Fourier transform of a discrete periodic signal
For a discrete periodic signal you normally compute the Fourier series coefficients. They can be obtained from the DFT by dividing the output of the DFT by N, where number of samples in a period.

The DFT assumes the signal is N-sample periodic anyway.

In Matlab you will implement this as

x=[-3 1 1];
ck=fft(x)/3;