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

This article proposes a method for estimating the local number of signals components using the short term Rényi entropy of signals in the time-frequency plane. (Additional details can be found in the comprehensive book on Time-Frequency Signal Analysis and Processing (see http://www.elsevier.com/locate/isbn/0080443354). In addition, the most recent upgrade of the original software package that calculates Time-Frequency Distributions and Instantaneous Frequency estimators can be downloaded from the web site: www.time-frequency.net. This was the first software developed in the field, and it was first released publicly in 1987 at the 1st ISSPA conference held in Brisbane, Australia, and then continuously updated).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

A comparison of quadratic TFDs for entropy based detection of components time supports in multicomponent nonstationary signal mixtures

This paper presents a method for extraction of different signal components from multicomponent mixtures by exploiting the information of the local components Renyi entropy. (Additional details can be found in the comprehensive book on Time-Frequency Signal Analysis and Processing (see http://www.elsevier.com/locate/isbn/0080443354). In addition, the most recent upgrade of the original software package that calculates Time-Frequency Distributions and Instantaneous Frequency estimators can be downloaded from the web site: www.time-frequency.net. This was the first software developed in the field, and it was first released publicly in 1987 at the 1st ISSPA conference held in Brisbane, Australia, and then continuously updated).Separation of different signal components, produced by one or more sources, is a problem encountered in many signal processing applications. This paper proposes a fully automatic undetermined blind source separation method, based on a peak detection and extraction technique from a signal time-frequency distribution (TFD). Information on the local number of components is obtained from the TFD Short-term Rényi entropy. It also allows to detect components time supports in the time-frequency plane, with no need for predefined thresholds on the components amplitude. This approach allows to extract different signal components without prior knowledge about the signal. The method is also used as a quality criterion to compare Quadratic TFDs. Results for synthetic and real data are reported for different TFDs, including the recently introduced Extended Modified B distribution

Signal content estimation based on the short-term time-frequency Rényi entropy of the S-method time-frequency distribution

A key characteristic of a nonstationary signal, when analyzed in the time-frequency domain, is the signal complexity, quantified as the number of components in the signal. This paper describes a method for the estimation of this number of components of a signal using the short-term Rényi entropy of its time-frequency distribution (TFD). We focus on the characteristics of TFDs that make them suitable for such a task. The performance of the proposed algorithm is studied with respect to the parameters of the S-method TFD, which combines the virtues of both the spectrogram and the Wigner-Ville distribution. Once the optimal parameters of the TFD have been determined, the applicability of the method in the analysis of signals in low SNRs and real life signals is assessedScopu

Signal content estimation based on the short-term time-frequency Rényi entropy of the S-method time-frequency distribution

A key characteristic of a nonstationary signal, when analyzed in the time-frequency domain, is the signal complexity, quantified as the number of components in the signal. This paper describes a method for the estimation of this number of components of a signal using the short-term Rényi entropy of its time-frequency distribution (TFD). We focus on the characteristics of TFDs that make them suitable for such a task. The performance of the proposed algorithm is studied with respect to the parameters of the S-method TFD, which combines the virtues of both the spectrogram and the Wigner-Ville distribution. Once the optimal parameters of the TFD have been determined, the applicability of the method in the analysis of signals in low SNRs and real life signals is assessedScopu

Measures, performance assessment, and enhancement of TFDs

This chapter describes a number of time-frequency (t,f) performance quality measures specifically developed as criteria for performance enhancement for a given application. The adopted performance measures are defined using objective criteria followed by time-frequency distribution (TFD) enhancement methods to improve the (t,f) concentration, resolution, and readability of TFDs. The topic is covered in nine articles. Hyperbolic FM signals are well described by a method related to time-scale analysis and the wavelet transform (Section 7.1). A general procedure for enhancing the time-frequency resolution and readability of TFDs is the reassignment principle described in Section 7.2. Techniques for measuring the concentration of TFDs and for automatic optimization of their parameters are presented based on entropy measures (Section 7.3). Another approach defines a resolution performance measure using local measurements in the (t,f) domain, such as relative amplitudes of auto-terms and cross-terms (Section 7.4). Then, attempts to unify time-frequency, time-scale, filter banks, wavelets, and the discrete-time Gabor transform using product functions and cascaded frames are presented briefly as they may assist in the selection of the best-performing method for a given application (Section 7.5). The last four topics focus on (1) time-frequency compressive sensing (Section 7.6); (2) signal complexity estimation using (t,f) entropy measures (Section 7.7); (3) time-frequency analysis using neural networks (Section 7.8); and (4) a comparison of postprocessing methods in the (t,f) domain (Section 7.9).Scopu