What question did this study set out to answer?

Investigate the asymptotic properties of a family of nonorthogonal polynomial spline wavelet transforms and evaluate their convergence to Gabor functions.

March 1, 1992IEEE Transactions on Information Theory

On the asymptotic convergence of B-spline wavelets to Gabor functions

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Authors

MUMichaël UnserBharathiar University AAAkram AldroubiVanderbilt University MEM. EdenUnited States Department of Health and Human Services

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Implication

Mathematical analysis demonstrates asymptotic convergence of polynomial B-spline wavelets to Gabor functions, highlighting optimal time-frequency localization.

Key Points

Investigate the asymptotic properties of a family of nonorthogonal polynomial spline wavelet transforms and evaluate their convergence to Gabor functions.
Analyzed a family of fully reversible, computationally efficient nonorthogonal polynomial spline wavelet transforms with compactly supported wavelet functions.
Performed analytical proofs evaluating asymptotic behavior, pointwise convergence, and convergence across Lp norms.
Proved that compactly supported B-spline wavelets converge asymptotically to Gabor functions (modulated Gaussians).
Demonstrated that convergence holds both pointwise and across all relevant Lp norms.

Cite This Study

Unser et al. (1992) studied this question.

synapsesocial.com/papers/6a6f3b12a528af2d65c2e29d https://doi.org/10.1109/18.119742

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Implication

Mathematical analysis demonstrates asymptotic convergence of polynomial B-spline wavelets to Gabor functions, highlighting optimal time-frequency localization.

On the asymptotic convergence of B-spline wavelets to Gabor functions

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Member takes

Implication

Key Points

Cite This Study

On the asymptotic convergence of B-spline wavelets to Gabor functions

Discussion

Member takes

Implication

Key Points

Cite This Study

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