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== What I wrote on my Exam (and how many points I got) ==
 
== What I wrote on my Exam (and how many points I got) ==
  
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=== I Wrote ===
 
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
 
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
  
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=== I Wrote ===
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My Definition:
 
My Definition:
  
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=== I Wrote ===
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My definition of the sampling theorem:  
 
My definition of the sampling theorem:  
  
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=== I Wrote ===
  
 
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
 
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
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=== I Wrote ===
  
 
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.
 
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.
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=== I Wrote ===
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If there's a signal, it can be recovered in the case of ws > 2wm" That's what I wrote. I got 3 points because I think I didn't mention signal should be band limited, what wm is. Also, I needed to mention what signal can be recovered from.
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=== I Wrote ===
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"If a signal x(t) is band limited X(j$\omega$)=0 for $\omega$>wm, then it can be recovered from its samples."
  
 
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Revision as of 21:02, 1 May 2008

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

I Wrote

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.


I Wrote

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


I Wrote

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.



I Wrote

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.


I Wrote

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.


I Wrote

If there's a signal, it can be recovered in the case of ws > 2wm" That's what I wrote. I got 3 points because I think I didn't mention signal should be band limited, what wm is. Also, I needed to mention what signal can be recovered from.



I Wrote

"If a signal x(t) is band limited X(j$\omega$)=0 for $\omega$>wm, then it can be recovered from its samples."


Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett