【正文】 in part by the Natural Sciences and Engineering Research Council of Canada. This paper was remended by Associate Editor . The authors are with the Department of Electrical and Computer Engineering, University of Windsor, Windsor, ON N9B 3P4,Canada employ the Steiglitz–McBride scheme to approach the optimal solution in some sense. Although,so far, the convergences of these methods cannot be strictly guaranteed, many examples in literature have shown their effectiveness. In this paper, we adopt the same iterative procedure using the Steiglitz–McBride scheme to design IIR digital filters. Stability is an important issue for IIR digital filter design. Recently, some positiverealnessbased andthe Rouch233。 學生簽名： 日 期： 年 月 日 2020 屆 本科生畢業(yè)設計（ 論文）資料 第二部分 外文資料翻譯 1 IIR Digital Filter Design With New Stability Constraint Based on Argument Principle Abstract—This paper presents a weighted least squares(WLS) method for IIR digital filter design using a new stability constraint. Utilizing the reweighting technique, an iterative secondorder cone programming(SOCP)method is employed to solve the design problem, such that either linear or secondorder cone constraints can be further incorporated. In order to guarantee the stability of designed IIR digital filters, a new stability constraint with a prescribed pole radius is derived from the argument principle(AP) of plex analysis. As pared with other frequencydomain stability constraints, the APbased stability constraint is both sufficient and necessary. Since the derived stability constraint cannot be directly incorporated in the iterative SOCP method, the similar reweighting technique is deployed to approximate the stability constraint in a quadratic form, which is then bined with the WLS iterative design process. Filter design examples are presented to demonstrate the effectiveness of the proposed iterative SOCP method. Index Terms—Argument principle(AP),infinite impulse response(IIR)digital filters, reweighting techniques, secondorder cone programming(SOCP),weighted least squares(WLS) approximation. I. INTRODUCTION COMPARED with FIR digital filter design, the major difficulties for designing an IIR digital filter are its nonlinearity and stability problems. Many algorithms have been developed to implement stable IIR digital filters. Some approaches[1]–[6]implement filters in an indirect way, ., an FIR digital filter satisfying the filter specifications is designed first, and then, model reduction techniques are applied to approximate the FIR digital filter by a reducedorder IIR digital filter. In such indirect designs, approximation procedures can substantially guarantee the stability of designed IIR digital filters, which facilitates the design procedures. However, it is difficult to design filters with accurate cutoff frequencies using this design strategy. Recently, many other algorithms have been proposed to design IIR digital filters in a direct way, which means that the cost function of the design problem is directly based on the ideal frequency responses. In order to tackle such a nonlinear design problem, some iterative methods. 2 Manuscript received October 25,2020。同時對軟件開發(fā)也有了更為全面的了解，通過自己的努力思考、學習研究與 指導 老師的認真指導，使自己的能力得到了進一步鍛煉與提高。 結(jié)果分析 從界面操作可以看出，該設計預測達到了以下要求。 end function pushbutton3_Callback(hObject, eventdata, handles) function axes1_CreateF(hObject, eventdata, handles) function axes1_DeleteF(hObject, eventdata, handles) % hObject handle to axes1 (see GCBO) % eventdata reserved to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)[7] 長沙學院畢業(yè)設計 (論文 ) 21 第四章 IIR 濾波器的具體實現(xiàn) 仿真結(jié)果 程序 1 運行后的的結(jié)果圖 ： 圖 這是一個 butterworth 濾波器， 對已設計的濾波器的頻率響應要進行校核，要得到幅頻相頻響應特性， 能夠 達到本設計的要求。 if usewhitebg set(hObject,39。)。BackgroundColor39。) returns contents of edit4 as text % str2double(get(hObject,39。)。BackgroundColor39。 end function untitled1_OpeningF(hObject, eventdata, handles, varargin) = hObject。, [] , ... 39。, mfilename, ... 39。是由各種圖形對象，如圖形窗口菜單按鈕、文本框等構(gòu)建的用戶界面，是人機交流信息的平臺和工具。)。 mag2=abs(y1)。輸出信號 39。)。 mag1=abs(s1)。輸入信號 39。 plot(W,20*log10(abs(H)))。%設定模擬低通原型的零極點增益參數(shù) [bp,ap]=zp2tf(z,p,k)。Fs=1000。 由 ?? ??Ni iia ps AsH1)( （ ） 得到： ?????? Ni nTpi nTueATnThTnh i1 )()()( （ ） 長沙學院畢業(yè)設計 (論文 ) 14 雙 線 性變換法 雙線性變換法的設計過程如下： 由積分器構(gòu)成的模擬濾波器的系統(tǒng)函數(shù)形式； ) NM( 1)(1000 以方便說明設 ??????????????NjjjNjjjNiiiMiiiasdscAsbsasH （ ） 2. 由傳遞函數(shù)得信流圖 ： 圖 滿足指標要求的低通 IIR數(shù)字濾波器的 幅度特性， 如果與 Butterworth模擬原形低通濾波器相比較可知，采用脈沖響應不變法轉(zhuǎn)換成的數(shù)字 濾波器的幅度特性與原形低通濾波器幅度特性有差別，且頻率愈高差別愈大，這是由于頻率混疊現(xiàn)象起的。對設計的各個步驟， MATLAB 提供了相應的工具箱函數(shù)，使 IIR數(shù)字濾波器的設計變得非常簡單。 7． image 函數(shù)：顯示圖片對象。用于保存程序代碼。如“確定”命按鈕對應的“ tag”標記為“ pushbutton2”；“濾波器類型選擇”下拉菜單對應的“ tag”是“ popupmenul” [4]。進行 GUI設計時，首先單擊面板左邊所需的控件，然后在右邊的圖形界面編輯區(qū)中再次單擊某一恰當位置，這時將在該位置上為圖形界面添加相應的控件?？捎糜诳茖W計算和工程繪圖。這些工具方便用戶使用 MATLAB 的函數(shù)和文件，其中許多工具采用的是圖形用戶界面。 其 應用范圍非常廣，包括信號和圖像處理、通訊、 控制系統(tǒng)設計、測試和測量、財務建模和分析以及計算生物學等眾多應用領域。 首先要明確 IIR 濾波器 的基本原理， IIR 濾波器在本質(zhì)上無限沖擊響應，必須要用逼近的方法來實現(xiàn)。該靈敏度與測量儀器或電路系統(tǒng)靈敏度概念不同，該靈敏度越小，標志著電路容錯能力越強，穩(wěn)定性也越高。①對低通濾波器通帶增益 pk 一般指ω =0 時的增益；高通指ω→∞時的增益；帶通則指中心頻率處的增益。當然，希望過渡帶越窄越好，也就是希望對通帶外的頻率成分衰減得越快、越多越好。嚴格的講，濾波器是一個能讓某些頻率通過而完全拒絕其他頻率成分的系統(tǒng)。數(shù)字濾波器還可根據(jù)不同原理編制專門的程序，對采集的信號進行特殊的計算來濾除特定頻率的信號。濾波器的作用主要是選擇所需頻帶的信號內(nèi)容而抑制不需要的其他頻帶的信號內(nèi)容。本文研究了 IIR 數(shù)字濾波器的常用設計方法，即沖 激 響應不變法和雙線性變換法。本文介紹了一種利用 MATLAB 信號處理工具箱（ Signal Processing Toolbox）快速有效的設計由軟件組成的常規(guī)數(shù)字濾波器的設計方法。常用的數(shù)字 濾波器有 FIR 濾波器和 IIR 濾波器，其中 IIR 數(shù)字濾波器因具有結(jié)構(gòu)簡單、占用存儲空間少、運算速度快、較高的計算精度和能夠用較低的階數(shù)實現(xiàn)、較好的選頻特性等特點，得到了廣泛應用。 ② .級聯(lián)型：將系統(tǒng)函數(shù) H(z)因式分解為較低的二階節(jié)的