【Matlab】信号系统实验

    t=-1:0.002:5
    t0=1
    x=stepfun(t,t0)
    y=-2*x
    plot(t,y)
    axis([-1 5 -3 1])
    xlabel('-2u(t-1)的波形')

    t=0:0.0001:30
    x=exp(-0.3*t).*sin((2/3)*t)
    plot(t,x)
    xlabel('e(-0.3t)sin(2/3t)的波形')

    t=-0.1:0.0001:0.1
    x=cos(100*t)+cos(300*t)
    plot(t,x)
    axis([-0.1 0.1 -3 3])
    xlabel('cos(100t)+cos(300t)的波形')

    f0=1;
    t=-2:0.01:2
    wc=2*pi*f0
    s=square(wc*t,50)+1
    plot(t,s)
    axis([-2,2,0,2.5]) 
    xlabel('矩形周期脉冲信号的波形E=2 τ=0.5 T=1')

    t=-5:0.001:5
    w=2*pi*1
    f=sawtooth(w*t,1)+1
    plot(t,f)
    axis([-5 5 0 2.5])
    xlabel('周期锯齿脉冲信号波形E=2 T=1')

    t=-5:0.001:5
    w=2*pi*1
    f=sawtooth(w*t,0.5)+1
    plot(t,f)
    axis([-5 5 0 2.5])
    xlabel('周期三角脉冲信号波形E=2 T=1')

    f0=1;
    t=-5:0.01:5
    wc=2*pi*f0
    y1=cos(wc*t)+1
    y2=(square(wc/2*(t+0.5),50)+1)/2
    y=y1.*y2
    plot(t,y)
    axis([-3,3,0,2.3]) 
    xlabel('矩形周期半波余弦信号的波形E=2 τ=1 T=2')

    t=-5:0.001:5
    f0=1
    w=2*pi*f0;
    y=0.5*square(w*(t+1/4),50)+0.5;
    Y=1/2;
    N=input('谐波次数N=');
    for n=1:N
    Y=Y+sinc(n*0.5)*cos(n*w*t); end
    plot(t,y, ' r', t,Y, ' b'); 
    axis([-2,2,0,1.5]);
    xlabel('周期矩形脉冲5次谐波叠加')
    legend('周期矩形','5次谐波',0)
    t=-5:0.001:5
    f0=1
    w=2*pi*f0;
    y=0.5*square(w*(t+1/4),50)+0.5;
    Y=1/2;
    N=input('谐波次数N=');
    for n=1:N
     Y=Y+sinc(n*0.5)*cos(n*w*t); end
    plot(t,y, ' r', t,Y, ' b'); 
    axis([-2,2,0,1.5]);
    xlabel('周期矩形脉冲10次谐波叠加')
    legend('周期矩形','10次谐波',0)
    t=-5:0.001:5
    f0=1
    w=2*pi*f0;
    y=0.5*square(w*(t+1/4),50)+0.5;
    Y=1/2;
    N=input('谐波次数N=');
    for n=1:N
     Y=Y+sinc(n*0.5)*cos(n*w*t); end
    plot(t,y, ' r', t,Y, ' b'); 
    axis([-2,2,0,1.5]);
    xlabel('周期矩形脉冲15次谐波叠加')
    legend('周期矩形','15次谐波',0)

    t=-2:0.0001:2;
    f0=1
    w=2*pi*f0;
    y=sawtooth(w*(t+0.5),1);
    N=input('请输入谐波次数N=');
    Y=0;
    for n=1:N
     	Y=Y+2/pi*((-1)^(n+1))*(1/n)*sin(n*w*t);
    end
    plot(t,y, ' G', t,Y, ' K'); 
    axis([-2,2,-2,2]);
    xlabel('周期锯齿波脉冲5次谐波叠加')
    legend('周期锯齿波','5次谐波',0)
    t=-2:0.0001:2;
    f0=1
    w=2*pi*f0;
    y=sawtooth(w*(t+0.5),1);
    N=input('请输入谐波次数N=');
    Y=0;
    for n=1:N
    	Y=Y+2/pi*((-1)^(n+1))*(1/n)*sin(n*w*t);
    end
    plot(t,y, ' G', t,Y, ' K'); 
    axis([-2,2,-2,2]);
    xlabel('周期锯齿波脉冲10次谐波叠加')
    legend('周期锯齿波','10次谐波',0)
    t=-2:0.0001:2;
    f0=1
    w=2*pi*f0;
    y=sawtooth(w*(t+0.5),1);
    N=input('请输入谐波次数N=');
    Y=0;
    for n=1:N
    	Y=Y+2/pi*((-1)^(n+1))*(1/n)*sin(n*w*t);
    end
    plot(t,y, ' G', t,Y, ' K'); 
    axis([-2,2,-2,2]);
    xlabel('周期锯齿波脉冲15次谐波叠加')
    legend('周期锯齿波','15次谐波',0)

    t=-2:0.0001:2;
    f0=1
    w=2*pi*f0;
    y=sawtooth(w*(t+0.5),0.5);
    N=input('谐波次数N=');
    Y=0;
    for n=1:N
    	 Y=Y+8/(pi^2)*1/(n^2)*sin(n*pi/2)^2*cos(n*w*t);;
    end
    plot(t,y, ' G', t,Y, ' K'); 
    axis([-2,2,-2,2]);
    xlabel('周期三角波脉冲5次谐波叠加')
    legend('周期三角波','5次谐波',0)
    t=-2:0.0001:2;
    f0=1
    w=2*pi*f0;
    y=sawtooth(w*(t+0.5),0.5);
    N=input('谐波次数N=');
    Y=0;
    for n=1:N
    	Y=Y+8/(pi^2)*1/(n^2)*sin(n*pi/2)^2*cos(n*w*t);;
    end
    plot(t,y, ' G', t,Y, ' K'); 
    axis([-2,2,-2,2]);
    xlabel('周期三角波脉冲10次谐波叠加')
    legend('周期三角波','10次谐波',0)
    t=-2:0.0001:2;
    f0=1
    w=2*pi*f0;
    y=sawtooth(w*(t+0.5),0.5);
    N=input('谐波次数N=');
    Y=0;
    for n=1:N
    	Y=Y+8/(pi^2)*1/(n^2)*sin(n*pi/2)^2*cos(n*w*t);;
    end
    plot(t,y, ' G', t,Y, ' K'); 
    axis([-2,2,-2,2]);
    xlabel('周期三角波脉冲15次谐波叠加')
    legend('周期三角波','15次谐波',0)

    t=-2:0.001:2;
    f0=1
    w=2*pi*f0;
    y1=cos(w*t);
    y2=0.5*square(w*(t+0.25),50)+0.5;
    y=y1.*y2;
    Y=1/pi+1/2*cos(w*t);
    N=input('请输入谐波次数N=');
    for n=2:N
    	Y=Y-2/pi*1/(n^2-1)*cos(n*pi/2)*cos(n*w*t);
    end
    plot(t,y, ' R', t,Y, ' K'); 
    axis([-2,2,0,1.5]);
    xlabel('周期三角波脉冲5次谐波叠加')
    legend('周期三角波','5次谐波',0)
    t=-2:0.001:2;
    f0=1
    w=2*pi*f0;
    y1=cos(w*t);
    y2=0.5*square(w*(t+0.25),50)+0.5;
    y=y1.*y2;
    Y=1/pi+1/2*cos(w*t);
    N=input('请输入谐波次数N=');
    for n=2:N
    	Y=Y-2/pi*1/(n^2-1)*cos(n*pi/2)*cos(n*w*t);
    end
    plot(t,y, ' R', t,Y, ' K'); 
    axis([-2,2,0,1.5]);
    xlabel('周期三角波脉冲10次谐波叠加')
    legend('周期三角波','10次谐波',0)
    t=-2:0.001:2;
    f0=1
    w=2*pi*f0;
    y1=cos(w*t);
    y2=0.5*square(w*(t+0.25),50)+0.5;
    y=y1.*y2;
    Y=1/pi+1/2*cos(w*t);
    N=input('请输入谐波次数N=');
    for n=2:N
    	Y=Y-2/pi*1/(n^2-1)*cos(n*pi/2)*cos(n*w*t);
    end
    plot(t,y, ' R', t,Y, ' K'); 
    axis([-2,2,0,1.5]);
    xlabel('周期三角波脉冲15次谐波叠加')
    legend('周期三角波','15次谐波',0)

    k=-14:15
    x=[zeros(1,9),ones(1,11),zeros(1,10)]
    stem(k,x)
    xlabel('分段序列离散图')

    k=-20:20;
    omega=pi/4;
    x=(0.9).^k.*(sin(omega.*k)+cos(omega.*k))
    stem(k,x)
    xlabel('(0.9)^[sin(0.25πn)+cos(0.25πn)]')

    x=[1,2,0,-1,3,2]
    h=[1,-1,1]
    y=conv(x,h)
    stem([0:length(y)-1],y)
    xlabel('求卷积和')