Time–frequency analysis

About: Time–frequency analysis is a research topic. Over the lifetime, 5407 publications have been published within this topic receiving 104346 citations.

Numerical implementation of matching pursuit for the analysis of complex ultrasonic signals

Abstract: Matching pursuit has typically been applied to ultrasonic signal analysis for the purpose of identifying or estimating discrete echoes. In this paper, a specific numerical implementation of matching pursuit designed for ultrasonic signal decomposition is proposed, consisting of the selection of a coarse set of basis functions, the search method for finding the best matching basis function, and interpolation of the basis function parameters to achieve high resolution. In addition, the use of matching pursuit is applied to the analysis of complex ultrasonic signals by interpreting the matching basis functions as characteristic wavelets. Changes in parameters of these wavelets are related to changes in the structure. The efficiency of the numerical implementation method is evaluated, and the capability of the feature extraction method for complex ultrasonic signals is demonstrated on experimental data from an aluminum plate in the context of structural health monitoring.

Parameter Estimation for Locally Linear FM Signals Using a Time-Frequency Hough Transform

Abstract: An estimator for the phase parameters of mono- and multicomponent FM signals, with both good numerical properties and statistical performance is proposed. The proposed approach is based on the Hough transform of the pseudo-Wigner-Ville time-frequency distribution (PWVD). It is shown that the numerical properties of the estimator can be improved by varying the PWVD window length. The effect of the window time extent on the statistical performance of the estimator is delineated. Experimental data is used for validation of the statistical properties.

The Wigner distribution of noisy signals with adaptive time-frequency varying window

Abstract: Time-frequency representations using the Wigner distribution (WD) may be significantly obscured by the noise in the observations. The analysis performed for the WD of discrete-time noisy signals shows that this time-frequency representation can be optimized by the appropriate choice of the window length. However, the practical value of this analysis is not significant because the optimization requires knowledge of the bias, which depends on the unknown derivatives of the WD. A simple adaptive algorithm for the efficient time-frequency representation of noisy signals is developed in this paper. The algorithm uses only the noisy estimate of the WD and the analytical formula for the variance of this estimate. The quality of this adaptive algorithm is close to the one that could be achieved by the algorithm with the optimal window length, provided that the WD derivatives were known in advance. The proposed algorithm is based on the idea that has been developed in our previous work for the instantaneous frequency (IF) estimation. Here, a direct addressing to the WD itself, rather than to the instantaneous frequency, resulted in a time and frequency varying window length and showed that the assumption of small noise and bias is no longer necessary. A simplified version of the algorithm, using only two different window lengths, is presented. It is shown that the procedure developed for the adaptive window length selection can be generalized for application on multicomponent signals with any distribution from the Cohen (1989, 1990, 1992) class. Simulations show that the developed algorithms are efficient, even for a very low value of the signal-to-noise ratio.