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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

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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."

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

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