A discrete fourier transform creates N bins, where the kth bin is given by: $$X_k=\sum_{n=0}^{N-1} f(n)e^{-j2\pi\frac{n}Nk}$$
Matlab's fft command is passed a vector with the N sampled values from $f(x)$. I assume it then uses the first $N-1$ integers as the values for k (if not, what does it actually use?). I am applying the dft in a situation where my k values are not integers (still equally spaced). How do I perform a dft in Matlab with custom k values?