Digital Signal Processing 34 (2014) 56–66 Contents lists available at ScienceDirect Digital Signal Processing www.elsevier.com/locate/dsp Analysis of local time-frequency entropy features for nonstationary signal components time supports detection Victor Sucic a , Nicoletta Saulig a,∗ , Boualem Boashash b,c a Faculty of Engineering, University of Rijeka, Croatia b College of Engineering, Qatar University, Doha, Qatar c Centre for Clinical Research, University of Queensland, Brisbane, Australia a r t i c l e i n f o a b s t r a c t Article history: Available online 24 July 2014 Keywords: Time-frequency Rényi entropy Spectrogram Component number 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 Rényi 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 Rényi 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.  2014 Elsevier Inc. All rights reserved. 1. Introduction Nonstationary signals encountered in engineering applications (civil, military, biomedical) are often characterized by multiple components with varying spectral contents. Different signal com- ponents may have overlapping time supports, making the classical time representation inadequate to correctly identify the energy contribution of each component. Similarly, the frequency repre- sentation fails to correctly map the spectral energy of different components if they share frequency content. Joint time and fre- quency representations, being energy distributions showing the signal local frequency content, overcome such limitations of the classical signal representations [1]. These time-frequency distribu- tions allow the isolation of different spectral components that are present in a signal, as well as their respective instantaneous fre- quencies [2]. The number of components that are present in a signal can thus be visually identified. However, for applications re- quiring the automated assessment of the number of components, objective criteria are needed. * Corresponding author at: Faculty of Engineering, University of Rijeka, Vuko- varska 58, 51000, Rijeka, Croatia. E-mail addresses: vsucic@riteh.hr (V. Sucic), nsaulig@riteh.hr (N. Saulig), boualem@qu.edu.qa (B. Boashash). Applications such as classification, require time-frequency fea- tures that can be used for pattern recognition as an aid to identifi- cation and detection. A simple but efficient feature is the measure of complexity, which is extensively reviewed in this paper and ap- plied to the estimation of the number of components in a signal. For blind source separation algorithms, based on peaks ex- traction and tracking from TFDs, the key information is the local number of components, i.e. the instantaneous number of compo- nents supported in time. The recently introduced Short-term Rényi entropy [3] provides reliable information about the time support of different components, and thus can be used as the input in- formation to peak detection and extraction techniques [1,4]. The Short-term Rényi entropy, as an indicator of the local number of time supported components, is discussed in Section 2. The simpli- fied model presented in [3] doesn’t clarify the role of the entropy order α and TFD features (local time and frequency supports) in the estimation. The Short-term Rényi entropy when applied to the spectrogram, being a widely used TFD, is therefore studied in Sec- tion 2. The analysis of particular situations occurring in nonstation- ary signals (ending/starting component, overlapping or intersecting components) is essential for correctly interpreting the information provided by the Short-term Rényi entropy, as explained in Sec- tion 3. Experimental results are provided in Section 4. In Section 5, the obtained results are discussed, and possible prospectives are considered. http://dx.doi.org/10.1016/j.dsp.2014.07.013 1051-2004/ 2014 Elsevier Inc. All rights reserved.