COMPACT SUPPORT KERNELS BASED TIME-FREQUENCY DISTRIBUTIONS: PERFORMANCE EVALUATION Mansour Abed 1,2 Adel Belouchrani 2 Mohamed Cheriet 3 Boualem Boashash 4,5 1 University of Mostaganem, Algeria 2 Ecole Nationale Polytechnique, El Harrach, Algiers, Algeria 3 Synchromedia, University of Quebec (ETS), 1100 Notre-Dam West, Montreal, Quebec, Canada 4 University of Queensland, Australia 5 Qatar University, Qatar ABSTRACT This paper presents two new time-frequency distributions based on kernels with compact support (KCS) namely the separable CB (SCB) and the polynomial CB (PCB) TFDs. The implementation of these distributions follows the method developed for the Cheriet-Belouchrani CB TFD. The perfor- mance of this family of TFDs is compared to the most known quadratic distributions through tests on multi-component signals with linear and nonlinear frequency modulations (FMs) considering the noise effects as well. Comparisons are based on the evaluation of an objective criterion namely the Boashash-Sucic’s normalized instantaneous resolution per- formance measure that allows to provide the optimized TFD using a specific methodology. In all presented examples, the KCS TFDs have been shown to have a significant interfer- ence mitigation, with the component energy concentration around their respective instantaneous frequency laws being well preserved giving high resolution measure values. Index Terms— Time-frequency distribution, compact support kernel, separable compact support kernel, polyno- mial compact support kernel, performance evaluation 1. INTRODUCTION Time-frequency distributions (TFDs) are the natural choice that allows to analyze and process nonstationary signals accurately and efficiently by performing a mapping of one- dimensional signal x(t) into a two dimensional function of time and frequency TFD x (t, f ). Herein, we are interested by the quadratic class of TFDs, also known in the literature as kernel-based transform [1]: TFD x (t, f ) =  +∞ −∞ e j2πη(s−t) φ(η,τ )x(s + τ/2) x ∗ (s - τ/2)e −j2πfτ dηdsdτ (1) where φ(η,τ ) is a two dimensional kernel. Unlike the Gaus- sian kernel that suffers from information loss due to reduc- tion in accuracy when the Gaussian is cut off to compute the time-frequency distribution [2], kernels with compact sup- port (KCS), derived from the Gaussian kernel, are found to recover this information loss, improves processing time and retains the most important properties of the Gaussian kernel [3]. These features are achieved thanks to the compact sup- port analytical property of this type of kernels since they van- ish themselves outside a given compact set. It turns out that through a control parameter of the kernel width, the corre- sponding time-frequency distributions allow a better elimina- tion of cross-terms while providing good resolution in both time and frequency. Motivated by these interesting charac- teristics, we propose in this contribution the use of two new kernels with compact support derived from the Gaussian ker- nel for time-frequency analysis namely the separable KCS (SKCS) [4] and the polynomial KCS (PKCS) [5]. Similarly to the CB TFD [6], the induced TFDs are referred to as SCB TFD and PCB TFD, respectively. Then, comparisons are es- tablished between results obtained by using the KCS based TFDs and the most commonly used time-frequency represen- tations. In order to provide objective assessment, our compar- ison is based on the Boashash-Sucic resolution performance measure [7]: P i =1 - 1 3 A s A m + A x 2A m + (1 - S) (2) where A m A s A x are respectively the average amplitudes of the main-lobes, side-lobes and cross-terms of two consecu- tive signal components, with S =(B 1 + B 2 )/[2(f 2 - f 1 )] being a measure of the components’ separation in frequency (B k and f k , k =1, 2, are respectively the instantaneous band- width and the instantaneous frequency (IF) of the k th compo- nent). P i is close to 1 for well-performing TFDs and 0 for poorly-performing ones. An overall measure P is taken to be the median of the instantaneous measures P i corresponding to different time slices in the relevant sections of the signals. This quantitative criterion permits the performances’ evalua- tion of different distributions and can be used for adaptive and automatic parameters selection in t-f analysis. 4180 978-1-4577-0539-7/11/$26.00 ©2011 IEEE ICASSP 2011