# Proving Nyquist Sampling theorem for strictly bandlimited signals

I understand that the Nyquist sampling theorem dictates that the minimum sampling frequency, $$f_s$$, be s.t. $$f_s > 2B$$, where $$B$$, is the bandwidth of the signal. I have read the explanation for what happens when the input signal contains an impulse/non zero ferquency spectrum at $$fs = fm$$. But is there any way to do a mathematical proof that sampling at $$fs = 2B$$ works when the signal is strictly bandlimited.

A little background : This is a HW problem

The given hint was to use the fact that "one way to interpret Nyquist Sampling theorem is to note that any bandlimited signal can be represented as a superposition of bandlimited signals that are orthogonal to each other."

• Google “generalized sampling theorem”. There is a paper by Papoulis – Stanley Pawlukiewicz Jan 13 at 9:55
• @StanleyPawlukiewicz I think you mean this Papoulis paper (paywall). – Olli Niemitalo Jan 15 at 7:20