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f(t)=fs(t)*h(t)
ÆäÖУºfs(t)=f(t)??(t?nT)=?f(nT)?(t?nT)
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f(t)=fs(t)*h(t)=?f(nTs)?(t?nTs)*Ts????cSa(?ct) ?? =Tsc??f(nT)Sa[?(t?nT)]
scs???ÉÏʽ±íÃ÷£¬Á¬ÐøÐźſÉÒÔÕ¹¿ª³É³éÑùº¯ÊýµÄÎÞÇÊý¡£
ÀûÓÃMATLABÖеÄsinc(t)?tsin(?t)À´±íʾSa(t)£¬ÓÐ Sa(t)?sinc()£¬ËùÒÔ¿ÉÒÔ?t?µÃµ½ÔÚMATLABÖÐÐźÅÓÉf(nTs)Öؽ¨f(t)µÄ±í´ïʽÈçÏ£º
?f(t)=Tsc?????f(nTs)sinc[?c(t?nTs)] ?ÎÒÃÇÑ¡È¡ÐźÅf(t)=Sa(t)×÷Ϊ±»²ÉÑùÐźţ¬µ±²ÉÑùƵÂÊ?s=2?mʱ£¬³ÆΪÁÙ½ç²ÉÑù¡£ÎÒÃÇÈ¡ÀíÏëµÍͨµÄ½ØֹƵÂÊ?c=?m¡£ÏÂÃæ³ÌÐòʵÏÖ¶ÔÐźÅf(t)=Sa(t)µÄ²ÉÑù¼°ÓɸòÉÑù
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Àý5-1 Sa(t)µÄÁÙ½ç²ÉÑù¼°ÐźÅÖع¹£»
wm=1; %ÐźŴø¿í
wc=wm; %Â˲¨Æ÷½ØֹƵÂÊ Ts=pi/wm; %²ÉÑù¼ä¸ô
ws=2*pi/Ts; %²ÉÑù½ÇƵÂÊ n=-100:100; %ʱÓò²ÉÑùµçÊý nTs=n*Ts %ʱÓò²ÉÑùµã f=sinc(nTs/pi);
Dt=0.005;t=-15:Dt:15;
fa=f*Ts*wc/pi*sinc((wc/pi)*(ones(length(nTs),1)*t-nTs'*ones(1,length(t)))); %ÐźÅÖع¹ t1=-15:0.5:15; f1=sinc(t1/pi); subplot(211); stem(t1,f1); xlabel('kTs'); ylabel('f(kTs)');
title('sa(t)=sinc(t/pi)µÄÁÙ½ç²ÉÑùÐźÅ'); subplot(212); plot(t,fa) xlabel('t'); ylabel('fa(t)');
title('ÓÉsa(t)=sinc(t/pi)µÄÁÙ½ç²ÉÑùÐźÅÖع¹sa(t)'); grid;
Àý5-2 Sa(t)µÄ¹ý²ÉÑù¼°ÐźÅÖع¹ºÍ¾ø¶ÔÎó²î·ÖÎö
³ÌÐòºÍÀý4-1ÀàËÆ£¬½«²ÉÑù¼ä¸ô¸Ä³ÉTs=0.7*pi/wm , Â˲¨Æ÷½ØֹƵÂʸóÉwc=1.1*wm £¬ Ìí¼ÓÒ»¸öÎó²îº¯Êý wm=1;
wc=1.1*wm; Ts=0.7*pi/wm; ws=2*pi/Ts; n=-100:100; nTs=n*Ts
f=sinc(nTs/pi);
Dt=0.005;t=-15:Dt:15;
fa=f*Ts*wc/pi*sinc((wc/pi)*(ones(length(nTs),1)*t-nTs'*ones(1,length(t)))); error=abs(fa-sinc(t/pi)); %Öع¹ÐźÅÓëÔÐźÅÎó²î t1=-15:0.5:15; f1=sinc(t1/pi); subplot(311); stem(t1,f1); xlabel('kTs');
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ylabel('f(kTs)');
title('sa(t)=sinc(t/pi)µÄ²ÉÑùÐźÅ'); subplot(312); plot(t,fa) xlabel('t'); ylabel('fa(t)');
title('ÓÉsa(t)=sinc(t/pi)µÄ¹ý²ÉÑùÐźÅÖع¹sa(t)'); grid;
subplot(313); plot(t,error); xlabel('t');
ylabel('error(t)');
title('¹ý²ÉÑùÐźÅÓëÔÐźŵÄÎó²îerror(t)');
Àý5-3 Sa(t)µÄÇ·²ÉÑù¼°ÐźÅÖع¹ºÍ¾ø¶ÔÎó²î·ÖÎö
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1£®Ñé֤ʵÑéÔÀíÖÐËùÊöµÄÏà¹Ø³ÌÐò£»
2£®Éèf(t)=0.5*(1+cost)*(u(t+pi)-u(t-pi)) £¬ÓÉÓÚ²»ÊÇÑϸñµÄƵ´øÓÐÏÞÐźţ¬µ«ÆäƵÆ״󲿷ּ¯ÖÐÔÚ[0£¬2]Ö®¼ä£¬´ø¿íwm¿É¸ù¾ÝÒ»¶¨µÄ¾«¶ÈÒªÇó×öһЩ½üËÆ¡£ÊÔ¸ù¾ÝÒÔÏÂÁ½ÖÖÇé¿öÓà MATLABʵÏÖÓÉf(t)µÄ³éÑùÐźÅfs(t)Öؽ¨f(t) ²¢ÇóÁ½ÕßÎó²î£¬·ÖÎöÁ½ÖÖÇé¿öϵĽá¹û¡£ (1) wm=2 , wc=1.2wm , Ts=1; (2) wm=2 , wc=2 , Ts=2.5
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s3?4s2?3s½â:ÆäMATLAB³ÌÐòΪ format rat; num=[1,2]; den=[1,4,3,0];
[r,p]=residue(num,den)
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