Topic
Time–frequency representation
About: Time–frequency representation is a research topic. Over the lifetime, 496 publications have been published within this topic receiving 13735 citations.
Papers published on a yearly basis
Papers
Book•
1 Jan 1995
TL;DR: In this article, the authors present a general approach and the Kernel Method for reduced interference in the representation of signal signals, which is based on the Wigner distribution and the characteristic function operator.
Abstract: 1. The Time and Frequency Description of Signals. 2. Instantaneous Frequency and the Complex Signal. 3. The Uncertainty Principle. 4. Densities and Characteristic Functions. 5. The Need for Time-Frequency Analysis. 6. Time-Frequency Distributions: Fundamental Ideas. 7. The Short-Time Fourier Transform. 8. The Wigner Distribution. 9. General Approach and the Kernel Method. 10. Characteristic Function Operator Method. 11. Kernel Design for Reduced Interference. 12. Some Distributions. 13. Further Developments. 14. Positive Distributions Satisfying the Marginals. 15. The Representation of Signals. 16. Density of a Single Variable. 17. Joint Representations for Arbitrary Variables. 18. Scale. 19. Joint Scale Representations. Bibliography. Index.
2,977 citations
TL;DR: A systematic review of over 20 major time-frequency analysis methods reported in more than 100 representative articles published since 1990 can be found in this article, where their fundamental principles, advantages and disadvantages, and applications to fault diagnosis of machinery have been examined.
901 citations
TL;DR: It is shown that feature sets based upon the short-time Fourier transform, the wavelets transform, and the wavelet packet transform provide an effective representation for classification, provided that they are subject to an appropriate form of dimensionality reduction.
686 citations
TL;DR: A new time-frequency distribution that adapts to each signal and so offers a good performance for a large class of signals is introduced that is formulated in Cohen's class as an optimization problem and results in a special linear program.
Abstract: A new time-frequency distribution (TFD) that adapts to each signal and so offers a good performance for a large class of signals is introduced. The design of the signal-dependent TFD is formulated in Cohen's class as an optimization problem and results in a special linear program. Given a signal to be analyzed, the solution to the linear program yields the optimal kernel and, hence, the optimal time-frequency mapping for that signal. A fast algorithm has been developed for solving the linear program, allowing the computation of the signal-dependent TFD with a time complexity on the same order as a fixed-kernel distribution. Besides this computational efficiency, an attractive feature of the optimization-based approach is the ease with which the formulation can be customized to incorporate application-specific knowledge into the design process. >
322 citations
TL;DR: A data-adaptive time-frequency representation is developed that overcomes some limitations of the short-time Fourier transform, while avoiding the cross-terms that make the Wigner distribution and other bilinear representations difficult to interpret.
Abstract: A data-adaptive time-frequency representation is developed that overcomes some limitations of the short-time Fourier transform, while avoiding the cross-terms that make the Wigner distribution and other bilinear representations difficult to interpret. The adaptive time-frequency representations uses Gaussian basis functions but varies their time width and chirp rate with time and frequency to achieve high signal concentration everywhere. A measure of local signal concentration allows fully automated determination of the optimal basis parameters. The adaptive method is computationally expensive, but may provide much better performance than any currently known technique. >
294 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 1 |
| 2024 | 2 |
| 2023 | 12 |
| 2022 | 19 |
| 2021 | 23 |
| 2020 | 10 |