【正文】 重要應(yīng)用，自適應(yīng)信號處理主要是研究結(jié)構(gòu)可變或可調(diào)整的系統(tǒng)，可以通過自身與外界的接觸來改善自身對信號處理的性能，通常這類系統(tǒng)是時(shí)變的非線性系統(tǒng)，可以自動適應(yīng)信號傳輸?shù)沫h(huán)境和要求，無須詳細(xì)的知道信號的結(jié)構(gòu)和實(shí)際知 識，無須精確設(shè)計(jì)處理系統(tǒng)本身。s goal is to make the filter output and signal statistical average of the squared error is minimal. The criteria according to the longterm statistical characteristics of the input data for optimal filter. Least squares method for different data sets derived different best filter. Thus derived the optimum filter often say leastsquare method is accurate. Recursive least squares (RLS) is a fast algorithm of the leastsquare method. this paper studies the performance of the filter input and SNR and simulation based on matlab. Convergence analysis and filtering effect by experiment, confirmed the filter selection of regularization coefficient, high SNR regularization coefficient selected normal number, instead take dazheng constant. For different types of filter input signal independent experiment, the cycle model and aperiodic signal filter effects are better, but the periodic signal filtering effect is better. But look from the program39。 但從程序的運(yùn)行時(shí)間上看，其復(fù)雜度高，計(jì)算量比較大。通過對比實(shí)驗(yàn)，分析收斂性和濾波效果，確定了濾波器正則化系數(shù)的選取，信噪比高正則化系數(shù)選取小正常數(shù)，反之取大正常數(shù)。遞推最小二乘法 (RLS)是最小二乘法的一類快速算法。最小二乘法對不同的數(shù)據(jù)組導(dǎo)出不同的“最佳”濾波器。自適應(yīng)算法的目標(biāo)在于，使濾波器輸出與需要信號的誤差的平方的統(tǒng)計(jì)平均值最小。這就是著名的最小二乘法。 I 摘 要 最小二乘 (RLS)法是一種典型的有效的數(shù)據(jù)處理方法。由著名學(xué)者高斯在 1795 年提出，他認(rèn)為根據(jù)所獲得的觀測數(shù)據(jù)來推斷未知參數(shù)時(shí)，未知參數(shù)最可能的值是這樣一個數(shù)據(jù)，即它使各項(xiàng)實(shí)際觀測值和計(jì)算值之間的差的平方乘以度量其精度的數(shù)值以后的和為最小。自適應(yīng)濾波算法根據(jù)的最佳準(zhǔn)則為最小均方誤差準(zhǔn)則。這個準(zhǔn)則根據(jù)輸入數(shù)據(jù)的長期統(tǒng)計(jì)特性尋求最佳濾波。因而常說最小二 乘法導(dǎo)出的最佳濾波器是“精確”的。 本文基于 matlab 進(jìn)行仿真，研究不同輸入和信噪比濾波器的性能。對不同類型濾波器輸入信號獨(dú)立實(shí)驗(yàn)，周期型號和非周期信號的濾波器效果都較好，但周期信號的濾波效果更好。 關(guān)鍵詞 ： 自適應(yīng)濾波器，最小二乘法， matlab 仿真 II Abstract Least squares (RLS) method is a kind of typical effective data processing method. Gauss proposed in 1795 by famous scholars, he thinks, according to the observed data to infer unknown parameter is obtained, the unknown parameters is the most possible values that a data, which make the actual observed value multiplied by the square measure of the difference between calculated value and the accuracy of numerical and later to a minimum. This is the famous leastsquare filtering algorithm based on optimum criterion for the minimum mean square error criterion. Adaptive algorithm39。s running time, its plexity is high, the relatively large amount of calculation. Key words： Adaptive filtering, the least square method, emulation verify by MATLAB 目 錄 第一章 前言 ..................................................................................................................... 1 自適應(yīng)濾波器簡介 ............................................................................................. 1 選題背景及研究意義 ......................................................................................... 1 國內(nèi)外研究發(fā)展現(xiàn)狀 ......................................................................................... 2 第二章 自 適應(yīng)濾波器的基礎(chǔ)理論 ................................................................................. 4 濾波器概述 ......................................................................................................... 4 濾波器簡介 ....................................................................................................4 濾波器分類 ....................................................................................................4 數(shù)字濾波 器概述 .............................................................................................4 自適應(yīng)濾波器基本理論 ..................................................................................... 7 自適應(yīng)濾波器的結(jié)構(gòu) ......................................................................................... 9 第三章 自適應(yīng)濾波器遞歸最小二乘算法 ....................................................................11 遞歸最小二乘算法 ............................................................................................11 遞歸最小二乘算法簡介 ................................................................................. 11 正則方程 ...................................................................................................... 11 加權(quán)因子和正則化 ........................................................................................ 16 遞歸計(jì)算 ...................................................................................................... 18 遞歸最小二乘 (RLS)算法的性能分析 .............................................................. 22 第四章 基于 MATLAB 自適應(yīng)濾波器仿真 ..................................................................... 23 正弦波去噪實(shí)驗(yàn) ............................................................................................... 23 濾波器正則化參數(shù)的確定 ............................................................................... 28 高信噪比 ...................................................................................................... 28 低信噪比 ...................................................................................................... 31 結(jié)論 ............................................................................................................. 33 輸入信號不同對濾波效果的影響 ................................................................... 33 輸入信號為周期信號 .................................................................................... 33 輸入信號為非周期信號 ................................................................................. 38 第五章 結(jié)論與展望 ....................................................................................................... 44 結(jié)論 ................................................................................................................... 44 對進(jìn)一步研究的展望 ....................................................................................... 44 參考文獻(xiàn) ......................................................................................................................... 45 致 謝 ............................................................................................................................... 46 附 錄