how to add harmonics to a sine wave ?

hi to all

i want to add to a sine wave (220volt and 50hz ) harmonics and to see them in a spectrum ( 50hz , 150hz ,250hz ....)

any suggestions ?

thanks

[Pham Duy Phuoc]

 function y = harmonic(x,k)
       % assumes that x is a column vector
       assert(size(x,1) > 0);
       assert(size(x,2) == 1);
       % Interpolate by k and add k-th harmonic:
       y = interp(x,k) + repmat(x,k,1);
   end

Answer 1

[Arturo Moncada-Torres]

Mmm, actually is very easy. Just add them to the original signal:

% Sampling
fs = 1000;     % Sampling rate [Hz]
Ts = 1/fs;     % Sampling period [s]
fNy = fs / 2;  % Nyquist frequency [Hz]
duration = 10; % Duration [s]
t = 0 : Ts : duration-Ts; % Time vector
noSamples = length(t);    % Number of samples

% Original signal
x = 220.*sin(2 .* pi .* 50 .* t);

% Harmonics
x1 = 100.*sin(2 .* pi .* 100 .* t);
x2 = 100.*sin(2 .* pi .* 200 .* t);
x3 = 100.*sin(2 .* pi .* 300 .* t);

% Contaminated signal
xn = x + x1 + x2 + x3;

% Frequency analysis
f = 0 : fs/noSamples : fs - fs/noSamples; % Frequency vector

% FFT
x_fft = abs(fft(x));
xn_fft = abs(fft(xn));

% Plot
figure(1);
subplot(2,2,1);
plot(t, x);
subplot(2,2,2);
plot(t, xn);
subplot(2,2,3);
plot(f,x_fft);
xlim([0 fNy]);
subplot(2,2,4);
plot(f,xn_fft);
xlim([0 fNy]);

Just some quick code. I tested it and it works.

Hope it helps ;-) . Keep coding!

[Arturo Moncada-Torres]

Notice how the harmonics have an amplitude of 100 in order to be visualized in the spectrum plot. Otherwise, the original signal's magnitude (220) would be too big compared to the harmonics one.

[yuvi]

THANKS A LOT !