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Homework Help: Bandwidth/Sampling Freq.

  1. Mar 25, 2010 #1
    1. The problem statement, all variables and given/known data
    What is the minimum sample rate for an audio system with a 3KHz bandwidth?


    2. Relevant equations
    This is the problem, I need the equation.


    3. The attempt at a solution
    Based on units, it seems as if the sampling rate is simply 1/bandwidth. Is this correct? It seems too easy of an answer. Thanks for the help!
     
  2. jcsd
  3. Mar 25, 2010 #2
    No this is not correct. You are off by at least a factor of 2. Look up the Nyquist-Shannon sampling theorem. This provides the minimum theoretical limit. Then non-ideal factors impose even greater sampling rates.
     
  4. Mar 25, 2010 #3
    Ok, so I wiki'ed Nyquist-Shannon theorem and I found the equation: sampling frequency = 2*B, where B = one-sided baseband bandwidth. is this what I want?

    Thanks again!
     
  5. Mar 25, 2010 #4
    another equation I found was instead of fs, I found fn. What is the difference between the two, and which is applicable?
     
  6. Mar 25, 2010 #5
    Bandwidth Equation

    I was curious to see if someone knew the equation for the sampling rate, if given a bandwidth frequency. Thank you much for all help.
     
  7. Mar 25, 2010 #6
    Re: Bandwidth Equation

    I have been told that the equation for the sampling rate frequency is equal to 2*bandwidth. Is this the correct formula to use (Nyquist - Shannon sampling theorem), or do I need to use an alternate?
     
  8. Mar 25, 2010 #7

    berkeman

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    Staff: Mentor

    Re: Bandwidth Equation

    What can you tell us about the Nyquist theorem? When does it apply? what are its limitations?

    BTW -- I moved your thread from Advanced Physics to here in Intro Physics. The Advanced Physics forum is for upper-division and graduate-level questions.
     
  9. Mar 25, 2010 #8
    Re: Bandwidth Equation

    Well for starters, Wiki tells me that: the magnitude of the frequency must be greater than the bandwidth frequency. This theorem can only be used for signals that are infinite, and I would assume in my homework problem (since not otherwise stated) that this signal of 3KHz bandwidth is infinite. Even for an idealized situation, this theorem can still be used for relatively easy problems. It also goes on to explain sampling intervals but I do not think this is applicable here since I am asked to find the "sampling rate."

    The formula I believe I need to use is sampling frequency > 2*bandwidth. If I'm giving a bandwidth of 3KHz, the sampling frequency would have to be a minimum of 6KHz, correct?!
     
  10. Mar 26, 2010 #9

    berkeman

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    Staff: Mentor

    Re: Bandwidth Equation

    (reposting my response after the PF crash and recovery...)

    Yes, I believe that is the correct answer to the question.
     
  11. Mar 26, 2010 #10
    I don't know what fs and fn are. However, your equation 2B is correct. In practice, you need to sample at a higher rate, but this is the theoretical limit from a mathematical point of view.
     
  12. Mar 26, 2010 #11

    berkeman

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    Staff: Mentor

    (Two threads merged. Please do not multiple post the same question.)
     
  13. Mar 27, 2010 #12
    Alright, that makes sense elect_eng. Thank you all for your help on this post!
     
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