Milos Dakovic

Performance of quadratic time-frequency distributions as instantaneous frequency estimators

General performance analysis of the shift covariant class of quadratic time-frequency distributions (TFDs) as instantaneous frequency (IF) estimators, for an arbitrary frequency-modulated (FM) signal, is presented. Expressions for the estimation bias and variance are derived. This class of distributions behaves as an unbiased estimator in the case of monocomponent signals with a linear IF. However, when the IF is not a linear function of time, then the estimate is biased. Cases of white stationary and white nonstationary additive noises are considered. The well-known results for the Wigner distribution (WD) and linear FM signal, and the spectrogram of signals whose IF may be considered as a constant within the lag window, are presented as special cases. In addition, we have derived the variance expression for the spectrogram of a linear FM signal that is quite simple but highly signal dependent. This signal is considered in the cases of other commonly used distributions, such as the Born-Jordan and the Choi-Williams distributions. It has been shown that the reduced interference distributions outperform the WD but only in the case when the IF is constant or its variations are small. Analysis is extended to the IF estimation of signal components in the case of multicomponent signals. All theoretical results are statistically confirmed.

Signal Decomposition by Using the S-Method With Application to the Analysis of HF Radar Signals in Sea-Clutter

This paper presents a new approach to the time-frequency signal analysis and synthesis, using the eigenvalue decomposition method. It is based on the S-method, the time-frequency representation that can produce a distribution equal or close to a sum of the Wigner distributions of individual signal components. The new time-frequency signal decomposition method is evaluated on the simulated and experimental high-frequency surface-wave radar (HFSWR) data. Results demonstrate that it provides an effective way for analyzing and detecting maneuvering air targets with significant velocity changes, including target signal separation from the heavy clutter. The analysis shows that this method can provide additional insight into the interpretation and processing of radar signals, with respect to the traditional Fourier transform based methods currently used by the HFSWRs. The proposed method could also be used in other signal processing applications

Adaptive variable step algorithm for missing samples recovery in sparse signals

Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analysed in the same way as compressive sensed signals by omitting the corrupted samples and considering them as unavailable during the recovery process. The reconstruction of the missing samples is done by using one of the well-known reconstruction algorithms. In this study, the authors will propose a very simple and efficient algorithm, applied directly to the concentration measures, without reformulating the reconstruction problem within the standard linear programming form. Direct application of the gradient approach to the non-differentiable forms of measures lead us to introduce a variable step size algorithm. A criterion for changing the adaptive algorithm parameters is presented. The results are illustrated on the examples with sparse signals, including approximately sparse signals and noisy sparse signals.

Instantaneous frequency in time-frequency analysis: Enhanced concepts and performance of estimation algorithms

Abstract The instantaneous frequency (IF) is a very important feature of nonstationary signals in numerous applications. The first overview of the concept and application of the IF estimators is presented in seminal papers by Boashash. Since then, a significant knowledge has been gained about the performance of the IF estimators. This knowledge has been used not only for development of various IF estimators but also for introduction of novel time–frequency (TF) representations. The IF estimation in environments characterized by low signal-to-noise (SNR) has achieved significant benefits from these theoretical developments. In this paper, we review some of the most important developments in the last two decades related to the concept of the IF, performance analysis of IF estimators, and development of IF estimators for low SNR environments.

Micro-Doppler Removal in the Radar Imaging Analysis

The micro-Doppler (m-D) effect is caused by fast moving reflectors. This effect may significantly decrease the readability of the inverse synthetic aperture radar/synthetic aperture radar (ISAR/SAR) images. An L-statistics-based method for m-D effects removal is proposed. The L-statistics approach is performed on the spectrogram, while the rigid body signal synthesis is done in the complex time-frequency (TF) domain. The proposed method is very simple to use and produces better results than the other TF-based approaches. In addition to being capable of separating the rigid body and the m-D parts, this approach is robust to the noise influence. It may also separate close rigid body points, which are not separated in the original radar image. In the numerical implementation of this approach for radar imaging, the computational efficiency is further improved by using two thresholds. The first threshold determines whether there is a target signal in a range cell, while the second threshold determines whether there are m-D effects in this range cell. These thresholds could significantly decrease the computation time in real-time applications. The theory is illustrated by examples.

Instantaneous Frequency Estimation Using the

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.

{\rm S}

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.

-Transform

The analysis, processing, and parameters estimation of signals whose spectral content changes in time are of crucial interest in many applications, including radar, acoustics, biomedicine, communications, multimedia, seismic, and the car industry [1]-[11]. Various signal representations have been introduced to deal with this kind of signals within the area known as time-frequency (TF) signal analysis. The oldest analysis tool in this area is the short-time Fourier transform (STFT), as a direct extension of the classical Fourier analysis. The other key tool is the Wigner distribution (WD), introduced in signal analysis from quantum mechanics. The aim of this lecture note is to present and relate these two of the most important tools in the TF signal analysis, the STFT and the WD (introduced by two Nobel prize winners, D. Gabor and E. Wigner, respectively). This relation is a basis for the S-method (SM), an efficient and simple TF signal analysis tool providing a gradual transition between these two representations.

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

The local polynomial Fourier transform (LPFT) based algorithm for auto-focusing SAR images has recently been proposed by the authors. It produces a well focused image of moving targets, without defocusing stationary targets or inducing undesired cross-terms. The drawback of this algorithm is its high computational burden caused by the large number of elements in the set of used chirp-rates. We propose an algorithm with decreased number of elements used for the LPFT-based SAR imaging. The product high-order ambiguity function (PHAF) is applied to estimate parameters of a radar signal. The estimated chirp-rate is used as an initial value for forming the set of chirp-rates. The proposed algorithm has significantly smaller set of chirp-rate values (tens comparing to several hundreds or thousands used in the previous algorithm version). In this manner, the calculation complexity is significantly reduced. The proposed procedure is fully automated, meaning that it follows the change of motion parameters. In addition, our procedure considers the third-order phase compensation.

From the STFT to the Wigner Distribution [Lecture Notes]

The concentration and sparsity of signal representation in the Hermite transform (HT) basis may highly depend on a properly chosen scaling factor and discrete time shift parameter. In that sense, we propose a simple and efficient iterative procedure for automatic determination of the optimal scaling factor. The optimization criterion is based on the ź1-norm acting as a measure of signal concentration in the HT domain. Instead of centering the signal at the zero time instant, we also propose to shift the center for a few points left or right, which will additionally improve the concentration. An important application of the proposed optimization approach is the compression of QRS complexes, where properly chosen scaling factor and time-shift increase the compression performance. The results are verified using synthetic and real examples and compared with the existing approach for the compression of QRS complexes. The algorithm for optimization of scaling factor and time-shift of Hermite functions is proposed.Parameters are optimized to provide the most concentrated representation of the observed signals.The simple iterative algorithm is based on gradient descent method.The concentration measure is employed as optimization criterion.The efficiency of the proposed approach is verified using both real and synthetic signals.The method is applied for QRS compression and tested on a database of QRS complexes.The efficiency is proven also for T waves of ECG signals and UWB signals.