用于信號(hào)逼近的最佳正交子波選擇方法
CHOOSING OPTIMAL ORTHOGONAL WAVELETS FOR SIGNAL APPROXIMATION
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摘要: 離散子波變換將離散時(shí)間信號(hào)分解為一系列分辨率下的離散逼近和離散細(xì)節(jié)。緊支的正交規(guī)范子波與完全重建正交鏡象濾波器組相對(duì)應(yīng)。本文提出一種用于信號(hào)最佳逼近的正交子波選擇方法,即選擇滿足一定條件的濾波器的方法。通過(guò)對(duì)濾波器參數(shù)化,可以將帶約束的最優(yōu)化問(wèn)題轉(zhuǎn)化為無(wú)約束最優(yōu)化問(wèn)題,通過(guò)對(duì)參數(shù)在一定范圍內(nèi)的搜索,得到最優(yōu)解。文中給出了計(jì)算機(jī)模擬的結(jié)果。
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關(guān)鍵詞:
- 子波; 正交鏡象濾波器; 最佳逼近
Abstract: The discrete wavelet transform decomposes a discrete time signal into an approximation sequence and a detail sequence at each level of resolution. Compactly supported orthonormal wavelets correspond to perfect reconstruction (PR) quadrature mirror filter (QMF) banks. This paper deals with the problem of choosing orthogonal wavelet (scaling) filters for best signal approximation at some scales. By using a kind of parametrization method, the constrained optimization can be converted into an unconstrained one.Some simulations are shown here. -
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