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What I wrote on my Exam (and how many points I got)

The sampling theorem states that for a signal x(t) to be uniquely reconstructed, its X(jw) = 0 when |w| > wm, and the sampling frequency, ws, must be greater than 2wm


I got a 7/10 on this because I did not say what it is being reconstructed from. Also I used w because I did not know how to type omega in this file.


My Definition:


A signal can be recovered from sampling if

  • The Signal is bandlimited and the Sample Frequency ($ \omega_s $) is greater than $ 2\omega_{max} $ (maximum frequency)


                    $ \omega_{s}>2\omega_{max} $  


Recieved 9/10 Points because it is not clear if I meant $ 2\omega_{max} $ or $ \omega_{max} $ is the maximum frequency


My definition of the sampling theorem:

In order to sample a signal that can be recovered back into the original sample, the sampling frequency, $ \omega_{s} $ , must be more than twice the highest frequency of the signal, $ \omega_{m} $.

I got $ \frac{7}{10} $ on it because I forgot to say that the signal must be band limited.



The sampling theorem states that a set of samples of a signal can be reconstructed into the original signal iff the original system is band limited and the sampling frequency is greater than twice the maximum frequency for non-zero values of the original function

I lost 1 point for saying "iff" since it is not an if and only if I lost 2 points for "for non-zero values of the original function" Not too sure why but I'm sure something about the statement must be ambiguous.

Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood