Here is a bandlimited function f(t) with bandwidth Ω:
The function f(t) is bounded in [-A,A].
Then the bound of the derivative of f(t) is bounded as: |f'(t)|≤2πΩA. So, what is the bound of its n-th order derivatives?
Is it as follows?
where n is the order of derivative.
If yes, then are the bounds of higher order derivatives much larger than the bound of f(t)?
I tried MATLAB simulations but the results were contrary.