【正文】 theorembased stability constraint ,which is less conservative than the positiverealnessbased stability constraint,is expressed as quadratic inequalities in terms of denominator coefficients. Note that both of them should be satisfied at all frequencies. A simple way ,to incorporate these constraints is to realize them on a set of densegrid frequency points over. The number of stability constraints is therefore large. Another way is to employ a multiple exchange algorithm ,which is used to identify a set of active , stability constraints are replaced by a finite number of active constraints. In ,by defining a convex stability domain, the design problem can be formulated as an iterative semi definite programming(SDP)problem. It has been proved in[7]that this stability domain contains the domain given by the Rouch233。current version published March 11, work was supported 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(xué)生簽名： 日 期： 年 月 日 2020 屆 本科生畢業(yè)設(shè)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。王老師工作勤奮的態(tài)度感染了我，這將對我以后的工作態(tài)度產(chǎn)生良好的影響。在課題的具體研究、開展和論文的寫作等各個方面，給予我很多的指導(dǎo)和幫助，對我的論文的順利完成起著非常重要的作用，也將使我終生受益。17(2):227230 [2]陳愛萍 ,胡曉東 .基于 MATLAB 的 IIR 數(shù)字濾波器的設(shè)計 [J].湖南工程學(xué)院學(xué)報 ,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(xué)習(xí)研究與 指導(dǎo) 老師的認(rèn)真指導(dǎo)，使自己的能力得到了進(jìn)一步鍛煉與提高。通過查閱相關(guān)的資料、指導(dǎo)老師的指點和自身的學(xué)習(xí)，最終解決了這一問題并完成仿真。 在本課題研究的過程中，也遇到了各種各樣的困難：理論轉(zhuǎn)換成實際成果，是一個由虛變實的過程。 長沙學(xué)院畢業(yè)設(shè)計 (論文 ) 26 結(jié) 論 通過前面的仿真，從結(jié)果來看，完全符合實驗預(yù)期，實現(xiàn)了利用 GUI設(shè)計實現(xiàn) IIR濾波器的整個過程，這次研究，對新技術(shù)的應(yīng)用開辟了一條新的道路：我們可以應(yīng)用 MATLAB的強大功能，系統(tǒng)的集合各種新技術(shù)，在虛擬的環(huán)境下，就可以實現(xiàn)技術(shù)的各種功能，這樣擺脫了對硬件的依賴性，也沒用了外界其他因素的干擾，又具有更高的性價比。 結(jié)果分析 從界面操作可以看出，該設(shè)計預(yù)測達(dá)到了以下要求。通帶波紋和阻帶衰減都是相對于增益 1 的下降，因此， Rp 和 Rs 越大則與通帶增益 1 的差距越大。按 exit 即可以退出界面。 長沙學(xué)院畢業(yè)設(shè)計 (論文 ) 23 圖 輸出信號 分析： 可以從輸出的信號可以看出，把高頻的信號濾除，讓低頻 信號通過。 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(xué)院畢業(yè)設(shè)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(shè)計的濾波器的頻率響應(yīng)要進(jìn)行校核，要得到幅頻相頻響應(yīng)特性， 能夠 達(dá)到本設(shè)計的要求。defaultUicontrolBackgroundColor39。BackgroundColor39。,[.9 .9 .9])。 if usewhitebg set(hObject,39。 end function pushbutton1_Callback(hObject, eventdata, handles) close(gcf)。defaultUicontrolBackgroundColor39。BackgroundColor39。)。,39。 end function edit5_Callback(hObject, eventdata, handles) function edit5_CreateF(hObject, eventdata, handles) if ispc set(hObject,39。defaultUicontrolBackgroundColor39。BackgroundColor39。)。,39。)) returns contents of edit4 as a double % Executes