Journal ArticleDOI
Time-frequency distributions with complex argument
TLDR
It is shown that the estimation can be improved with respect to the Wigner distribution based one since the bias can be significantly reduced with only a slight increase of the variance.Abstract:
A distribution highly concentrated along the group delay or the instantaneous frequency (IF) is presented. It has been defined by introducing a signal with a complex argument in time-frequency (TF) analysis. Realization of a signal with a complex argument, using a signal with a real argument, is described. The reduced interference realization of the complex argument distribution, in the case of multicomponent signals, is presented. The proposed distribution is used for the IF estimation. It is shown that the estimation can be improved with respect to the Wigner distribution based one since the bias can be significantly reduced with only a slight increase of the variance. The theory is illustrated by examples.read more
Citations
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Time-Frequency Signal Analysis and Processing: A Comprehensive Reference
TL;DR: Time Frequency Signal Analysis and Processing focuses on advanced techniques and methods that allow a refined extraction and processing of information, allowing efficient and effective decision making that would not be possible with classical techniques.
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Time--frequency feature representation using energy concentration: An overview of recent advances
TL;DR: Time-frequency domain signal processing using energy concentration as a feature is a very powerful tool and has been utilized in numerous applications and the expectation is that further research and applications of these algorithms will flourish in the near future.
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TL;DR: Introduction to Fourier Analysis Linear Time-Frequency Representations Quadratic Time- frequency Distributions Higher Order Time-f frequency Representations Analysis of Non-Stationary Noisy Signals Some Applications of Time- Frequency Analysis.
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Synchrosqueezing-based time-frequency analysis of multivariate data
TL;DR: The modulated oscillation model is extended to multivariate signals, in order to identify oscillations common to multiple data channels, by introducing a multivariate extension of the synchrosqueezing transform, and using the concept of joint instantaneous frequency multivariate data.
References
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Journal ArticleDOI
Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals
TL;DR: The concept of instantaneous frequency (IF), its definitions, and the correspondence between the various mathematical models formulated for representation of IF are discussed in this paper, and the extent to which the IF corresponds to the intuitive expectation of reality is also considered.
Journal ArticleDOI
Improving the readability of time-frequency and time-scale representations by the reassignment method
François Auger,Patrick Flandrin +1 more
TL;DR: The reassignment method, first applied by Kodera, Gendrin, and de Villedary (1976) to the spectrogram, is generalized to any bilinear time-frequency or time-scale distribution.
Journal ArticleDOI
The discrete polynomial-phase transform
S. Peleg,Benjamin Friedlander +1 more
TL;DR: The authors define the discrete polynomial-phase transform, derive its basic properties, and use it to develop computationally efficient estimation and detection algorithms.
Journal ArticleDOI
A method for time-frequency analysis
TL;DR: This method provides some substantial advantages over the Wigner distribution, including the fact that the well-known cross term effects are reduced or completely removed, and the computation time can be significantly shorter.
Book
Basic Complex Analysis
TL;DR: This book combines an exposition of basic theory with a variety of applications to the physical sciences and engineering for mathematics, engineering and physical science students taking complex analysis for the first time.