Bounds of the difference of a bounded band-limited function

  • #1
alwaystudent
1
0
for continues signal (function) we have Bernstein inequality :
$$
|{df(t)}/dt| \le 2AB\pi
$$
where A=sup$|f(t)|$ and B is Bandwidth f(t),

the question is:Is there a relationship for discrete function x[n] like this?
$$
|x[n] -x[n-1] | \le\ \mu\ W
$$
where
$$
X[k] = \sum\limits_{k = 0}^{N - 1} {x[n]{e^{ - j\frac{{2\pi }}{N}nk}}}
$$
is DFT for x[n] , X[k]=0 for k> W
 

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