What are the restrictions on DFT input sequences in order to produce valid spectral results
The only restriction imposed on the input of the discrete finite dimensional transform DFT (Discrete Fourier Transform) is that the input has finite energy ; i.e., $$\sum_{n=0}^{N-1} |x[n]|^2 &lt; \infty$$
And a necessary &amp; sufficient condition for an $N$-point sequence $x[n]$ to have finite energy is that all of its samples are bounded.
There's no more restriction on the discrete-time sequence $x[n]$ to be transformable into $X[k]$ by means of the linear mapping implied by DFT.
However, I guess, from your previous question, that you want to investigate whether periodicity is a restriction on the input or not? The (my) answer is of course not. DFT works on finite length input, and since it's impossible to tell (by anyone) whether a block of data belongs to one period of a periodic waveform, or it's just the whole data itself, hence it's not possible to restrict the input to be periodic (because it cannot be tested)...
But the DFT algorithm has been designed to operate on one period of periodic inputs. If you evaluate the inverse DFT of a given set of DFT coefficents for all $n$, you can see that data periodically extends outside of the base interval $0 \leq n &lt; N$.