update

close;

% 3.5(f)

m=0:1:31;

a3_2=[a3(1:3) zeros(1,27) a3(31:32)];

a3_8=[a3(1:9) zeros(1,15) a3(25:32)];

a3_12=[a3(1:13) zeros(1,7) a3(21:32)];

a3_all=a3;

x3_2=32*ifft(a3_2);

x3_8=32*ifft(a3_8);

x3_12=32*ifft(a3_12);

x3_all=32*ifft(a3_all);

subplot(2,2,1);

stem(m,x3_2,'y');

xlabel('n');

title('x3 2[n]');

subplot(2,2,2);

stem(m,x3_8,'m');

xlabel('n');

title('x3 8[n]');

subplot(2,2,3);

stem(m,x3_12,'r');

xlabel('n');

title('x3 12[n]');

subplot(2,2,4);

stem(m,x3_all,'b');

xlabel('n');

title('x3 all[n]');

saveas(gcf, "plots/P3_5_f_out.png");

close;

% 3.5(g)

subplot(2,1,1);

stem(m,real(x3_all),'r');

xlabel('n');

title('real(x3 all[n])');

subplot(2,1,2);

stem(m,imag(x3_all),'g');

xlabel('n');

title('imag(x3 all[n])');

saveas(gcf, "plots/P3_5_g_out.png");

close;

% 3,5(h)

a3_5=[a3(1:3) zeros(1,27) a3(31:32)];

a3_15=[a3(1:8) zeros(1,17) a3(26:32)];

a3_25=[a3(1:13) zeros(1,7) a3(21:32)];

a3_29=[a3(1:15) zeros(1,3) a3(19:32)];

a3_32=a3;

x3_5=32*ifft(a3_5);

x3_15=32*ifft(a3_15);

x3_25=32*ifft(a3_25);

x3_29=32*ifft(a3_29);

x3_32=32*ifft(a3_32);

subplot(3,2,1);

stem(m,x3_5,'y');

xlabel('n');

title('use 5 series');

subplot(3,2,2);

stem(m,x3_15,'m');

xlabel('n');

title('use 15 series');

subplot(3,2,3);

stem(m,x3_25,'r');

xlabel('n');

title('use 25 series');

subplot(3,2,4);

stem(m,x3_29,'b');

xlabel('n');

title('use 29 series');

subplot(3,2,5);

stem(m,x3_32,'b');

xlabel('n');

title('use 32 series');

saveas(gcf, "plots/P3_5_h_out.png");

close;

% 3.5最后一问

function a=dtfs(x,n_init);

if n_init==0

    a=1/length(x)*fft(x);

else if n_init<0

        for i=1:-n_init

            x=[x x(i)];

        end

        x=x(1-n_init:length(x));

         a=1/length(x)*fft(x);

    else n_init>0

        for i=i:n_init

            x=[x(length(x)-i+1) x];

        end

        x=x(1:length(x)-n_init);

        a=1/length(x)*fft(x);

    end

end

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