Fourier transform of a discrete periodic signal The given sequence
$$x[k]=\delta[k-1]-3 \delta[k] + \delta[k-2]$$
represents a period of some discrete periodic signal $e[k]$ with period N=3. Find the Fourier transform  of $e[k]$.

This is an exercise in my textbook and i don't get it. Is $x[k]$ the first period of $e[k]$? If so, does that mean that the DFT of $x[k]$ is the same as the DFT of $e[k]$?
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;