Question

9. Use Matlab to calculate the harmonic frequency (nwo), the harmonic amplitude (cn), and the nth phase angle (δ.) for n 0, 1, 2, ...-10 for Problem 1. Plot (cn) and (6n) as a function of (nwo).

Answer 1

n_max = input('Enter vector of highest harmonic values desired
(odd):');
f = 1;
N = n_max;
t = 0:0.002:1;
omega_0 = 2*pi*f;
x=zeros(size(t));
n=1:1:N;
b_n=zeros(size(n));
for i=1:(N+1)/2;
k=2*i-1;
b_n(k)=4/(pi*k);

figure(1)
subplot(2,1,1),stem(b_n);
xlabel('Integer Multiple of Fundamental Frequency');
ylabel('Amplitude'),grid;
% This part is for plotting the partial Fourier sum
x=x+b_n(k)*sin(omega_0*k*t);
subplot(2,1,2),plot(t,x),xlabel('t'),ylabel('partial sum');
axis([0 1 -1.5 1.5]),text(0.05,-0.5, ['max.har.=',num2str(k)]);
grid;
end

For the first 50 harmonic the below function can be used

Y = fft(i_w,1024)

an = real(Y)
bn = imag (Y)
[r,k]=size(an)

n=50

ann = an(1:n,k)
bnn = bn(1:n,k)
ampl = 2/1024*sqrt(ann.^2+bnn.^2)
phi=atan(ann./(bnn+.000001));
harm = 1:1:n
bar(harm,ampl)
xlabel('harmonics')
ylabel('amplitude')