What question did this study set out to answer?

Establish the relationship between Fourier spectra and wavelet-derived spectra and define the mathematical constraints required for meaningful wavelet spectral estimation.

March 1, 1995Journal of Mathematical Physics

Wavelet spectra compared to Fourier spectra

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Authors

VPValérie PerrierInstitut polytechnique de Grenoble TPThierry PhilipovitchCentre National de la Recherche Scientifique CBClaude BasdevantCentre National de la Recherche Scientifique

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Implication

Mathematical analysis demonstrates conditions linking wavelet and Fourier spectra across signal spaces, suggesting vanishing moment requirements for meaningful spectral representation.

Key Points

Establish the relationship between Fourier spectra and wavelet-derived spectra and define the mathematical constraints required for meaningful wavelet spectral estimation.
Conducted small-scale asymptotic analysis to evaluate the correspondence between wavelet and Fourier spectra.
Applied regularity theorems within Besov spaces to assess spectral validity across different signal smoothness classes.
Demonstrated that wavelet spectra are mathematically meaningful only when the analyzing wavelet possesses an adequate number of vanishing moments.
Formulated a new wavelet featuring an infinite number of cancellations designed specifically for analyzing infinitely regular signals.

Cite This Study

Perrier et al. (1995) studied this question.

synapsesocial.com/papers/6a74c327f1e99ff85ab1cc00 https://doi.org/10.1063/1.531340

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Implication

Mathematical analysis demonstrates conditions linking wavelet and Fourier spectra across signal spaces, suggesting vanishing moment requirements for meaningful spectral representation.

Wavelet spectra compared to Fourier spectra

Discussion

Member takes

Implication

Key Points

Cite This Study

Wavelet spectra compared to Fourier spectra

Discussion

Member takes

Implication

Key Points

Cite This Study

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