Victor Sucic

Resolution measure criteria for the objective assessment of the performance of quadratic time-frequency distributions

This paper presents the essential elements for developing objective methods of assessment of the performance of time-frequency signal analysis techniques. We define a measure for assessing the resolution performance of time-frequency distributions (TFDs) in separating closely spaced components in the time-frequency domain. The measure takes into account key attributes of TFDs, such as components mainlobes and sidelobes and cross-terms. The introduction of this measure allows to quantify the quality of TFDs instead of relying solely on visual inspection of their plots. The method of assessment of performance of TFDs also allows the improvement of methodologies for designing high-resolution quadratic TFDs for time-frequency analysis of multicomponent signals. Different TFDs, including the modified B distribution, are optimized using this methodology. Examples of a performance comparison of quadratic TFDs in resolving closely spaced components in the time-frequency domain, using the proposed resolution measure, are provided.

Nonlinear IF Estimation Based on the Pseudo WVD Adapted Using the Improved Sliding Pairwise ICI Rule

A method for the instantaneous frequency (IF) estimation of a monocomponent nonlinear frequency modulated (FM) signal based on the pseudo Wigner-Ville distribution (PWVD) with an adaptive window width is presented. In order to improve the IF estimation accuracy, the original sliding pair-wise intersection of confidence intervals (SPICI) rule has been modified. An additional criterion for a proper window width selection is introduced, which takes into account the amount of overlap between the current and the previous confidence interval relative to the current interval length. The presented results show that the proposed method outperforms the original SPICI-based method by up to 42% in terms of the mean absolute error and up to 73% in terms of the mean squared error. It is also less sensitive to the window widths set selection than the original method.

Estimating the number of components of a multicomponent nonstationary signal using the short-term time-frequency Rényi entropy

The time-frequency Rényi entropy provides a measure of complexity of a nonstationary multicomponent signal in the time-frequency plane. When the complexity of a signal corresponds to the number of its components, then this information is measured as the Rényi entropy of the time-frequency distribution (TFD) of the signal. This article presents a solution to the problem of detecting the number of components that are present in short-time interval of the signal TFD, using the short-term Rényi entropy. The method is automatic and it does not require a prior information about the signal. The algorithm is applied on both synthetic and real data, using a quadratic separable kernel TFD. The results confirm that the short-term Rényi entropy can be an effective tool for estimating the local number of components present in the signal. The key aspect of selecting a suitable TFD is also discussed.

An Efficient Algorithm for Instantaneous Frequency Estimation of Nonstationary Multicomponent Signals in Low SNR

A method for components instantaneous frequency (IF) estimation of multicomponent signals in low signal-to-noise ratio (SNR) is proposed. The method combines a new proposed modification of a blind source separation (BSS) algorithm for components separation, with the improved adaptive IF estimation procedure based on the modified sliding pairwise intersection of confidence intervals (ICI) rule. The obtained results are compared to the multicomponent signal ICI-based IF estimation method for various window types and SNRs, showing the estimation accuracy improvement in terms of the mean squared error (MSE) by up to 23%. Furthermore, the highest improvement is achieved for low SNRs values, when many of the existing methods fail.

A Signal Denoising Method Based on the Improved ICI Rule

In this letter, we have proposed a signal denoising method based on a modification of the intersection of confidence intervals (ICI) rule. The ICI rule is complemented by the relative intersection of confidence intervals length which is used as an additional criterion for adaptive filter support selection. It is shown that the proposed method outperforms the original ICI method equipped with the local polynomial approximation (LPA), as well as various conventional wavelet shrinkage methods.

Adaptive 2-D Wavelet Transform Based on the Lifting Scheme With Preserved Vanishing Moments

In this paper, we propose novel adaptive wavelet filter bank structures based on the lifting scheme. The filter banks are nonseparable, based on quincunx sampling, with their properties being pixel-wise adapted according to the local image features. Despite being adaptive, the filter banks retain a desirable number of primal and dual vanishing moments. The adaptation is introduced in the predict stage of the filter bank with an adaptation region chosen independently for each pixel, based on the intersection of confidence intervals (ICI) rule. The image denoising results are presented for both synthetic and real-world images. It is shown that the obtained wavelet decompositions perform well, especially for synthetic images that contain periodic patterns, for which the proposed method outperforms the state of the art in image denoising.

Analysis of local time-frequency entropy features for nonstationary signal components time supports detection

Identification of different specific signal components, produced by one or more sources, is a problem encountered in many signal processing applications. This can be done by applying the local time-frequency-based Renyi entropy for estimation of the instantaneous number of components in a signal. Using the spectrogram, one of the most simple quadratic time-frequency distributions, the paper proves the local applicability of the counting property of the Renyi entropy. The paper also studies the influence of the entropy order and spectrogram parameters on the estimation results. Numerical simulations are provided to quantify the observed behavior of the local entropy in the case of intersecting components. The causes of decrements in the local number of time supports in the time-frequency plane are also studied. Finally, results are provided to illustrate the findings of the study and its potential use as a key step in multicomponent instantaneous frequency estimation.

A resolution performance measure for quadratic time-frequency distributions

This paper presents two novel results which are significant for the application of time-frequency signal analysis techniques to real life signals. First, we introduce a measure for comparing the resolution performance of TFDs in separating closely spaced components in the time-frequency domain. The measure takes into account key attributes of TFDs such as main-lobes, side-lobes, and cross-terms. The introduction of this measure is an improvement of current techniques which rely on visual inspection of plots. The second result consists in proposing a methodology for designing high resolution quadratic TFDs for the time-frequency analysis of multicomponent signals when components are close to each other. A recently introduced TFD, the B-distribution, and its modified version are defined using this methodology. Finally, the performance comparison of quadratic TFDs using the proposed resolution measure shows that the B-distribution outperforms existing quadratic TFDs in resolving closely spaced components in the time-frequency domain.

Multicomponent noisy signal adaptive instantaneous frequency estimation using components time support information

This study proposes an adaptive method for components instantaneous frequency (IF) estimation of noisy non-stationary multicomponent signals, combined with the components time-support estimation method based on the shorttime Renyi entropy (STRE). Components localisation and separation are done using a double-direction component tracking and extraction method presented here, while the IF estimation is done using the adaptive algorithms based on the intersection of confidence intervals (ICI) rule and the relative intersection of confidence intervals (RICI) rule. The results obtained using the ICI and RICI rules are compared for various window types, signal-to-noise ratios and time-frequency distributions, both with and without using the information on components time support. Most of the errors in IF estimation using the ICI and RICI-based methods are caused by imprecise components time-support estimation. The proposed methods combined with the STRE have achieved a significant accuracy improvement in terms of the mean absolute error and the mean squared error, reducing them by up to 73 and 93%, respectively. The method has been applied to real-life signals and proven to be an efficient tool for IF estimation of noisy non-stationary multicomponent signals.

An approach for selecting a real-life signal best-performing time-frequency distribution

The difficulty of selecting the optimal time-frequency distribution (TFD) for a given real-life signal has been one of the major limiting factors to a wider use of time-frequency analysis tools in practice. This paper, by extending our earlier works on the objective assessment of the performance of TFDs, presents a novel automatic approach for selecting a real-life signal best-performing time-frequency distribution from a set of considered TFDs. The practical applicability of the approach is illustrated on real-life signals examples.