【正文】 50輸入信號(hào) a0 1000 2020 3000 4000 5000 6000 7000 8000 9000 2 00204060期望信號(hào) d 0 50 100 150 200 250 300 350 400 450 500 0 . 100 . 10 . 20 . 3L M S 輸出信號(hào) w50 100 150 200 250 300 350 400 450 500 5 0050DCT 輸出信號(hào) y 0 1000 2020 3000 4000 5000 6000 7000 8000 9000 1 001020304050誤差 E 隨著自適應(yīng)算法迭代次數(shù)的增加，濾波器輸出估計(jì)誤差逐漸變小 。DCT 輸出信號(hào) y39。輸入信號(hào) a39。輸入信號(hào) a39。*w。 w=zeros(N,1)。 d=zeros(1,length+N)。 a=zeros(1,length+N)。 仿真結(jié)果圖： 0 0 . 0 2 0 . 0 4 0 . 0 6 0 . 0 8 0 . 1 0 . 1 2 0 . 1 4 0 . 1 6 0 . 1 8 0 . 2101原始信號(hào)0 50 100 150 200 250505DCT 輸出信號(hào)0 50 100 150 200 250505D C T 壓縮后的信號(hào)0 0 . 0 2 0 . 0 4 0 . 0 6 0 . 0 8 0 . 1 0 . 1 2 0 . 1 4 0 . 1 6 0 . 1 8 0 . 2202恢復(fù)的信號(hào) 可以看出，當(dāng)波形數(shù)據(jù)做 DCT 變換后壓縮到原數(shù)據(jù)的 %左右時(shí) ，根據(jù)壓縮信號(hào)重建的時(shí)域波形存在失真，但在工程上這樣的失真是允許的。plot(t,z)。DCT 壓縮后的信號(hào) 39。 y1=y.*(abs(y))。 plot(y)。原始信號(hào) 39。x=sawtooth(2*pi*45*t)。在傅立葉級(jí)數(shù)展開式中，如果被展開的函數(shù)是實(shí)偶函數(shù)，那么其傅立葉級(jí)數(shù)中只包含余弦項(xiàng)，再將其離散化可導(dǎo)出余弦變換，因此稱之為離散余弦變換 。 詳細(xì)算法如下所示。 針對(duì) LMS 算法存在特征值 分散度的問題，我們可以采用牛頓法來進(jìn)行克服，牛頓法使得濾波器各系數(shù)（各收斂模式）的收斂速度一致，與特征值分布無關(guān)，從根本上消除了最陡梯度下降法受特征值分布影響的缺陷。表 1 詳細(xì)地給出 LMS 算法，其中 x(n)為 n 時(shí)刻濾波器的輸入信號(hào)， w(n)為n 時(shí)刻的濾波器系數(shù)， y(n)為濾波器的輸出信號(hào) ， d(n)為濾波器的期望信號(hào)， e(n)為濾波器的估計(jì)誤差 ， u 為更新步長(zhǎng) 。 自適應(yīng)信號(hào)處理論文 基于 MATLAB 的自適應(yīng)濾波算法 研究 摘要 ： 自適應(yīng)濾波算法是自適應(yīng)濾波器設(shè)計(jì)的核心部分，本文主要介紹了 兩種算法： LMS 算法 和 DCT 變換。 LMS算法是在最陡下降法的基礎(chǔ)上導(dǎo) 出的，可以說 LMS 算法是最陡下降法的隨機(jī)實(shí)現(xiàn)。這必然導(dǎo)致其它收斂模式的收斂速度下降，輸入信號(hào)自相關(guān)矩陣 R 的特征值分散度在很大程度上影響了算法 的收斂性能 。TDAF 就是變換域中的 LMS 算法，所以也稱為 TDLMS 算法。 DCT 變換 離散余弦變換（ Discrete Cosine Transform ，簡(jiǎn)稱 DCT ） 變換 是一種與傅 立葉變換緊密相關(guān)的數(shù)學(xué)運(yùn)算。 一維 N 點(diǎn) 離散余弦 變換 (DCT)可表示為： 10( 2 1 )c o s 2Nk k nnnky C x N ????? ? 其中， xn 是輸入時(shí)域序列中的第 n 項(xiàng)， yk 是輸出頻域序列的第 k 項(xiàng)，系數(shù) Ck定義如下： 102 1 , 2 , ..., 1kNkCN k N? ??? ????? 一維 N 點(diǎn)離散余弦逆變換 (IDCT)可以表示為： 10( 2 1 )c o s 2Nn k knnkx C y N ????? ? MATLAB 仿真 實(shí)驗(yàn) DCT 變換對(duì)語音信號(hào)的壓縮 DCT 變換的 MATLAB 實(shí)現(xiàn)方法，基于 FFT 的快速算法 ， 這是通過 MATLAB 工具箱提供的 dct 和 idct 函數(shù)實(shí)現(xiàn)的 ，仿真結(jié)果如下 程序： t=0:1/1000:。title(39。 %DCT 變換輸出 subplot(4,1,2)。)。title(39。 %DCT 反變換 subplot(4,1,4)。)。%設(shè)置信號(hào)長(zhǎng)度 N=500。%產(chǎn)生輸入信號(hào) end end %%%%% LSM 算法 %%%%%%%%%%%%%%%%%%%%% a=a39。%產(chǎn)生期望信號(hào) end end d=d39。 %收斂因子 for i=1:length E(i)=d(i)a(i:i+N1)39。% DCT 變換 %%%%% 畫圖 %%%%%%%%%%%%%%%%%%%%%%%% figure:subplot(211),plot(a),title(39。) figure:subplot(211),plot(a),title(39。) subplot(212),plot(y),title(39。)。 TDAF 對(duì)特征值分散度不敏感，在特征值分散度大的情況下，仍然保持了很快的收斂速度。道爾完成了 《 福爾摩斯偵探集 》 的第一篇小說《血字的研究》。道爾在 1886年至 1927 年創(chuàng)作的 《 福爾摩斯偵探集 》 中的前四部 為基礎(chǔ)， 即《血字的研究》、《四 簽名》、《冒險(xiǎn)經(jīng)歷》以及《回憶錄》，以文本分析的方法， 通過 分析 小說中 對(duì)倫敦各方面的描寫， 結(jié)合相關(guān)的歷史文獻(xiàn)資料，研究維多利亞時(shí)期的倫敦 ，還原其當(dāng)時(shí)的面貌， 并挖掘其隱藏的形象， 為讀者呈現(xiàn)一個(gè)福爾摩斯真正“生活”過的倫敦 。 Sherlock Holmes。700 today) to his name, he set up a medical practice at 1 Bush Villas in Elm Grove, Southsea. The practice was initially not very successful. While waiting for patients, Conan Doyle again began writing stories1. For his great work, the tales of Sherlock Holmes, he was recognized as one of the most important detective novel writers. He successfully created a ―consulting detective‖—Sherlock Holmes, who was cold and full of talent, and finally became the symbol of detectives. Actually, Sir Arthur Conan Doyle wrote many other kinds of works, like plays, poetry, romances, fantasy and science fiction stories, nonfiction and historical novels. Joshua Hammer said in his journal paper—Sherlock Holmes39。 and I hope modern readers will sympathize with the pedestrians plagued by prams, and infuriated by the postal service, even if our forebears had slightly higher standards.‖(Lee Jackson, 2020: 12) It must make a help to study the London of Victorian Era. By the way, the website ―Wikipedia‖ provides the related information, too. The domestic scholars‘ studies in this field are meritorious. Li Zeng and his partner Long Ruicui study the classes system in Victorian Era in their The Shift of Dominative Moral Trend in Victorian Britain. They point out that ―… the people essentially establish their moral trends with their real social estate in the class system…‖ (Li Zeng and Long Ruicui, 2020: 190) This thesis provides some references to the social class system in Victorian Era. Liu Xiaohan‘s study, The colonialism London in Holmes’s Eyes which is published in ANHUIWENXUE, presents the side of colonialism in London of Victorian Era. ―Industrialization, Urbanization and Colonialism 寧波大學(xué)科學(xué)技術(shù)學(xué)院本科畢業(yè)設(shè)計(jì)（論文） 10 change the original structure of London, and the cultures which e from colonies, as same as drugs, are injected into the heart of the developed empire.‖(Liu Xiaohan, 2020: 22) It is worth mentioning, she realizes the side of hero from Sherlock Holmes in this study. ―… Holmes represents the scientific and rational. He tries his best to dislodge all the colonialism poisons which are invading his mind and recovers the original British cultures and orders.‖(Liu Xiaohan, 2020: 22) Wang Ting‘s Complete Sherlock Holmes: the Panorama Gram of Victorian Era studies various aspects in Victorian Era with the descriptions in Conan Doyle‘s tales of Sherlock Holmes. ―The popularity of Complete Sherlock Holmes is not only for its attractive stories, but also for its making readers understand a real London, a real Victorian Era.‖(Wang Ting, 2020: 104) Wang Ting analyzes the economy, science, culture, social classes and the minds of the public. What is more, Wang Ting realizes the change of women‘s power in this work. ―The women widely expend their views and realize the importance to strive the rights for themselves. The Feminist Consciousness is awakening.‖(Wang Ting, 2020: 106) The points in the thesis are useful in this study, providing the detailed date of Victorian Era. Feng Xinhua holds that the word ―gentleman‖ originates in Victorian Era. Yu Xiaoqun points the Sherlock Holmes‘ influences to the society in Victorian Era in his Discussion on the Social Condition of Holmes