Time-Frequency Distributions Based on Compact Support Kernels: Properties and Performance Evaluation

This paper presents two new time-frequency distributions (TFDs) based on kernels with compact support (KCS) namely the separable (CB) (SCB) and the polynomial CB (PCB) TFDs. The implementation of this family of TFDs follows the method developed for the Cheriet-Belouchrani (CB) TFD. The mathematical properties of these three TFDs are analyzed and their performance is compared to the best classical quadratic TFDs using several tests on multicomponent signals with linear and nonlinear frequency modulation (FM) components including the noise effects. Instead of relying solely on visual inspection of the time-frequency domain plots, comparisons include the time slices' plots and the evaluation of the Boashash-Sucic's normalized instantaneous resolution performance measure that permits to provide the optimized TFD using a specific methodology. In all presented examples, the KCS-TFDs show a significant interference rejection, with the component energy concentration around their respective instantaneous frequency laws yielding high resolution measure values.

[1]  Alfred Mertins,et al.  Signal Analysis: Wavelets, Filter Banks, Time-Frequency Transforms and Applications , 1999 .

[2]  Mohamed Cheriet,et al.  KCS-new kernel family with compact support in scale space: formulation and impact , 2000, IEEE Trans. Image Process..

[3]  Mj Martin Bastiaans.  Time-frequency signal analysis , 2008 .

[4]  Boualem Boashash,et al.  Parameter selection for optimising time-frequency distributions and measurements of time-frequency characteristics of non-stationary signals , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[5]  Boualem Boashash,et al.  The T-class of time-frequency distributions: Time-only kernels with amplitude estimation , 2006, J. Frankl. Inst..

[6]  Mohamed Cheriet,et al.  PKCS: A Polynomial Kernel Family With Compact Support for Scale- Space Image Processing , 2007, IEEE Transactions on Image Processing.

[7]  B. Boashash,et al.  Multi-component IF estimation , 2000, Proceedings of the Tenth IEEE Workshop on Statistical Signal and Array Processing (Cat. No.00TH8496).

[8]  Boualem Boashash,et al.  Resolution measure criteria for the objective assessment of the performance of quadratic time-frequency distributions , 2003, IEEE Trans. Signal Process..

[9]  Mohamed Cheriet,et al.  SKCS-new kernel family with compact support , 2004, 2004 International Conference on Image Processing, 2004. ICIP '04..

[10]  Isaac Weiss.  High-Order Differentiation Filters that Work , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  Braham Barkat,et al.  A high-resolution quadratic time-frequency distribution for multicomponent signals analysis , 2001, IEEE Trans. Signal Process..

[12]  Ronald L. Allen,et al.  Signal Analysis: Time, Frequency, Scale and Structure , 2003 .

[13]  L. Stanković.  An analysis of some time-frequency and time-scale distributions , 1994 .

[14]  Boualem Boashash,et al.  The Optimal Smoothing of the Wigner-Ville Distribution For Real-Life Signals Time-Frequency Analysis , 2003 .

[15]  Moeness G. Amin,et al.  High spectral resolution time-frequency distribution kernels , 1998, IEEE Trans. Signal Process..

[16]  Ljubisa Stankovic,et al.  Auto-term representation by the reduced interference distributions: a procedure for kernel design , 1996, IEEE Trans. Signal Process..

[17]  Robert J. Marks,et al.  The use of cone-shaped kernels for generalized time-frequency representations of nonstationary signals , 1990, IEEE Trans. Acoust. Speech Signal Process..

[18]  A. Belouchrani,et al.  On the use of a new compact support kernel in time frequency analysis , 2001, Proceedings of the 11th IEEE Signal Processing Workshop on Statistical Signal Processing (Cat. No.01TH8563).

[19]  William J. Williams,et al.  Improved time-frequency representation of multicomponent signals using exponential kernels , 1989, IEEE Trans. Acoust. Speech Signal Process..