In this paper, we propose the peak of the polynomial Wigner-Ville distribution as an instantaneous frequency estimator for polynomial frequency modulated signals in the presence of multiplicative and additive complex Gaussian processes. We show that this estimator is unbiased and we derive an analytic expression of its asymptotic variance. Simulation results, based on Monte-Carlo realisations, ...

Cohen's class of Time-Frequency Distributions (CTFDs), which includes the spectrogram and the Wigner-Ville distribution, has significant potential for the analysis of non-stationnary signals. In order to efficiently compute long signals time-frequency representations, we propose fast algorithms using a recursive approach. First, we introduce a recursive algorithm dedicated to the spectrogram co...

A new member of the Cohen’s class time-frequency distribution is proposed. The kernel function is determined adaptively based on the signal of interest. The kernel preserves the chirp-like components while removing interference terms generated due to the quadratic characteristic of Wigner-Ville distribution. This approach is based on the chirplet as an underlying model of biomedical signals. We...

Vladimir Makarenkov, Dmytro Kevorkov and Pierre Legendre Département d’informatique, Université du Québec à Montréal, C.P. 8888, succ. Centre-Ville, Montréal (Québec) Canada H3C 3P8 (makarenkov.vladimir at uqam.ca); Département d’informatique, Université du Québec à Montréal, C.P. 8888, succ. Centre-Ville, Montréal (Québec) Canada H3C 3P8. (kevorkov at lacim.uqam.ca); Département de Sciences Bi...

Department of Electrical Engineering, École Polytechnique de Montréal, P.O. Box 6079, Station Centre-ville, Montreal (Quebec) Canada, H3C 3A7 CRC Chair on the Optimization of Communication Networks, Department of Computer Science and Operations Research, Université de Montréal, P.O. Box 6128, Station Centre-ville, Montreal (Quebec) Canada, H3C 3J7 Department of Computer Science, Université du Q...

Time-frequency representations have been of great interest in the analysis and classification of non-stationary signals. The use of highly selective transformation techniques is a valuable tool for obtaining accurate information for studies of this type. The Wigner-Ville distribution has high time and frequency selectivity in addition to meeting some interesting mathematical properties. However...

The large variance of the Wigner Ville distribution makes smoothing essential for producing readable estimates of the time varying power spectrum of noise corrupted signals Since linear smoothing trades reduced variance for increased bias of the signal components we explore two nonlinear estimation techniques based on soft thresholding in an orthonormal basis representation Soft thresholding pr...

New generations of spark ignition engines require a correct ignition adjustment to guarantee optimal performance. In this paper, we address the challenge of knock detection improvements with time-frequency analysis. Two real time knock detection methodologies based on the sliding Discrete Fourier Transform and the pseudo Wigner-Ville distribution are exposed. Their relative performances and rob...