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Overcompleteness is a concept from linear algebra that is widely used in mathematics, computer science, engineering, and statistics (usually in the form of overcomplete frames). It was introduced by R. J. Duffin and A. C. Schaeffer in 1952. Formally, a subset of the vectors $${\displaystyle \{\phi _{i}\}_{i\in J}}$$ 展开
The theory of frames originates in a paper by Duffin and Schaeffer on non-harmonic Fourier series. A frame is defined to be a set of non-zero vectors $${\displaystyle \{\phi _{i}\}_{i\in J}}$$ such that for an arbitrary 展开
In modern analysis in signal processing and other engineering field, various overcomplete frames are proposed and used. Here two common used frames, Gabor frames and wavelet … 展开
Overcomplete Gabor frames and Wavelet frames have been used in various research area including signal detection, image representation, … 展开
CC-BY-SA 许可证中的维基百科文本 Density, Overcompleteness, and Localization of Frames. II. Gabor …
网页2005年10月17日 · New results are obtained on the excess and overcompleteness of Gabor frames, on the relationship between frame bounds and density, and on the structure of …
网页Gabor frame, the HAP essentially states that the rate of approximation of a given function by Gabor frame elements is invariant under time-frequency shifts of the function. This is …
网页new results are obtained on the excess and overcompleteness of frames, on the relationship between frame bounds and density, and on the structure of the dual frame …
Gabor transform | Wikipedia
The Gabor transform, named after Dennis Gabor, is a special case of the short-time Fourier transform. It is used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. The function to be transformed is first multiplied by a Gaussian function, which can be regarded as a window function, and the resulting function is then transformed with a Fourie…
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网页for Gabor frames are recovered as special cases, and in the process both their meaning and implications are clarified. New results are obtained on the excess and …
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网页presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames F = …
网页Gabor frames are recovered as special cases, but in the process both their meaning and implications are clarified. New results are obtained on the excess and …
Gabor Frames: Characterizations and Coarse Structure
网页2019年11月27日 · This chapter offers a systematic and streamlined exposition of the most important characterizations of Gabor frames over a lattice.
Density, Overcompleteness, and Localization of Frames. II. Gabor ...
网页New results are obtained on the excess and overcompleteness of Gabor frames, on the relationship between frame bounds and density, and on the structure of the dual frame …
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