Topic
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.
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TL;DR: The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions, chosen in order to best match the signal structures.
Abstract: The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions. These waveforms are chosen in order to best match the signal structures. Matching pursuits are general procedures to compute adaptive signal representations. With a dictionary of Gabor functions a matching pursuit defines an adaptive time-frequency transform. They derive a signal energy distribution in the time-frequency plane, which does not include interference terms, unlike Wigner and Cohen class distributions. A matching pursuit isolates the signal structures that are coherent with respect to a given dictionary. An application to pattern extraction from noisy signals is described. They compare a matching pursuit decomposition with a signal expansion over an optimized wavepacket orthonormal basis, selected with the algorithm of Coifman and Wickerhauser see (IEEE Trans. Informat. Theory, vol. 38, Mar. 1992). >
9,380 citations
Book•
01 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.
2,951 citations
Book•
15 Dec 2000
TL;DR: The topics range from the elemen- tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita- tive methods in time-frequency analysis and the theory of pseudodifferential operators.
Abstract: Time-frequency analysis is a modern branch of harmonic analysis. It com- prises all those parts of mathematics and its applications that use the struc- ture of translations and modulations (or time-frequency shifts) for the anal- ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym- metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen- tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita- tive methods in time-frequency analysis and the theory of pseudodifferential operators. This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications. The main ori- entation is toward the detailed mathematical investigation of the rich and elegant structures underlying time-frequency analysis. Time-frequency analysis originates in the early development of quantum mechanics by H. Weyl, E. Wigner, and J. von Neumann around 1930, and in the theoretical foundation of information theory and signal analysis by D.
2,626 citations
01 Jan 2003
TL;DR: In this article, it is shown that the representation of a signal in the frequency domain is well localized in frequency, but is poorly localized in time, and as a consequence it is impossible to tell when certain events occurred in time.
Abstract: Conventionally, time series have been studied either in the time domain or the frequency domain. The representation of a signal in the time domain is localized in time, i.e. the value of the signal at each instant in time is well defined. However, the time representation of a signal is poorly localized in frequency, i.e. little information about the frequency content of the signal at a certain frequency can be known by looking at the signal in the time domain. On the other hand, the representation of a signal in the frequency domain is well localized in frequency, but is poorly localized in time, and as a consequence it is impossible to tell when certain events occurred in time.
2,317 citations
TL;DR: A set of simple new procedures has been developed to enable the real-time manipulation of speech parameters by using pitch-adaptive spectral analysis combined with a surface reconstruction method in the time–frequency region.
1,741 citations