Ljubisa Stankovic

A method for time-frequency analysis

A method for time-frequency signal analysis is presented. The proposed method belongs to the general class of smoothed pseudo Wigner distributions. It is derived from the analysis of the Wigner distribution defined in the frequency domain. This method provides some substantial advantages over the Wigner distribution. The well-known cross term effects are reduced or completely removed. The oversampling of signal is not necessary. In addition, the computation time can be significantly shorter. The results are demonstrated on two numerical examples with frequency modulated signals. >

Instantaneous frequency estimation using the Wigner distribution with varying and data-driven window length

The estimation of the instantaneous frequency (IF) of a harmonic complex-valued signal with an additive noise using the Wigner distribution is considered. If the IF is a nonlinear function of time, the bias of the estimate depends on the window length. The optimal choice of the window length, based on the asymptotic formulae for the variance and bias, can be used in order to resolve the bias-variance tradeoff. However, the practical value of this solution is not significant because the optimal window length depends on the unknown smoothness of the IF. The goal of this paper is to develop an adaptive IF estimator with a time-varying and data-driven window length, which is able to provide quality close to what could be achieved if the smoothness of the IF were known in advance. The algorithm uses the asymptotic formula for the variance of the estimator only. Its value may be easily obtained in the case of white noise and relatively high sampling rate. Simulation shows good accuracy for the proposed adaptive algorithm.

A measure of some time-frequency distributions concentration

Abstract A criterion that can provide a measure of time–frequency distribution concentration is proposed. In contrast to the norm-based concentration measures it does not need normalization in order to behave properly when cross-terms are present, and also it does not discriminate low concentrated components with respect to the highly concentrated ones within the same distribution. This measure has been used for the automatic window selection in the spectrogram, as well as in finding the optimal distribution that can be produced in a transition from the spectrogram toward the pseudo Wigner distribution.

Fractional Fourier transform as a signal processing tool: An overview of recent developments

Fractional Fourier transform (FRFT) is a generalization of the Fourier transform, rediscovered many times over the past 100 years. In this paper, we provide an overview of recent contributions pertaining to the FRFT. Specifically, the paper is geared toward signal processing practitioners by emphasizing the practical digital realizations and applications of the FRFT. It discusses three major topics. First, the manuscripts relates the FRFT to other mathematical transforms. Second, it discusses various approaches for practical realizations of the FRFT. Third, we overview the practical applications of the FRFT. From these discussions, we can clearly state that the FRFT is closely related to other mathematical transforms, such as time-frequency and linear canonical transforms. Nevertheless, we still feel that major contributions are expected in the field of the digital realizations and its applications, especially, since many digital realizations of the FRFT still lack properties of the continuous FRFT. Overall, the FRFT is a valuable signal processing tool. Its practical applications are expected to grow significantly in years to come, given that the FRFT offers many advantages over the traditional Fourier analysis.

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 targets 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.

Fast communication: Missing samples analysis in signals for applications to L-estimation and compressive sensing

This paper provides statistical analysis for efficient detection of signal components when missing data samples are present. This analysis is important for both the areas of L-statistics and compressive sensing. In both cases, few samples are available due to either noisy sample elimination or random undersampling signal strategies. The analysis enables the determination of the sufficient number of observation and as such the minimum number of missing samples which still allow proper signal detection. Both single component and multicomponent signals are considered. The results are verified by computer simulations using different component frequencies and under various missing-available samples scenarios.

Time-frequency analysis of multiple resonances in combustion engine signals

Abstract This paper presents time–frequency analysis of multiple resonances in combustion chamber pressure signals and corresponding structure-born sound signals of the cylinder block of a combustion engine considering only one combustion cycle. Since the Wigner distribution proved itself as a good tool for these kinds of signals, the requirement which we imposed here was to produce a sum of the Wigner distributions of the signal components separately, but without cross-terms using only one signal realization. A distribution having this property can be achieved using the S-method. Based on this property of the method, we investigate a procedure to estimate the instantaneous frequencies that are functions of temperature within the combustion chamber and the energies of the components that are used for knock detection. The calculation delay is smaller than the duration of one combustion cycle. This can provide an efficient and accurate combustion control of spark-ignition car engines. The procedure is demonstrated on several simulated and experimental signals.

An algorithm for the Wigner distribution based instantaneous frequency estimation in a high noise environment

Estimation of the instantaneous frequency (IF) in a high noise environment, by using the Wigner distribution (WD), is considered. In this case the error is of impulse nature. An algorithm for the IF estimation, which combines the nonparametric method based on the WD maxima with the minimization of the IF variations between consecutive points, is proposed. The off-line and on-line realizations are presented. The on-line realization is an instance of the (generalized) Viterbi algorithm. Application of this algorithm on the monocomponent and multicomponent frequency modulated signals is demonstrated. For multicomponent signals, the algorithm is applied on other (reduced interference) distributions. Numerical examples, including statistical study of the algorithm performance, are given.

Robust L-estimation based forms of signal transforms and time-frequency representations

The L-estimation based signal transforms and time-frequency (TF) representations are introduced by considering the corresponding minimization problems in the Huber (1981, 1998) estimation theory. The standard signal transforms follow as the maximum likelihood solutions for the Gaussian additive noise environment. For signals corrupted by an impulse noise, the median-based transforms produce robust estimates of the non-noisy signal transforms. When the input noise is a mixture of Gaussian and impulse noise, the L-estimation-based signal transforms can outperform other estimates. In quadratic and higher order TF analysis, the resulting noise is inherently a mixture of the Gaussian input noise and an impulse noise component. In this case, the L-estimation-based signal representations can produce the best results. These transforms and TF representations give the standard and the median-based forms as special cases. A procedure for parameter selection in the L-estimation is proposed. The theory is illustrated and checked numerically.

Compressive Sensing Based Separation of Nonstationary and Stationary Signals Overlapping in Time-Frequency

A compressive sensing (CS) approach for nonstationary signal separation is proposed. This approach is motivated by challenges in radar signal processing, including separations of micro-Doppler and main body signatures. We consider the case where the signal of interest assumes sparse representation over a given basis. Other signals present in the data overlap with the desired signal in the time and frequency domains, disallowing conventional windowing or filtering operations to be used for desired signal recovery. The proposed approach uses linear time-frequency representations to reveal the data local behavior. Using the L-statistics, only the time-frequency (TF) points that belong to the desired signal are retained, whereas the common points and others pertaining only to the undesired signals are deemed inappropriate and cast as missing samples. These samples amount to reduced frequency observations in the TF domain. The linear relationship between the measurement and sparse domains permits the application of CS techniques to recover the desired signal without significant distortion. We focus on sinusoidal desired signals with sparse frequency-domain representation but show that the analysis can be straightforwardly generalized to nonsinusoidal signals with known structures. Several examples are provided to demonstrate the effectiveness of the proposed approach.