基于MATLAB的AM信號(hào)的調(diào)制

1、高頻大作業(yè)基于MATLAB的AM信號(hào)的調(diào)制 摘要：現(xiàn)在的社會(huì)越來(lái)越發(fā)達(dá)，科學(xué)技術(shù)不斷的在更新，在信號(hào)和模擬電路里面經(jīng)常要用到調(diào)制與解調(diào)，而AM的調(diào)制與解調(diào)是最基本的，也是經(jīng)常用到的。用AM調(diào)制與解調(diào)可以在電路里面實(shí)現(xiàn)很多功能，制造出很多有用又實(shí)惠的電子產(chǎn)品，為我們的生活帶來(lái)便利。在我們?nèi)粘Ｉ钪杏玫氖找魴C(jī)也是采用了AM調(diào)制方式，而且在軍事和民用領(lǐng)域都有十分重要的研究課題。 本文主要的研究?jī)?nèi)容是了解AM信號(hào)的數(shù)學(xué)模型及調(diào)制方式以及調(diào)制結(jié)果的分析。不同的調(diào)制系數(shù)對(duì)調(diào)制的影響以及單頻信號(hào)和多頻信號(hào)調(diào)制的不同點(diǎn)。先從AM的調(diào)制研究，研究它的實(shí)現(xiàn)方法及功能。其次研究不同的調(diào)制系數(shù)下，對(duì)已調(diào)波的頻譜進(jìn)行分

2、析與研究，探究其與功率的關(guān)系。最后再通過(guò)建立數(shù)學(xué)模型分析功率關(guān)系，與前面得出的結(jié)論作對(duì)比，最終得出正確的結(jié)論。利用MATLAB編程語(yǔ)言實(shí)現(xiàn)對(duì)AM信號(hào)的調(diào)制，給出不同調(diào)制系數(shù)情況下的調(diào)制結(jié)果對(duì)比。 關(guān)鍵詞：AM信號(hào)，調(diào)制，調(diào)制系數(shù)，功率，MATLABModulation of AM signal based on MATLABAbstract: Society becomes more developed now, science and technology in the update, in which signal and analog circuits often used in mod

3、ulation and demodulation, and AM modulation and demodulation is the most basic, is also frequently used. To participate in the identification of such artificial methods, the ruling includes subjective factors, will vary from person to person, can identify the type of modulation is very limited. Auto

4、matic modulation recognition technology can be overcome not only to participate in recognition of artificial difficulties, and the center frequency and bandwidth of the estimation error, adjacent channel crosstalk, noise and interference factors such as the decline of effect is relatively robust. Us

5、ing AM modulation and demodulation circuit which can achieve a lot of features, creating a lot of useful and affordable electronic products, in order to facilitate our lives. Used in our daily lives is the use of AM radio modulation, but also in the field of military and civilian research topics are

6、 very important. The main content of this paper is to understand the mathematical model of the AM signal and the modulation and the demodulation method. Demodulation different methods in different circumstances of the demodulation signal to noise ratio the results of methods that better, to make the

7、 comparison. Requirement is more than double the sound and the AM signal modulation and demodulation. AM modulation first study of its function and in real life use. AM demodulation followed by research, as well as some related knowledge, as well as through its use of communications more in-depth un

8、derstanding of it. AM signal from the tone of the mathematical model and the modulation and demodulation methods, the two-tone AM signal to draw a mathematical model and the block diagram of modulation and demodulation and modulation and demodulation waveforms. MATLAB programming language to use to

9、achieve the two-tone AM signal modulation and demodulation, given the different circumstances of the demodulation signal to noise ratio compared the results. Keyword: AM signal, Modulation, rate of work, MATLAB引言：MATLAB軟件由美國(guó)Math Works公司于1984年推出，經(jīng)過(guò)不斷的發(fā)展和完善，如今己成為覆蓋多個(gè)學(xué)科的國(guó)際公認(rèn)的最優(yōu)秀的數(shù)值計(jì)算仿真軟件。MATLAB具備強(qiáng)大的數(shù)值計(jì)

10、算能力，許多復(fù)雜的計(jì)算問(wèn)題只需短短幾行代碼就可在MATLAB中實(shí)現(xiàn)。作為一個(gè)跨平臺(tái)的軟件，MATLAB已推出Unix、Windows、Linux和Mac等十多種操作系統(tǒng)下的版本，大大方便了在不同操作系統(tǒng)平臺(tái)下的研究工作。圖形處理功能MATLAB自產(chǎn)生之日起就具有方便的數(shù)據(jù)可視化功能，以將向量和矩陣用圖形表現(xiàn)出來(lái)，并且可以對(duì)圖形進(jìn)行標(biāo)注和打印。高層次的作圖包括二維和三維的可視化、圖象處理、動(dòng)畫(huà)和表達(dá)式作圖?？捎糜诳茖W(xué)計(jì)算和工程繪圖。MATLAB的應(yīng)用領(lǐng)域十分廣闊，可應(yīng)用于數(shù)據(jù)分析、數(shù)值與符號(hào)計(jì)算、控制系統(tǒng)設(shè)計(jì)、航天工業(yè)、汽車工業(yè)、生物醫(yī)學(xué)工程、語(yǔ)音處理、圖像與數(shù)字信號(hào)處理、財(cái)務(wù)、金融分析、建模、

11、仿真及樣機(jī)開(kāi)發(fā)、新算法研究開(kāi)發(fā)、圖形用戶界面設(shè)計(jì)等領(lǐng)域。通過(guò)仿真，學(xué)生可以更好地理解理論課程中所涉及到的概念、原理與計(jì)算方法。由于在理論課上必須將復(fù)雜性限制在較低的程度，以保證能夠進(jìn)行分析。在仿真過(guò)程中，允許我們方便地改變系統(tǒng)參數(shù)，而且通過(guò)仿真結(jié)果進(jìn)行交互式和可視化的顯示，可以迅速評(píng)估這些改變的影響，因此可以學(xué)習(xí)到更復(fù)雜和更實(shí)際的系統(tǒng)工作特性。一.AM信號(hào)的調(diào)制原理所謂調(diào)制，就是在傳送信號(hào)的一方將所要傳送的信號(hào)附加在高頻振蕩上，再由天線發(fā)射出去。這里高頻振蕩波就是攜帶信號(hào)的運(yùn)載工具，也叫載波。振幅調(diào)制，就是由調(diào)制信號(hào)去控制高頻載波的振幅，直至隨調(diào)制信號(hào)做線性變化。在線性調(diào)制系列中，最先應(yīng)用的一

12、種幅度調(diào)制是全調(diào)幅或常規(guī)調(diào)幅，簡(jiǎn)稱為調(diào)幅（AM）。在頻域中已調(diào)波頻譜是基帶調(diào)制信號(hào)頻譜的線性位移；在時(shí)域中，已調(diào)波包絡(luò)與調(diào)制信號(hào)波形呈線性關(guān)系。 設(shè)載波電壓為 調(diào)制電壓為 通常滿足c。根據(jù)振幅調(diào)制信號(hào)的定義，已調(diào)信號(hào)的振幅隨調(diào)制信號(hào)u線性變化，由此可得振幅調(diào)制信號(hào)振幅Um(t)為 Um(t)=UC+UC(t)=UC+kaUcost =UC(1+mcost) 式中，UC(t)與調(diào)制電壓u成正比，其振幅UC=kaU與載波振幅之比稱為調(diào)幅度（調(diào)制度）式中，ka為比例系數(shù)，一般由調(diào)制電路確定，故又稱為調(diào)制靈敏度。由此可得調(diào)幅信號(hào)的表達(dá)式 uAM(t)=UM(t)cosct=UC(1+mcost)cos

13、ct 上面的分析是在單一正弦信號(hào)作為調(diào)制信號(hào)的情況下進(jìn)行的，而一般傳送的信號(hào)并非為單一頻率的信號(hào)，例如是一連續(xù)頻譜信號(hào)f(t),這時(shí)，可用下式來(lái)描述調(diào)幅波:式中，f(t)是均值為零的歸一化調(diào)制信號(hào)，|f(t)|max=1。若將調(diào)制信號(hào)分解為則調(diào)幅波表示式為二MATLAB仿真一.單頻信號(hào)調(diào)制1.MATLAB程序Utm1=1; %調(diào)制信號(hào)振幅Ft1=500; %調(diào)制信號(hào)頻率Ucm=1; %載波振幅fc=5000; %載波頻率Ma=0.5; %調(diào)制系數(shù)N=fc*10;k=0:N-1;t=k/N;Ut=Utm1*cos(2*pi*ft1*t); %調(diào)制信號(hào)Uc=Ucm*cos(2*pi*fc*t);

14、%載波Uam=Ucm*(1+Ma*Ut).*cos(2*pi*fc*t); %已調(diào)波PP1=fft(Ut); PP2=fft(Uc);PP3=fft(Uam);figure(1)subplot(3,2,1);plot(t,Ut);title(調(diào)制信號(hào)波形);axis(0,0.1,-2,2);subplot(3,2,2);plot(abs(PP1);axis(0,6000,0,50000);title(調(diào)制信號(hào)頻譜); %畫(huà)出頻譜波形subplot(3,2,3);plot(t,Uc);title(載頻信號(hào)波形);axis(0,0.1,-2,2);subplot(3,2,4); plot(abs(

15、PP2); axis(0,6000,0,50000);title(載波信號(hào)頻譜);subplot(3,2,5);plot(t,Uam);title(AM波形);axis(0,0.1,-2,2);subplot(3,2,6); plot(abs(PP3); axis(0,6000,0,50000);title(AM信號(hào)頻譜);2.調(diào)制信號(hào)頻率為500HZ，載波頻率為5000HZ時(shí)的結(jié)果ft=500HZ; fc=5000HZ(1)Ma=0.1包絡(luò)不太明顯，上下邊頻頻率振幅較小。(2)Ma=0.5包絡(luò)變明顯，上下邊頻頻率振幅變大。(3)Ma=1包絡(luò)波谷為0，上下邊頻頻率振幅進(jìn)一步變大。(4)Ma=1

16、.5已產(chǎn)生包絡(luò)失真，即過(guò)量調(diào)幅，上下邊頻頻率振幅進(jìn)一步變大。(5)Ma=2上下邊頻頻率振幅與載波頻率振幅相等。(6) Ma=2.5上下邊頻頻率振幅超過(guò)載波頻率振幅。3.ft=700HZ; fc=3000HZ;Ma=2在調(diào)制系數(shù)為2時(shí)，不同的調(diào)制信號(hào)頻率和載波信號(hào)頻率，雖然波形不同，但上下邊頻頻率振幅與載波頻率振幅相等，上下邊帶與載波消耗的功率相等。結(jié)論：從頻譜圖看出：隨著調(diào)制系數(shù)的增大，調(diào)制信號(hào)的頻率分量所對(duì)應(yīng)的幅值也增大，即上下邊頻所消耗的功率增大，載波信號(hào)頻率所對(duì)應(yīng)的幅值不變，即載波所消耗的功率不變。如果單從功率分析，從頻譜上可以看出，調(diào)制系數(shù)等于2時(shí)，上下邊帶與載波消耗的功率相等，繼續(xù)增

17、大調(diào)制系數(shù)，就會(huì)大于載波消耗功率。但從信號(hào)波形來(lái)看，一旦調(diào)制系數(shù)大于1，就會(huì)產(chǎn)生包絡(luò)失真，即過(guò)量調(diào)幅。所以，調(diào)制系數(shù)應(yīng)小于1，又要盡量大，以提高功率利用率。4.調(diào)制信號(hào)與載波頻率相差不大的調(diào)制（1）ft=3000HZ; fc=5000HZ（2）t=700HZ; fc=1000HZ結(jié)論：調(diào)制信號(hào)的頻率如果與載波信號(hào)的頻率相差不大，調(diào)制之后對(duì)頻率的搬移較小，甚至還有小于調(diào)制信號(hào)的頻率的頻率產(chǎn)生，所以對(duì)于調(diào)制信號(hào)的頻率與載波信號(hào)的頻率相近的信號(hào)做調(diào)制的作用并不大。二多頻率信號(hào)的調(diào)制1.MATLAB程序Utm1=1; Utm2=3; Utm3=2; Utm4=2; %調(diào)制信號(hào)振幅ft1=10; ft2

18、=500; ft3=1000; ft4=100; %調(diào)制信號(hào)頻率Ucm=2; %載波振幅fc=10000; %載波頻率Ma=0.1; %調(diào)制系數(shù)N=fc*10;k=0:N-1;t=k/N;Ut=Utm1*cos(2*pi*ft1*t)+Utm2*cos(2*pi*ft2*t)+Utm3*cos(2*pi*ft3*t)+Utm4*cos(2*pi*ft4*t); %調(diào)制信號(hào)Uc=Ucm*cos(2*pi*fc*t); %載波Uam=Ucm*(1+Ma*Ut).*cos(2*pi*fc*t); %已調(diào)波PP1=fft(Ut); PP2=fft(Uc);PP3=fft(Uam);figure(1)s

19、ubplot(3,2,1);plot(t,Ut);title(調(diào)制信號(hào)波形);axis(0,0.02,-10,10);subplot(3,2,2);plot(abs(PP1);axis(0,15000,0,200000);title(調(diào)制信號(hào)頻譜); %畫(huà)出頻譜波形subplot(3,2,3);plot(t,Uc);title(載頻信號(hào)波形);axis(0,0.02,-10,10);subplot(3,2,4); plot(abs(PP2); axis(0,15000,0,200000);title(載波信號(hào)頻譜);subplot(3,2,5);plot(t,Uam);title(AM波形);

20、axis(0,0.02,-10,10);subplot(3,2,6); plot(abs(PP3); axis(0,15000,0,200000);title(AM信號(hào)頻譜);2.提供第一組多頻信號(hào)此組信號(hào)頻率相差不大，振幅相差也不大。Utm1=1; Utm2=3; Utm3=2; Utm4=2; ft1=10; ft2=500; ft3=1000; ft4=100;（1）Ma=0.1包絡(luò)不太明顯，上下邊頻頻率振幅較小。(2)Ma=0.5包絡(luò)變明顯，上下邊頻頻率振幅增大。(3)Ma=1上下邊頻頻率振幅進(jìn)一步增大。(4)Ma=2產(chǎn)生包絡(luò)失真，但不易觀察到。 3.提供第二組多頻信號(hào)此組信號(hào)較第一組

21、來(lái)說(shuō)，頻率相差較大，振幅相差也較大。Utm1=1; Utm2=6; Utm3=2; Utm4=2; ft1=100; ft2=500; ft3=5000; ft4=1000;(1)Ma=0.1上下邊頻頻率振幅較小。(2)Ma=0.5與Ma=0.1時(shí)的包絡(luò)不同，上下邊頻頻率振幅增大。(3)Ma=1與Ma=0.5時(shí)的包絡(luò)不同，上下邊頻頻率振幅進(jìn)一步增大。(4)Ma=1.5包絡(luò)失真。結(jié)論：整體與單頻信號(hào)調(diào)制相似，也是隨著調(diào)制系數(shù)增大，調(diào)制信號(hào)的頻率分量所對(duì)應(yīng)的幅值越大，上下邊頻所消耗的功率增大，載波信號(hào)頻率所對(duì)應(yīng)的幅值不變，載波所消耗的功率不變。但從波形來(lái)看，多頻率信號(hào)較單頻信號(hào)來(lái)說(shuō)，由于波形比較復(fù)雜，過(guò)度調(diào)幅的現(xiàn)象不易觀察。另外一點(diǎn)，由于調(diào)制信號(hào)所含分量增多，各個(gè)分量振幅不一，在改變調(diào)制系數(shù)時(shí)，已調(diào)波不僅僅是振幅發(fā)生變化，包絡(luò)也會(huì)發(fā)生變化。三功率1.MATLAB程序Rl=100;Ucm=10;Ma=0:0.001:1;Pc=0.5*(Ucm*Ucm./Rl); %載波功率Pu=0.25*Ma.*Ma.*Pc; %上下邊頻消耗功率Pam=(1+Ma.*Ma*0.5).*