How do I find the Fourier series of a Sawtooth wave?

I have the following sawtooth wave function :

T = 2* 4; Fs = 1000; dt = 1/Fs; t=-5:dt:T-dt; x = -sawtooth (pi/2*t, 0.5); plot(t,x) grid on axis ([-5 5 -1.5 1.5]);

I am having a hard time finding the Fourier series and coefficients. Where do I even begin?

Answer 1

[Star Strider]

Try this:

T = 2* 4;
Fs = 1000;
dt = 1/Fs;
t=-5:dt:T-dt; 
x = -sawtooth (pi/2*t, 0.5);

figure(1)
plot(t,x)
grid on
axis ([-5 5 -1.5 1.5]);

Fn = Fs/2;                                          % Nyquist Frequency
N = length(t);
FTx = fft(x)/N;                                     % Fourier Transform
Fv = linspace(0, 1, fix(N/2)+1)*Fn;                 % Frequency Vector
Iv = 1:length(Fv);                                  % Index Vector

figure(2)
plot(Fv, abs(FTx(Iv))*2)
grid
xlabel('Frequency')
ylabel('Amplitude')
title('Fourier Transform of Sawtooth Wave')
axis([0  15    ylim])

The coefficients are in ‘FTx’ with respect to each frequency in the ‘Fv’ vector. The coefficients of the cosine component are the real values, and the coefficients of the sine component are the imaginary values.