新的低複雜度之適應性訊處理演算法

Abstract

在本論文中，提出三種低複度之新適應性濾波器架構：其中包括多頻率 ( muti-rate )適應性濾波器架構，相乘性脈衝 ( MFIR ) 適應性濾波器 架構，以及新快速 ( New decomposed ) 適應性濾波器架構。在濾波器長 度為Ｎ情況下，多頻率適應性架構可降低四分之一Ｎ乘法量以及加法量， 另外新快速適應性濾波器架構則可以降低二分之一Ｎ的乘法量。相乘性有 限脈衝適應性濾波器架構若是和有限脈衝（ＦＩＲ）適應性濾波器架構比 較起來則可以節省指數比例的運算量除了一維的適應性濾波器架構之外， 在本論文中還將這些適應性濾波器架構擴展到二維的架構。因此，此三種 適應性濾波器架構可根據他們的特性，應用在適應性濾波器的處理上。諸 如，系統辨認（ @SYSTEM IDENTIFICATION)，雜訊(Noise Cancellation) 等等。 In this thesis, three mew efficient adaptive filtering algorithm:the muti-rate adaptive filtering algorithm,the MFIR (mutiplicative finite impulse response) adaptive filtering algorithm, and new decomposed adaptive filtering algorithms are proposed. They all can efficiently reduce the complexity of the adaptive filter. The muti-rate adaptive algorithm can reduce N/4 multiplications and additions while the new decomposed algorithm can reduce N/2 multiplications if the filter length is N, compared with the direct form LMS adaptive algorithm. Not only the one dimensional adaptive algorithm is proposed, but also the 2-dimensional adaptive algorithms for multi-rate and the new decomposed adaptive filtering are also derived successfully. They are attractive to most of the adaptive signal processing applications, such as inverse filtering, system identification, noise cancellations, and 2-D line enhancing,just to name a few.