Exact indices of $\tt fft$
The FFT calculates the spectrum at N points in the range from $[0, 2\pi)$ where due to the cyclic property the relative frequency 0 must be equal to the frequency $2\pi$. This is best shown via an example. Note that $2\pi$ corresponds to your sampling frequency.

Example:
For a length 3 impulse response, say $h=[0.5, 1, 0.5]$, the FFT calculates the spectrum at the relative frequencies $[0, \frac{1}{3}2\pi, \frac{2}{3}2\pi]$, instead of the frequencies $[0, \frac{1}{2}2\pi, 2\pi]$. One way to calculate these frequencies in Matlab for an $N$ points FFT is as follows: 

N = 3;
h = [0.5 1 0.5];
fq = linspace(0, 2*pi, N+1);
fq = fq(1:end-1);
H = fft(h);
figure; 
plot(fq, abs(H)); 


The function fftshift takes the right part of the spectrum and places it on the left such that you obtain the frequencies $[\frac{2}{3}2\pi, 0, \frac{1}{3}2\pi]$.

When you are not using the fftshift function and just plot the range $[0, 2\pi]$, then you can use positive time indices for t.