1/f信号的积分多小波变换表示
Integral Multiwavelet Representation of 1/f Signal
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摘要: 在积分多小波变换理论的基础上，研究了1/f信号的积分多小波变换表示，给出了用积分多小波逆变换产生1/f信号(非近似1/f信号)的条件。并对1/f信号的积分多小波变换的统计特性进行了研究，证明1/f信号的统计自相似性在多小波域内可由积分多小波系数的自相关函数矩阵来表达。基于单小波变换的1/f信号表示是其特例。Abstract: Based on the theory of integral multiwavelet transformation, the representation of 1/f signal (not near-1/f signal) is explored by inverse integral multiwavelet transforma-tion, and the conditions of representing 1/f signal are acquired. The statistical characteris-tics of integral multiwavelets transformation are studied, and it is proved that the self-similar characteristics of 1/f signal can be represented by the autocorrelation matrix of coefficients of integral multiwavelet in multiwavelet domain. The representation of 1/f signal by singular wavelet is only the special case of the representation.
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