What is the minimum sampling rate for a 3KHz bandwidth audio system?

[satchmo05]

Homework Statement

What is the minimum sample rate for an audio system with a 3KHz bandwidth?

Homework Equations

This is the problem, I need the equation.

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!

 

[elect_eng]

Homework Statement

What is the minimum sample rate for an audio system with a 3KHz bandwidth?

Homework Equations

This is the problem, I need the equation.

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!

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.

 

[satchmo05]

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!

 

[satchmo05]

another equation I found was instead of f_s, I found f_n. What is the difference between the two, and which is applicable?

 

[satchmo05]

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.

 

[satchmo05]

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?

 

[berkeman]

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.

 

[satchmo05]

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?!

 

[berkeman]

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?!

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

Yes, I believe that is the correct answer to the question.

 

[elect_eng]

another equation I found was instead of f_s, I found f_n. What is the difference between the two, and which is applicable?

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.

 

[berkeman]

(Two threads merged. Please do not multiple post the same question.)

 

[satchmo05]

Alright, that makes sense elect_eng. Thank you all for your help on this post!