隨機(jī)分形信號(hào)參數(shù)的分?jǐn)?shù)差分估計(jì)
FRACTIONAL DIFFERENCE ESTIMATION FOR THE PARAMETERS OF RANDOM FRACTAL SIGNAL
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摘要: 本文首先簡(jiǎn)要介紹隨機(jī)分形信號(hào)的定義、性質(zhì)和時(shí)域表達(dá)式。接著采用差分算子替代微分算子,導(dǎo)出隨機(jī)分形序列的分?jǐn)?shù)差分方程,構(gòu)造和分析了使隨機(jī)分形信號(hào)通過后變?yōu)榘自肼暤姆謹(jǐn)?shù)差分白化濾波器。最后提出基于該濾波器的參數(shù)估計(jì)方法,其實(shí)質(zhì)是通過計(jì)算輸出信號(hào)的統(tǒng)計(jì)測(cè)試表達(dá)式的極值獲得分形參數(shù)。實(shí)驗(yàn)結(jié)果表明該方法有效。Abstract: The definition, property and time-domain expression of random fractal signal are introduced in brief. The fractional difference equation of random fractal series is induced by substituting difference operator for differential operator, and the fractional differenced whiten-ing filter, through which random fractal signal is converted to white noise, is analyzed and constructed. The method for parameters estimation based on fractional differenced whitening filter is proposed, the essentiality of which is to find out a factor by calculating the extremum of the statistic test expression for the output. Experimental results demonstrate its effectiveness.
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