PLOTTING A SINE WAVE USING TRIGNOMETRIC FOURIER SERIES

[Thiago Henrique Gomes Lobato]

What have you tried so far?

[Devika Sunil]

I tried to plot the waveform using fourier function, but I'm new to MATLAB and don't know how to proceed.

Answer 1

[Thiago Henrique Gomes Lobato]

You have an analytical waveform, so you can generate it for 4 cycles without using any fourier function. Then, if you use the fft function you can become the coefficients (The results are complex numbers, how do they related with sin and cos?). Also, to plot the approximation with a reduced number of coefficients you can simply set all the unwanted coefficients to 0 (why?). Here is an example implementation that will plot some approximations of your waveform as a function of the number of coefficients:

% Analytical waveform
t = 0:1/100:2*pi-1/100;
y = exp(-t);
y = [y,y,y,y]; % 4 cycles
t = 0:1/100:2*pi*4-2/100;


NofCoeff = 60;
figure
plot(t,y)
FFT = fft(y);
FFT(NofCoeff+1:end) = 0; % Remove unwanted coefficients
hold on
plot(t,ifft(FFT,'symmetric'))
legend({'Analytical function',['Fourier with ',num2str(NofCoeff),' coeff']})

[Devika Sunil]

Thank you