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.
If there exists an w_m such that X(w) = 0 for |w| > w_m (band limited), then a signal sampled at a frequency w_s of > 2*w_m will be capable of being reconstructed. This frequency of 2*w_m is called the Nyquist rate.
