using the Phase Vocoder Framework

Abstract: This paper proposes an extension of the applicability of phase-vocoder-based frequency estimators for generalized sinusoidal models, which include phase and amplitude modulations. A first approach, called phase corrected vocoder (PCV), takes into account the modification of the Fourier phases resulting from these modulations. Another approach is based on an adaptation of the principles of the time-frequency reassignment and is referred to as the reassigned vocoder (RV). The robustness of the estimation against noise is studied, both theoretically and experimentally, and the performance is assessed in comparison with two state-of-the-art algorithms: an unmodified version of the reassignment method and a quadratically interpolated fast Fourier transform method (QIFFT).

Local Polynomial Fourier Transform Receiver for Nonstationary Interference Excision in DSSS Communications

Abstract: The problem treated in this paper is monocomponent nonstationary interference excision in direct sequence spread spectrum (DSSS) communication systems by means of the local polynomial Fourier transform (LPFT). First, the interference is optimally concentrated in the time-frequency (t-f) plane and then its t-f signature is removed via a binary mask. The LPFT receiver is derived in matrix form and its optimization is performed, having in mind an influence of the binary mask on the received signal. The conventional (suboptimal) and the optimal LPFT receiver performances are compared by means of simulations carried out on the received signal corrupted by different FM types of interferences. The short-time Fourier transform (STFT) receiver is considered as a special case of the LPFT receiver and its performance is assessed simultaneously with the LPFT receiver, both in conventional and optimal case.

Time-Frequency Analysis for the Localization of Multiple Moving Targets Using Dual-Frequency Radars

Abstract: A dual-frequency radar, which estimates the range of a target based on the phase difference between two closely spaced frequencies, has been shown to be a cost-effective approach to accomplish both range-to-motion estimation and tracking. This approach, however, suffers from two drawbacks: it cannot deal with multiple moving targets, and it has poor performance in noisy environments. In this letter, we propose the use of time-frequency signal representations to overcome these drawbacks. The phase, and subsequently the range information, is obtained based on the moving target instantaneous Doppler frequency law, which is provided through time-frequency signal representations. The case of multiple moving targets is handled by separating the different Doppler signatures prior to phase estimation.

Signal adaptive system for time–frequency analysis

Abstract: An efficient multi-cycle signal adaptive hardware design of a system for time-frequency (TF) analysis is proposed. By taking a variable number of clock (CLK) cycles (the only necessary ones regarding the high auto-term quality) in different TF points within the execution, the proposed design allows the implemented system both to optimise execution time and to produce a pure cross-terms-free Wigner distribution (WD) signal representation.

Optimal Particle Filters for Tracking a Time-Varying Harmonic or Chirp Signal

Abstract: We consider the problem of tracking the time-varying (TV) parameters of a harmonic or chirp signal using particle filtering (PF) tools. Similar to previous PF approaches to TV spectral analysis, we assume that the model parameters (complex amplitude, frequency, and frequency rate in the chirp case) evolve according to a Gaussian AR(1) model; but we concentrate on the important special case of a single TV harmonic or chirp. We show that the optimal importance function that minimizes the variance of the particle weights can be computed in closed form, and develop procedures to draw samples from it. We further employ Rao-Blackwellization to come up with reduced-complexity versions of the optimal filters. The end result is custom PF solutions that are considerably more efficient than generic ones, and can be used in a broad range of important applications that involve a single TV harmonic or chirp signal, e.g., TV Doppler estimation in communications, and radar.

Optimal Signal Reconstruction Using the Empirical Mode Decomposition

Abstract: The empirical mode decomposition (EMD) was recently proposed as a new time-frequency analysis tool for nonstationary and nonlinear signals. Although the EMD is able to find the intrinsic modes of a signal and is completely self-adaptive, it does not have any implication on reconstruction optimality. In some situations, when a specified optimality is desired for signal reconstruction, a more flexible scheme is required. We propose a modified method for signal reconstruction based on the EMD that enhances the capability of the EMD to meet a specified optimality criterion. The proposed reconstruction algorithm gives the best estimate of a given signal in the minimum mean square error sense. Two different formulations are proposed. The first formulation utilizes a linear weighting for the intrinsic mode functions (IMF). The second algorithm adopts a bidirectional weighting, namely, it not only uses weighting for IMF modes, but also exploits the correlations between samples in a specific window and carries out filtering of these samples. These two new EMD reconstruction methods enhance the capability of the traditional EMD reconstruction and are well suited for optimal signal recovery. Examples are given to show the applications of the proposed optimal EMD algorithms to simulated and real signals.

Adaptive optimal kernel smooth-windowed wigner-ville distribution for digital communication signal

Abstract: Time-frequency distributions (TFDs) are powerful tools to represent the energy content of time-varying signal in both time and frequency domains simultaneously but they suffer from interference due to cross-terms. Various methods have been described to remove these cross-terms and they are typically signal-dependent. Thus, there is no single TFD with a fixed window or kernel that can produce accurate time-frequency representation (TFR) for all types of signals. In this paper, a globally adaptive optimal kernel smooth-windowed Wigner-Ville distribution (AOK-SWWVD) is designed for digital modulation signals such as ASK, FSK, and M-ary FSK, where its separable kernel is determined automatically from the input signal, without prior knowledge of the signal. This optimum kernel is capable of removing the cross-terms and maintaining accurate time-frequency representation at SNR as low as 0 dB. It is shown that this system is comparable to the system with prior knowledge of the signal.

Discrete Fourier Transform Computation Using Neural Networks

Abstract: In this paper, a method is introduced how to process the Discrete Fourier Transform (DFT) by a single-layer neural network with a linear transfer function. By implementing the suggested solution into neuro- hardware, advantage can be taken of actual parallel processing of spectral components of different frequencies and of different coefficients of each spectral line. When computing the DFT due to input data pre-processing for a certain neural network solution, a stand alone solution of neural networks without the necessity of additional computational resources can be achieved.

Time–frequency representation of musical rhythm by continuous wavelets

Abstract: A method is described that exhaustively represents the periodicities created by a musical rhythm. The continuous wavelet transform is used to decompose an interval representation of a musical rhythm into a hierarchy of short-term frequencies. This reveals the temporal relationships between events over multiple time-scales, including metrical structure and expressive timing. The analytical method is demonstrated on a number of typical rhythmic examples. It is shown to make explicit periodicities in musical rhythm that correspond to cognitively salient ‘rhythmic strata’ such as the tactus. Rubato, including accelerandos and ritardandos, are represented as temporal modulations of single rhythmic figures, instead of timing noise. These time varying frequency components are termed ridges in the time–frequency plane. The continuous wavelet transform is a general invertible transform and does not exclusively represent rhythmic signals alone. This clarifies the distinction between what perceptual mechanisms a pul...

On the TT-Transform and Its Diagonal Elements

Abstract: The TT-transform stands for time-time transform and has been derived as an inverse Fourier transform of the time-frequency S-transform. Up to date, only the diagonal of the TT-transform has been used for signal characterization. We show here an alternative and simplified derivation of the TT-transform which enables a better understanding of this transform. In particular, we demonstrate that the diagonal elements of the TT-transform represent a simple frequency filtered version of the original signal and, thus, that little additional information is gained through the TT-transform.