fourier series for function and period

hi, trying to calculate the fourier series expansion in the period -3<t<3

f(t)={2, -3<t<0; {0, 0<t<3.

any help would be appreciated.

Answer 1

[Star Strider]

You can actually do this by hand quite easily. Using the Symbolic Math Toolbox to do the same thing:

syms t w

f1 = 2;
f1_lims = [-3  0];

f2 = 0;
f2_lims = [0  3];

% Integrate to get the Fourier series for ‘f1’: 
F1 = int(exp(-j*w*t) * f1, t, f1_lims(1), f1_lims(2))

% Do the same for ‘f2’: 
F2 = int(exp(-j*w*t) * f2, t, f2_lims(1), f2_lims(2))

% Add them
FT = F1 + F2;

% Plot the result: 
figure(1)
subplot(2,1,1)
ezplot(abs(FT), [-10*pi,  10*pi])
subplot(2,1,2)
ezplot(angle(FT), [-10*pi,  10*pi])

Experiment with this on your own to see how the transform changes if the function is symmetrical about t=0 instead ( i.e. f2=2 instead of 0 ) . How would you code a symmetric or asymmetric triangle pulse? Have some fun with it!

Note that the value of the Fourier transform at w=0 is not NaN. Think L’Hôpital’s rule...