For continuous signals (functions) we have that Bernstein inequality holds: $$ \left|\frac{\mathrm{d}f(t)}{\mathrm{d}t}\right| \le 2AB\pi $$ where $A=\sup|f(t)|$ and $B$ is the bandwidth of $f(t)$.
My question is: does there exists a similar a relationship for discrete function $x[n]$ like this one $$ |x[n] - x[n-1]| \le\ \mu W, $$ where
- $ X[k] = \sum\limits_{k = 0}^{N - 1} {x[n]{e^{ - j\frac{{2\pi }}{N}nk}}} $ is the DFT (Discrete Fourier transform) of $x[n]$ and
- $X[k]=0$ for $k > W$?