Beginner question on aperiodic samples and DFT behavior
It sounds to me like you are experiencing time-domain aliasing. First, two basic facts:


Recall that if $x[n]$ is of length $N$ and $h[n]$ is of length $M$ then $x[n]\ast h[n]$ is of length $N+M-1$. 


Fact 1 does not matter in what domain you perform the convolution/filtering. So, if you modify the DFT of $x[n]$ by "shaping" its spectrum, then there exists an  equivalent filter $h[n]$ in the time domain, which defines an implicit length $M$. 


Taking an $N_1$-point IDFT of an $N_2$-point signal for $N_1 &lt; N_2$ results in time-aliasing.


Fact 2 is the dual to frequency aliasing by undersampling. I'll illustrate this as follows: let $x_1[n]$ denote a signal of size $N_1$. Then, if we take an $N_1$-point DFT of $x_1$ and modify its spectrum so the size should be $N_2&gt;N_1$, then taking an $N_1$-point IDFT is equivalent to obtaining the signal $x_2$ given by: 
\begin{eqnarray}
x_2[n] = \sum_{p=0}^{\infty}x[n+pN_1]
\end{eqnarray}

This seems to be consistent with what you have mentioned. As you correctly noted, zero padding the original signal is exactly the solution! Essentially just zero-pad such that the terms in the above equation for $p&gt;0$ are all zero-valued. Also, using the ideas above gives you a way to understand the exact amount of zero-padding necessary based on the implicit filter $h[n]$ your frequency domain shaping yields. Good luck!