Generate signals from trigonometric

te=1e-5;
fe=1/te;
c=3e8;
lambda= c/fe;
time =((-lambda/2):1:(lambda/2))*te;
a = -1*(sign(time)) ;

%rect= 1*[zeros(0,1) ones(1,(lambda/2)-1) zeros(1,1) -ones(1,(lambda/2)-1) zeros(1,1)];
figure(1);
hold on
plot(a, 'k');
xlim([0 lambda]);
set(gca,'XTick',0:lambda/2:lambda);
set(gca,'XTickLabel',{'0','\lambda/2','\lambda'},'Fontsize',11);
xlabel('Lambda \lambda');
ylabel('A');

    
n=[2 4 6 8 10];
e=0;     
for i=1:n
    an= (1/lambda)*(integral(a,0,lambda));
    bn= (2/lambda)*(a*(integral(sin(2*pi*fe*i*te),0,lambda)));
    cn= (2/lambda)*(a*(integral(cos(2*pi*fe*i*te),0,lambda)));
    
    xn=an+bn*sin(2*pi*fe*i*te)+cn*cos(2*pi*fe*i*te);
    e=e+xn;
end

figure (2)
plot(e)

Hello,

I have generated a square signal f (z) (code a)

f (z) can be written

In practice, m varies from 1 to n

I want to generate signals according to trigonometric formula. However, my code is not very correct. Can you check for me where am I wrong?

Thank you

Answer 1

[Alan Stevens]

More like this perhaps

lambda= 1000;
dz = 1;
z = 0:dz:lambda;
f = @(z) (z<lambda/2) - (z>lambda/2);
    
n= 6; %[2 4 6 8 10];
SN = zeros(numel(n),numel(z));  % pre-allocate storage space
CS = zeros(numel(n),numel(z));
A = zeros(1,numel(n));
B = zeros(1,numel(n));

B0 = (1/lambda)*sum(f(z)*dz);
for m=1:n
    SN(m,:) = sin(2*pi*m*z/lambda);
    CS(m,:) = cos(2*pi*m*z/lambda);
    A(m) = (2/lambda)*sum(f(z).*SN(m,:))*dz;
    B(m) = (2/lambda)*sum(f(z).*CS(m,:))*dz;
end

F = B0 + A*SN + B*CS;
figure(1);
plot(z,f(z), 'k',z,F),grid;
xlim([0 lambda]);
set(gca,'XTick',0:lambda/2:lambda);
set(gca,'XTickLabel',{'0','\lambda/2','\lambda'},'Fontsize',11);
xlabel('Lambda \lambda');
ylabel('Amplitude');
legend('step','fourier')

[triet tran]

THANK YOU, your code, it's more correct.