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Discuss the Method of Choice and Construction of Wavelet Bases

Author: BianWei
Tutor: XiaoQing
School: Northeast Normal University
Course: Circuits and Systems
Keywords: Wavelet Tight frame Orthonormal basis
CLC: TN911.7
Type: Master's thesis
Year: 2007
Downloads: 300
Quote: 16
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Abstract


Wavelet analysis is a new subject in recent years and also in a near future it is also a hotspot. Wavelet analysis has been shown to be useful mathematical tool for many practical applications and become to focus of attention recently.Wavelet transform is a good analytical method in the time domain and the frequency domain, especially applicable for non-stationary signal processing. However, how to choose proper biorthogonal wavelet bases and its scale tection in the wavelet transform is an important and disputable issue. It is based on the fact that the wavelet is similar with the signal to be analyzed in regularity .That means we can use smooth wavelet to present smooth signal and singular one to present nonsmooth signal.The relation between frame and orthonormal bases is discussed and a new method for constructing the wavelet basis based on the wavelet frame is also presented. An orthonormal wavelet basis is constructed. It has relatively good time-frequency localization as well as is orthonormal.

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