The wavelet transform, time-frequency localization and signal analysis

@article{Daubechies1990TheWT,
  title={The wavelet transform, time-frequency localization and signal analysis},
  author={Ingrid Daubechies},
  journal={IEEE Trans. Inf. Theory},
  year={1990},
  volume={36},
  pages={961-1005}
}
  • I. Daubechies
  • Published 1 September 1990
  • Physics
  • IEEE Trans. Inf. Theory
Two different procedures for effecting a frequency analysis of a time-dependent signal locally in time are studied. [] Key Method The similarities and the differences between these two methods are discussed. For both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time-frequency density. Finally, the notion of time-frequency localization is made precise, within this framework, by two localization theorems. >

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References

SHOWING 1-10 OF 75 REFERENCES

Time-frequency localization operators: A geometric phase space approach

The author defines a set of operators which localize in both time and frequency. These operators are similar to but different from the low-pass time-limiting operator, the singular functions of which

THE WIGNER DISTRIBUTION - A TOOL FOR TIME-FREQUENCY SIGNAL ANALYSIS

In this second part of the paper the Wigner distribution is adapted to the case of discrete-time signals. It is shown that most of the properties of this time-frequency signal representation carry

Time-frequency localisation operators-a geometric phase space approach: II. The use of dilations

Operators which localise both in time and frequency are constructed. They restrict to a finite time interval and cut off low as well as high frequencies (band-pass filters). Explicit expressions for

Multifrequency channel decompositions of images and wavelet models

  • S. Mallat
  • Computer Science
    IEEE Trans. Acoust. Speech Signal Process.
  • 1989
The author describes the mathematical properties of such decompositions and introduces the wavelet transform, which relates to the decomposition of an image into a wavelet orthonormal basis.

A Theory for Multiresolution Signal Decomposition: The Wavelet Representation

  • S. Mallat
  • Computer Science
    IEEE Trans. Pattern Anal. Mach. Intell.
  • 1989
It is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2/Sup j/ can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions.

Analysis of Sound Patterns through Wavelet transforms

The main features of so-called wavelet transforms are illustrated through simple mathematical examples and the first applications of the method to the recognition and visualisation of characteristic features of speech and of musical sounds are presented.

A Sampling Theorem For The Complex Spectrogram, And Gabor's Expansion Of A Signal In Gaussian Elementary Signals

The complex spectrogram of a signal is defined as the Fourier transform of the product of the signal and the shifted and complex conjugated version of a so-called window function; it is thus a

Wave propagation and sampling theory—Part II: Sampling theory and complex waves

Morlet et al (1982, this issue) showed the advantages of using complex values for both waves and characteristics of the media. We simulated the theoretical tools we present here, using the

Wavelet Transform Analysis of Invariant Measures of Some Dynamical Systems

The wavelet transform is presented as a mathematical microscope which is well suited for studying the local scaling properties of fractal measures and is applied to probability measures on self-similar Cantor sets, to the 2∞ cycle of period-doubling and to the golden-mean trajectories on two-tori at the onset of chaos.

Sampling Theorem For The Complex Spectrogram, And Gabor's Expansion Of A Signal In Gaussian Elementary Signals

The complex spectrogram of a signal φ(t) is defined by ∫φ(t)g*(t-to)exp[-iwot]dt ; it is, in fact, the Fourier transform of the product of the signal and the complex conjugated and shifted version of
...