Let $x[n]$ be a infinite-length discrete-time signal with $x[n] = 0$ for $0 \leq n \leq N$ . We can compute the discrete DFT $X[k]$ and the continuous DTFT $X(\omega)$. The DFT is a sampled version of the DTFT, i.e., $$ X[k] = X(2\pi k / N). $$ Please also see posts here and here. Now, we consider the maximum magnitudes $m_{\textrm{d}} = \max_k |X[k]|$ and $m_{\textrm{c}} = \max_\omega |X(\omega)|$. Because of above, we have $m_{\textrm{d}} \leq m_{\textrm{c}}$.

*What is the relation between these maximum values? Is there $\gamma > 1$ such that $\gamma m_{\textrm{d}} \geq m_{\textrm{c}}$? *