寧波大學(xué)信號(hào)與系統(tǒng)第二版實(shí)驗(yàn)報(bào)告34

1、信號(hào)與系統(tǒng)實(shí)驗(yàn)報(bào)告時(shí)間：2010年4月17日專業(yè)：無線通信班級(jí)：通信081班姓名：蔣浩學(xué)號(hào)：084774412信息科學(xué)與工程學(xué)院信息樓121實(shí)驗(yàn)室寧波大學(xué)實(shí)驗(yàn)三 連續(xù)時(shí)間周期信號(hào)的傅里葉級(jí)數(shù)一、實(shí)驗(yàn)?zāi)康恼莆者B續(xù)時(shí)間周期信號(hào)的傅里葉級(jí)數(shù)的展開和合成，理解吉布斯現(xiàn)象，掌握周期矩形脈沖信號(hào)的頻譜及不同周期、脈沖寬度對(duì)周期信號(hào)頻譜的影響。二、實(shí)驗(yàn)內(nèi)容1周期信號(hào)的傅里葉級(jí)數(shù)的展開和合成畫出教材(上冊)p99圖3-6(b)(c)(d)，進(jìn)一步畫出對(duì)稱方波的7、9、11次諧波的傅里葉級(jí)數(shù)合成波形，觀察吉布斯現(xiàn)象。實(shí)驗(yàn)程序：t=-0.75:0.01:0.75;y1=2*cos(2*pi*t)/pi;y3=-2

2、*cos(6*pi*t)/(3*pi);y5=2*cos(10*pi*t)/(5*pi);y7=-2*cos(14*pi*t)/(7*pi); y9=2*cos(18*pi*t)/(9*pi);y11=-2*cos(22*pi*t)/(11*pi);s1=y1;s2=y1+y3;s3=y1+y3+y5;s4=y1+y3+y5+y7+y9+y11;subplot(2,2,1),plot(t,s1);xlabel(t),ylabel(s1),grid on;subplot(2,2,2),plot(t,y1,t,y3,t,s2);xlabel(t),ylabel(s2),grid on;subplo

3、t(2,2,3),plot(t,y1,t,y3,t,y5,t,s3);xlabel(t),ylabel(s3),grid on;subplot(2,2,4),plot(t,y1,t,y3,t,y5,t,y7,t,y9,t,y11,t,s4);xlabel(t),ylabel(s4),grid on;2周期矩形脈沖信號(hào)的頻譜a. 畫出周期矩形脈沖的傅里葉級(jí)數(shù)的頻譜p104圖3-9(d)；實(shí)驗(yàn)程序：w=-6*pi:pi/2:6*pi,w1=-6*pi:0.01:6*pi; f1=sin(w/2)./(2*w);ww=w+(w=0)*eps;yy=sin(ww/2)./(2*ww);f2=sin(w

4、1/2)./(2*w1);stem(ww,yy);hold onplot(w1,f2,r-);axis(-20,20,-0.1,0.4)xlabel(w),ylabel(fn)b. 取e=1，=1, 畫出教材(上冊)p105圖3-11(a)(b)；實(shí)驗(yàn)程序：t=-1:0.01:14;t1=0.001:0.01:6*pi;w=0.4*pi:0.4*pi:6*pi;w1=0.2*pi:0.2*pi:6*pi;f1=square(2*pi*0.2*(t+0.5),20);f2=square(2*pi*0.1*(t+0.5),10); cn1=2*sin(w/2)./(2.5*w);c1=2*sin(

5、t1/2)./(2.5*t1);cn2=2*sin(w1/2)./(5*w1);c2=2*sin(t1/2)./(5*t1);subplot(2,2,1),plot(t,f1),title(f1);axis(-1,14,0,1.5);subplot(2,2,2),stem(w,cn1)axis(0,20,-0.1,0.5);hold onstem(0,0.2),plot(t1,c1,r-);hold offsubplot(2,2,3),plot(t,f2),title(f2);axis(-1,14,0,1.5);subplot(2,2,4),stem(w1,cn2);axis(0,20,-0.

6、05,0.25)hold onstem(0,0.1),plot(t1,c2,r-);hold offc. 取e=1，t1=10, 畫出教材(上冊)p106圖3-12。實(shí)驗(yàn)程序：t=-1:0.01:22;t1=0.001:0.01:3*pi;w=0.2*pi:0.2*pi:3*pi;w1=0.2*pi:0.2*pi:2.8*pi;f1=square(2*pi*0.1*(t+1),20);f2=square(2*pi*0.1*(t+0.5),10);cn1=2*sin(w)./(5*w);c1=2*sin(t1)./(5*t1);cn2=2*sin(w1/2)./(5*w1);c2=2*sin(t

7、1/2)./(5*t1);subplot(2,2,1),plot(t,f1),title(f1);axis(-1,22,0,1.5);subplot(2,2,2),stem(w,cn1)hold onstem(0,0.2),plot(t1,c1,r-);hold offsubplot(2,2,3),plot(t,f2),title(f2); axis(-1,22,0,1.5);subplot(2,2,4),stem(w1,cn2);hold onstem(0,0.1),plot(t1,c2,r-);hold off實(shí)驗(yàn)四 非周期信號(hào)的頻域分析一、實(shí)驗(yàn)?zāi)康睦斫夥侵芷谛盘?hào)的頻域分析方法，掌握典型信

8、號(hào)的幅度譜和相位譜，理解信號(hào)的調(diào)制特性，掌握傅里葉變換的性質(zhì)：尺度變換、時(shí)移、頻移、卷積定理、對(duì)稱性、微分特性。二、實(shí)驗(yàn)內(nèi)容1、利用符號(hào)函數(shù)fourier和ifourier求傅里葉變換和傅里葉逆變換。a. 利用符號(hào)函數(shù)fourier求教材(上冊)p114雙邊指數(shù)信號(hào)當(dāng)a=3時(shí)的傅里葉變換表達(dá)式。試驗(yàn)程序：syms tx=exp(-3*abs(t);f=fourier(x);執(zhí)行，并在命令窗口中輸入f，按回車即可得到傅里葉變換表達(dá)式為：f =6/(9+w2)b. 利用符號(hào)函數(shù)ifourier求教材(上冊)p114公式(3-32)第一式當(dāng)a=1時(shí)的傅里葉逆變換表達(dá)式。試驗(yàn)程序：syms wx=2/

9、(1+w2);f=ifourier(x);執(zhí)行，并在命令窗口中輸入f，按回車即可得到傅里葉變換表達(dá)式為：f =exp(-x)*heaviside(x)+exp(x)*heaviside(-x)c. 利用符號(hào)函數(shù)fourier和ezplot畫出f (t ) =e-2tu ( t)及其幅頻譜。syms w t;f=exp(-2*t).*heaviside(t)/2;f=abs(fourier(f,t,w);subplot(2,1,1),ezplot(f);subplot(2,1,2),ezplot(f); 2、矩形脈沖信號(hào)和周期矩形脈沖信號(hào)的頻譜比較畫出教材(上冊)p110圖3-18右邊的離散譜和

10、連續(xù)譜。試驗(yàn)程序：syms t1t=-3:0.01:3;n1=-3:0.5:3;n2=-3:0.25:3;y1=sinc(n1/2);y11=sinc(t/2);y2=sinc(n2/2);y22=sinc(t/2);y4=heaviside(t1+0.5)-heaviside(t1-0.5);y44=fourier(y4);ezplot(y44);subplot(2,2,1),stem(n1,y1);hold onplot(t,y11,r-);hold offsubplot(2,2,2),stem(n2,y2);hold onplot(t,y22,r-);hold off3、幅度調(diào)制信號(hào)及其

11、頻譜已知線性調(diào)制信號(hào)表示式如下：a. cos(t) cos(0 t) b. 1.5 + sin(t)cos(0 t) 式中0 = 9，試分別畫出它們的波形圖和頻譜圖試驗(yàn)程序：syms ty1=cos(t).*cos(9*t);y2=(1.5+sin(t).*cos(9*t);y11=fourier(y1);y22=fourier(y2);subplot(2,2,1),ezplot(y1);subplot(2,2,2),ezplot(y11);axis(-10,10,0,1.5)subplot(2,2,3),ezplot(y2); subplot(2,2,4),ezplot(y22);4、傅里葉

12、變換的性質(zhì)（尺度變換、時(shí)移、頻移、卷積定理、對(duì)稱性）a. 設(shè)f (t) = u(t +1) u(t 1) = g2 (t)，求y(t) = u(2t +1) u(2t 1) = g1 (t)的頻譜y( j)，并與f (t)的頻譜f( j)進(jìn)行比較。實(shí)驗(yàn)程序：syms t;f=heaviside(t+1)-heaviside(t-1);y=heaviside(2*t+1)-heaviside(2*t-1);f=fourier(f); y=fourier(y);subplot(1,2,1),ezplot(y);subplot(1,2,2),ezplot(f); b. 畫出f(t)=e-2tu(t)

13、/2,f1(t)=e-2(t-0.4)u(t-0.4), f1(t)=e-2(t+0.4)u(t+0.4)的幅度譜和相位譜，觀察信號(hào)時(shí)移對(duì)信號(hào)頻譜的影響。實(shí)驗(yàn)程序：syms t;f0=heaviside(t);f=exp(-2*t)*f0/2;f1=exp(-2*(t-0.4)*subs(f0,t,t-0.4)/2;f2=exp(-2*(t+0.4)*subs(f0,t,t+0.4)/2;f=abs(fourier(f); subplot(2,3,1),ezplot(f);f1=abs(real(fourier(f1); subplot(2,3,2),ezplot(f1);f2=abs(rea

14、l(fourier(f2); subplot(2,3,3),ezplot(f2);h=atan(imag(fourier(f)/real(fourier(f); subplot(2,3,4),ezplot(h);h1=atan(imag(fourier(f1)/real(fourier(f1); subplot(2,3,5),ezplot(h1);h2=atan(imag(fourier(f2)/real(fourier(f2); subplot(2,3,6),ezplot(h2);c. 畫出f (t) = u(t +1) u(t 1)、f1(t)=f(t)e-j20t、f2(t)=f(t)e

15、j20t的頻譜，進(jìn)行相互比較。syms t f0=heaviside(t);f1=subs(f0,t,t-1);f2=subs(f0,t,t+1); f=f2-f1;f1=f*exp(-20*j*t);f2=f*exp(20*j*t);h1=fourier(f1);h2=fourier(f2);subplot(1,2,1),ezplot(h1);subplot(1,2,2),ezplot(h2);d. 畫出f (t) = u(t +1) u(t 1)、y(t) = f (t)* f (t)及其f( j)、f( j) f( j)和y( j)的圖形，驗(yàn)證時(shí)域卷積定理。實(shí)驗(yàn)程序：syms t t1=

16、-2:0.01:2;t2=-4:0.01:4;f1=stepfun(t1,-1)-stepfun(t1,1); %矩形脈沖信號(hào) y1=conv(f1,f1)*0.01/2; %矩形脈沖的卷積f2=heaviside(t+1)-heaviside(t-1);%矩形脈沖信號(hào)f=fourier(f2); %求傅里葉變換f1=f*f; %f(jw)f(jw)subplot(2,3,1),plot(t1,f1); %矩形脈沖信號(hào)圖像subplot(2,3,2),plot(t2,y1); %卷積圖像subplot(2,3,3),ezplot(f);subplot(2,3,4),ezplot(f1);y2=(heaviside(t+2)-heaviside(t)*(t+2)/2+(heaviside(t)-heaviside(t-2)*(2-t)/2;y=fourier(y2);subplot(2,3,5),ezplot(y);e. 設(shè)f (t) = sa(t)