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The Stability of Gabor Frames with Arbitrary Time-frequency Parameters

Author: DangYunGui
Tutor: HeXingGang
School: Central China Normal University
Course: Applied Mathematics
Keywords: Gabor frames stability time-frequency parameters
CLC: O174.2
Type: Master's thesis
Year: 2011
Downloads: 34
Quote: 0
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Abstract


Wavelet analysis is a branch of applied mathematics. Frame theory is an impotant part of the wavelet analysis. The stability of frames is one of the main research of frame theory. Gabor frames with arbitrary time-frequency parameters have been widely used in time-frequency analysis, quantum mechanics, communication theory, and many other fields. Therefore, we need necessitily study the stability.In this paper we study:if the windowed function g(x) satisfies:g(x), xg(x), x2g(x)∈H2, Gabor frames{eibnxg(x-an):n∈Z} with arbitrary time-frequency param-eters are stable. It remains a frame when the windowed function g(x) has some small perturbation, and explicit stability bounds are given.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions > Fourier analysis ( classical harmonic analysis )
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