The high noise sensitivity of the Wigner distribution makes smoothing a necessity for producing readable time-frequency images of noise corrupted signals. Since linear smoothing suppresses noise at the expense of considerable smearing of the signal components, we explore two nonlinear denoising techniques based on soft-thresholding in an orthonormal basis representation. Soft-thresholding provi...

Corrections concern the results given in Section 4 of the above paper for the local polynomial Wigner-Ville estimator. These corrections refine the assumption about the correlation function of the continuous time observation noise and Eq. (38) for the covariance matrix of the local polynomial WVD estimator. We wish to emphasize that the produced corrections do not influence the comparative accu...

Recently we have proposed the T-class of time-frequency distributions (TFD’s) with time-only kernels to provide high-resolution and considerable cross-terms reduction for multicomponent FM signals. In this work we investigate the instantaneous frequency (IF) properties of two members of this class: the hyperbolic and the exponential T-distributions in the presence of noise. A comparison with tw...

This paper deals with a new framework in analyzing the formal mathematical correspondence between quantum mechanics and time-frequency representations of a signal. It is also shown that joint time-frequency distributions have a close link with Heisenberg uncertainty relations if the observables are taken as fuzzy entities. This result contradicts the arguments of Cohen [IEEE Proc. 77(7):941 (19...

Harmonic wavelets have simple formulations in the fi-equency domain and they have proved a good basis for the time-frequency mapping of transient signals. Moreover their computational algorithm allows bandwidth to be chosen arbitrarily so that they offer a variable Q transform, where Q is the ratio of centre frequency to bandwidth. In contrast, the short-time Fourier transform and the Wlgner-Vi...

This paper investigates the mean square error optimal timefrequency kernel for estimation of the Wigner-Ville spectrum of a certain class of nonstationary processes. The class of locally stationary processes have a simplified covariance structure which facilitates analysis. We give a formula for the optimal kernel in the ambiguity domain and conditions that are sufficient for the optimal time-f...

Imperfection in a bonding point can affect the quality of an entire integrated circuit. Therefore, time–frequency analysis method was proposed to detect and identify fault bonds. First, voltage current signals were acquired from ultrasonic generator. Second, with Wigner–Ville distribution empirical mode decomposition methods, features electrical extracted. Then, principal component further used...