update

a1=[1 -0.8];

b1=1;

a2=[1 0.8];

b2=1;

 No newline at end of file

a1=[1 -0.8];

b1=1;

a2=[1 0.8];

b2=1;

[H1 Omega] = freqz(b1, a1, 1024, 'whole');

[H2 Omega] = freqz(b2, a2, 1024, 'whole');

subplot(2,1,1);

%这是一个低通滤波器

plot(Omega, abs(H1),'r');

xlabel('\omega');

ylabel('H1(e^{j\omega} )');

title('frequency responses of Systems 1');

subplot(2,1,2);

%这是一个高通滤波器

plot(Omega, abs(H2),'g');

xlabel('\omega');

ylabel('H2(e^{j\omega} )');

title('frequency responses of Systems 2');

saveas(gcf, "plots/P3_8_b_out.png");

close;

x=0:1:19; 

a_x=[0 0.75 zeros(1,7) -0.5 0 -0.5 zeros(1,7) 0.75];

Wk=(pi/10).*x;

subplot(3,1,1);

stem(Wk,a_x);

title('DTFS coefficients of x[n]');

xlabel('w_k=(2pi/20)k');

ylabel('a_k');

%以下与b部分相同

a1=[1 -0.8];

b1=1;

a2=[1 0.8];

b2=1;

[H1 Omega] = freqz(b1, a1, 1024, 'whole');

[H2 Omega] = freqz(b2, a2, 1024, 'whole');

subplot(3,1,2);

%这是一个低通滤波器

plot(Omega, abs(H1),'r');

xlabel('\omega');

ylabel('H1(e^{j\omega} )');

title('frequency responses of Systems 1');

subplot(3,1,3);

%这是一个高通滤波器

plot(Omega, abs(H2),'g');

xlabel('\omega');

ylabel('H2(e^{j\omega} )');

title('frequency responses of Systems 2');

saveas(gcf, "plots/P3_8_c_out.png");

close;

% d部分

x=0:1:19; 

a_x=[0 0.75 zeros(1,7) -0.5 0 -0.5 zeros(1,7) 0.75];

Wk=(pi/10).*x;

N=20;

x_20=N*ifft(a_x);

n=-20:1:99;

x_6t=[x_20 x_20 x_20 x_20 x_20 x_20];

figure (1);

stem(n,x_6t);

xlabel('n');

ylabel('x[n]');

saveas(gcf, "plots/P3_8_d_out.png");

close;

% e部分

a1=[1 -0.8];

b1=1;

a2=[1 0.8];

b2=1;

y1=filter(b1,a1,x_6t);

y2=filter(b2,a2,x_6t);

figure (2);

subplot(2,1,1);

stem(n(21:120),y1(21:120));

xlabel('n');

ylabel('y_1[n]');

subplot(2,1,2);

stem(n(21:120),y2(21:120));

xlabel('n');

ylabel('y_2[n]');

saveas(gcf, "plots/P3_8_e_out.png");

close;

% f部分

a_y1=(1/20)*fft(y1(1:20));

a_y2=(1/20)*fft(y2(1:20));

figure(3);

subplot(2,1,1);

stem(x,abs(a_y1));

xlabel('n');

ylabel('a_y1');

title('the DTFS coefficient of yl');

subplot(2,1,2);

stem(x,abs(a_y2));

xlabel('n');

ylabel('a_y2');

title('the DTFS coefficient of y2');

saveas(gcf, "plots/P3_8_f_out.png");

close;